text
stringlengths 100
957k
| meta
stringclasses 1
value |
|---|---|
GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
It is currently 02 Jul 2020, 08:56
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
Foodmart customers regularly buy at least one of the
Author Message
TAGS:
Hide Tags
Intern
Joined: 09 Feb 2010
Posts: 39
Show Tags
02 Sep 2010, 07:47
7
00:00
Difficulty:
15% (low)
Question Stats:
76% (01:37) correct 24% (02:18) wrong based on 168 sessions
HideShow timer Statistics
Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
A. 5%
B. 10%
C. 15%
D. 25%
E. 30%
M03-07
Math Expert
Joined: 02 Sep 2009
Posts: 64891
Show Tags
02 Sep 2010, 08:19
Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
A. 5%
B. 10%
C. 15%
D. 25%
E. 30%
100%={customers who buy milk}+{customers who buy chicken}+{customers who buy apples} - {customer who buy exactly 2 products} - 2*{customers who by exactly 3 products}+{customers who buy neither of the products}
$$100=60+50+35-x-2*10+0$$ --> $$x=25$$.
For more about the formulas for 3 overlapping sets please see my post at: http://gmatclub.com/forum/formulae-for- ... 69014.html
Hope it helps.
_________________
Intern
Joined: 21 Aug 2009
Posts: 33
Show Tags
02 Sep 2010, 08:26
1
60-(x+10+z) + 50-(x+10+y) + 35-(z+10+y) + x + +y + z +10 = 100
where x = people who bought Milk & Chicken
y = people who bought chicken & Apples
z= people who bought Milk and Apples
x+y+z= the number of people who bought just exactly two products.
Hence solving the above equation we get,
125 -(x+y+z) = 100
Thus, x+y+z= 25
Intern
Joined: 09 Feb 2010
Posts: 39
Show Tags
03 Sep 2010, 10:07
Hi Bunuel
I was looking at this post
formulae-for-3-overlapping-sets-69014.html?hilit=rather%20memorize
Can you tell me the above question of milk, chicken and apples would be as per which of the below points and how
1. For 3 sets A, B, and C: P(A u B u C) : P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) + P(A n B n C)
2. To determine the No of persons in exactly one set : P(A) + P(B) + P(C) – 2P(A n B) – 2P(A n C) – 2P(B n C) + 3P(A n B n C)
3. To determine the No of persons in exactly two of the sets : P(A n B) + P(A n C) + P(B n C) – 3P(A n B n C)
4. To determine the No of persons in exactly three of the sets : P(A n B n C)
5. To determine the No of persons in two or more sets (at least 2 sets) : P(A n B) + P(A n C) + P(B n C) – 2P(A n B n C)
Math Expert
Joined: 02 Sep 2009
Posts: 64891
Show Tags
21 Sep 2010, 23:11
4
Retired Moderator
Joined: 03 Aug 2010
Posts: 156
Show Tags
23 Dec 2010, 21:51
@rtaha... the bunuel's approach of addressing this problem with formula is invincible, and is the best approach.
I was facing a lot of problems in set thory, i improved a lot by solving every problem 1) by formula of bunuel and 2) actual ven diagram
By solving this problems with ven diagram, you would basically learn why this formula is applied.
Manager
Status: swimming against the current
Joined: 24 Jul 2009
Posts: 123
Location: Chennai, India
Show Tags
25 Dec 2010, 18:59
Bunuel wrote:
rtaha2412 wrote:
Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
a * 5%
b * 10%
c * 15%
d * 25%
e * 30%
100%={customers who buy milk}+{customers who buy chicken}+{customers who buy apples} - {customer who buy exactly 2 products} - 2*{customers who by exactly 3 products}+{customers who buy neither of the products}
$$100=60+50+35-x-2*10+0$$ --> $$x=25$$.
For more about the formulas for 3 overlapping sets please see my post at: formulae-for-3-overlapping-sets-69014.html?hilit=rather%20memorize
Also discussed here: m03-74439.html?hilit=chicken%20milk#p786229
Hope it helps.
I have seen these 2 formulaes being used. What is the difference between them
P (A u B u C) = P (A) + P (B) + P (C) - [ P (A n B) + P (A n C) + P (B n C) ] + P (A n B n C)
and P (A u B u C) = P (A) + P (B) + P (C) - [ P (A n B) + P (A n C) + P (B n C) ] - 2(P (A n B n C))
Math Expert
Joined: 02 Sep 2009
Posts: 64891
Show Tags
25 Dec 2010, 23:41
1
mailnavin1 wrote:
Bunuel wrote:
rtaha2412 wrote:
Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
a * 5%
b * 10%
c * 15%
d * 25%
e * 30%
100%={customers who buy milk}+{customers who buy chicken}+{customers who buy apples} - {customer who buy exactly 2 products} - 2*{customers who by exactly 3 products}+{customers who buy neither of the products}
$$100=60+50+35-x-2*10+0$$ --> $$x=25$$.
For more about the formulas for 3 overlapping sets please see my post at: formulae-for-3-overlapping-sets-69014.html?hilit=rather%20memorize
Also discussed here: m03-74439.html?hilit=chicken%20milk#p786229
Hope it helps.
I have seen these 2 formulaes being used. What is the difference between them
P (A u B u C) = P (A) + P (B) + P (C) - [ P (A n B) + P (A n C) + P (B n C) ] + P (A n B n C)
and P (A u B u C) = P (A) + P (B) + P (C) - [ P (A n B) + P (A n C) + P (B n C) ] - 2(P (A n B n C))
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10623
Location: Pune, India
Show Tags
11 Oct 2011, 22:07
Some good methods have been discussed above. Let me add a small discussion on Venn diagrams
You will not have any confusion if you visualize it. The total number of people is 100 (assume it since numbers are in %). These 100 people are spread around in the 3 circles. One person can be in only one area.
Attachment:
Ques6.jpg [ 17.57 KiB | Viewed 2602 times ]
60+50+35 (= 145) is more than 100 because
60 = the entire left top circle = the left top red part + x + z + 10.
50 = the entire right top circle = the right top red part + x + y + 10
35 = the bottom circle = the bottom red part + y + z + 10
so x, y and z are counted twice and 10 is counted thrice
45 = x + y + z + 2*10
x+ y + z = 25
_________________
Karishma
Veritas Prep GMAT Instructor
Manager
Joined: 09 Jun 2011
Posts: 75
Show Tags
12 Oct 2011, 22:48
@Karishma:
How did you get:
"45 = x + y + z + 2*10
x+ y + z = 25"
I lost the part here..
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10623
Location: Pune, India
Show Tags
13 Oct 2011, 07:46
OptimusPrimea1 wrote:
@Karishma:
How did you get:
"45 = x + y + z + 2*10
x+ y + z = 25"
I lost the part here..
145 is 45 more than 100. Why is it 45 extra? Because x, y and z were counted twice (so they appear once extra) and 10 was counted thrice ( so it appears twice extra). check out the diagram. These extras make up the 45. In 100, there is no double/triple counting. It is equal to the actual number of people.
That is why 45 = x + y + z + 2*10
25 = x+y+z
_________________
Karishma
Veritas Prep GMAT Instructor
Retired Moderator
Joined: 15 Jun 2012
Posts: 968
Location: United States
Show Tags
29 Mar 2013, 23:32
4
I used venn diagram. Here is my solution.
Attachments
Untitled.jpg [ 57.32 KiB | Viewed 6008 times ]
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10997
Location: United States (CA)
Show Tags
03 Apr 2020, 07:33
zest4mba wrote:
Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
A. 5%
B. 10%
C. 15%
D. 25%
E. 30%
M03-07
We can use the formula:
Total = n(M) + n(C) + n(A) - n(exactly two) - 2 * n(all three)
100 = 60 + 50 + 35 - n(exactly two) - 2 * 10
100 = 125 - n(exactly two)
n(exactly two) = 25
_________________
Scott Woodbury-Stewart
Founder and CEO
Scott@TargetTestPrep.com
225 Reviews
5-star rated online GMAT quant
self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
Re: Foodmart customers regularly buy at least one of the [#permalink] 03 Apr 2020, 07:33
|
{}
|
# Gamma ray observations of black hole candidates nova Ophiuchus 1993 and nova Velorum 1993
### Files in this item
Files Size Format View
9727585.PDF 4.733Mb application/pdf
Title: Gamma ray observations of black hole candidates nova Ophiuchus 1993 and nova Velorum 1993 Moss, Michael Jamieson Haymes, R. C. Doctor of Philosophy thesis Results of spectral analysis and time series analysis of the transient source x-ray nova Velorum 1993 (GRS 1009-45) and x-ray nova Ophicuhus 1993 (GRS 1716-249) are presented. These data were accumulated using the OSSE (Oriented Scintillation Spectrometer Experiment) low-energy gamma ray telescope on the Compton Gamma Ray Observatory. Spectral observations of the two x-ray novae showed the presence of gamma ray emission to greater than 100 keV, which is thought to be a signature of a binary system with an accreting black hole. Observations of GRS 1009-45 shows that it was in a gamma-ray soft state during the one-day OSSE observation, which occurred during the exponential decay phase of the outburst. The spectrum of GRS 2716-249 acquired during the plateau stage of outburst indicated a hard state, while spectra acquired during the sawtooth outbursts suggest that a hard to soft transition occurs as the decay progresses. The 40-200 keV pre-outburst luminosity of GRS 1716-249 is shown to be two orders of magnitude less than that estimated during the plateau-stage observation. The only significant power density spectrum was that acquired for GRS 1716-249 during the plateau stage of outburst. It is consistent with the sum of two QPO peaks at 0.128 and 0.32 Hz and a red noise ($\nu\sp{-1}$) component. This power spectrum is consistent with other black hole candidate power spectra for which the source is in the low state. Power spectra for GRS 1009-45 and GRS 1716-249 during the peak of a sawtooth outburst are also presented. They are consistent with band-limited white noise. Corresponding autocorrelations are shown for all observations. Moss, Michael Jamieson. (1997) "Gamma ray observations of black hole candidates nova Ophiuchus 1993 and nova Velorum 1993." Doctoral Thesis, Rice University. http://hdl.handle.net/1911/19190. http://hdl.handle.net/1911/19190 1997
|
{}
|
# Uniqueness of compact topology for a group
Suppose $G$ is a compact $T_2$ group. Can there be other compact $T_2$ topologies on $G$ which also turn $G$ into a topological group? ($T_2$ refers to the Hausdorff separation axiom)
-
The topology of a compact Hausdorff space is maximal compact and minimal Hausdorff; that is, no finer topology is compact, and no coarser topology is compact. So if you have another compact Hausdorff topology, then it is neither finer nor coarser to the original one. – Mariano Suárez-Alvarez Feb 15 '12 at 9:00
It may be worth stating that if you pick a topology once and for all and ask about uniqueness of smooth structures (if it has any at all!), then the answer is yes. – Jason DeVito Feb 15 '12 at 13:49
Take the circle group $G=S^1=\mathbb R/\mathbb Z$. Any non-continuous automorphism of $\mathbb R$ which fixes pointwise the subgroup $\mathbb Z$ passes to the quotient and gives an automorphism $f$ of the abstract group $G$, which is not continuous. Now define a topology on $G$ so that a set $U$ is open iff $f(U)$ is open in the usual topology. This new topology is of course Hausdorff and compact, but it is different to the usual topology.
Interesting, the resulting topological group is isomorphic (as topological group) to the original topological group, still the topology on the set $G$ is different. But I wonder more whether I could somehow prevent the implicit use of the axiom of choice. One idea would be to prescribe the Borel $\sigma$-algebra of a second-countable space and only allow topologies whose open sets belong to that $\sigma$-algebra. – Thomas Klimpel Feb 15 '12 at 15:50
|
{}
|
liu.seSearch for publications in DiVA
Change search
Refine search result
1 - 25 of 25
CiteExportLink to result list
Cite
Citation style
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• oxford
• Other style
More styles
Language
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf
Rows per page
• 5
• 10
• 20
• 50
• 100
• 250
Sort
• Standard (Relevance)
• Author A-Ö
• Author Ö-A
• Title A-Ö
• Title Ö-A
• Publication type A-Ö
• Publication type Ö-A
• Issued (Oldest first)
• Issued (Newest first)
• Created (Oldest first)
• Created (Newest first)
• Last updated (Oldest first)
• Last updated (Newest first)
• Disputation date (earliest first)
• Disputation date (latest first)
• Standard (Relevance)
• Author A-Ö
• Author Ö-A
• Title A-Ö
• Title Ö-A
• Publication type A-Ö
• Publication type Ö-A
• Issued (Oldest first)
• Issued (Newest first)
• Created (Oldest first)
• Created (Newest first)
• Last updated (Oldest first)
• Last updated (Newest first)
• Disputation date (earliest first)
• Disputation date (latest first)
Select
The maximal number of hits you can export is 250. When you want to export more records please use the Create feeds function.
• 1.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology.
Complex magnetism in nanolaminated Mn2GaC2014Manuscript (preprint) (Other academic)
We have used first-principles calculations and Heisenberg Monte Carlo simulations to search for the magnetic ground state of Mn2GaC, a recently synthesized magnetic nanolaminate. We have, independent on method, identified a range of low energy collinear as well as non-collinear magnetic configurations, indicating a highly frustrated magnetic material with several nearly degenerate magnetic states. An experimentally obtained magnetization of only 0.29 per Mn atom in Mn2GaC may be explained by canted spins in an antiferromagnetic configuration of ferromagnetically ordered sub-layers with alternating spin orientation, denoted AFM[0001]$\smal\text{A}\atop\text{4}$. Furthermore, low temperature X-ray diffraction show a new basal plane peak appearing upon a magnetic transition, which is consistent with the here predicted change in inter-layer spacing for the AFM[0001]$\smal\text{A}\atop\text{4}$ configuration.
• 2.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Magnetically driven anisotropic structural changes in the atomic laminate Mn2GaC2016In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 93, no 1, p. 014410-Article in journal (Refereed)
Inherently layered magnetic materials, such as magnetic M(n+1)AX(n) (MAX) phases, offer an intriguing perspective for use in spintronics applications and as ideal model systems for fundamental studies of complex magnetic phenomena. The MAX phase composition M(n+1)AX(n) consists of M(n+1)AX(n) blocks separated by atomically thin A-layers where M is a transition metal, A an A-group element, X refers to carbon and/or nitrogen, and n is typically 1, 2, or 3. Here, we show that the recently discovered magnetic Mn2GaC MAX phase displays structural changes linked to the magnetic anisotropy, and a rich magnetic phase diagram which can be manipulated through temperature and magnetic field. Using first-principles calculations and Monte Carlo simulations, an essentially one-dimensional (1D) interlayer plethora of two-dimensioanl (2D) Mn-C-Mn trilayers with robust intralayer ferromagnetic spin coupling was revealed. The complex transitions between them were observed to induce magnetically driven anisotropic structural changes. The magnetic behavior as well as structural changes dependent on the temperature and applied magnetic field are explained by the large number of low energy, i.e., close to degenerate, collinear and noncollinear spin configurations that become accessible to the system with a change in volume. These results indicate that the magnetic state can be directly controlled by an applied pressure or through the introduction of stress and show promise for the use of Mn2GaC MAX phases in future magnetoelectric and magnetocaloric applications.
fulltext
• 3.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Origin of Chemically Ordered Atomic Laminates (i-MAX): Expanding the Elemental Space by a Theoretical/Experimental Approach2018In: ACS Nano, ISSN 1936-0851, E-ISSN 1936-086X, Vol. 12, no 8, p. 7761-7770Article in journal (Refereed)
With increased chemical diversity and structural complexity comes the opportunities for innovative materials possessing advantageous properties. Herein, we combine predictive first-principles calculations with experimental synthesis, to explore the origin of formation of the atomically laminated i-MAX phases. By probing (Mo2/3M1/32)(2)AC (where M-2 = Sc, Y and A = Al, Ga, In, Si, Ge, In), we predict seven stable i-MAX phases, five of which should have a retained stability at high temperatures. (Mo2/3Sc1/3)(2)GaC and (Mo2/3Y1/3)(2)GaC were experimentally verified, displaying the characteristic in-plane chemical order of Mo and Sc/Y and Kagome-like ordering of the A-element. We suggest that the formation of i-MAX phases requires a significantly different size of the two metals, and a preferable smaller size of the A-element. Furthermore, the population of antibonding orbitals should be minimized, which for the metals herein (Mo and Sc/Y) means that A elements from Group 13 (Al, Ga, In) are favored over Group 14 (Si, Ge, Sn). Using these guidelines, we foresee a widening of elemental space for the family of i-MAX phases and expect more phases to be synthesized, which will realize useful properties. Furthermore, based on i-MAX phases as parent materials for 2D MXenes, we also expect that the range of MXene compositions will be expanded.
fulltext
• 4.
Forschungszentrum Julich, Germany; JARA, Germany.
Forschungszentrum Julich, Germany; JARA, Germany. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Univ Duisburg Essen, Germany; Univ Duisburg Essen, Germany. Univ Duisburg Essen, Germany. Univ Duisburg Essen, Germany. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Forschungszentrum Julich, Germany; JARA, Germany. Forschungszentrum Julich, Germany; JARA, Germany; Univ Duisburg Essen, Germany; Univ Duisburg Essen, Germany.
Direct measurement of anisotropic conductivity in a nanolaminated (Mn0.5Cr0.5)(2)GaC thin film2019In: Applied Physics Letters, ISSN 0003-6951, E-ISSN 1077-3118, Vol. 115, no 9, article id 094101Article in journal (Refereed)
The direct and parameter-free measurement of anisotropic electrical resistivity of a magnetic M(n+1)AX(n) (MAX) phase film is presented. A multitip scanning tunneling microscope is used to carry out 4-probe transport measurements with variable probe spacing s. The observation of the crossover from the 3D regime for small s to the 2D regime for large s enables the determination of both in-plane and perpendicular-to-plane resistivities rho(ab) and rho(c). A (Cr0.5Mn0.5)(2)GaC MAX phase film shows a large anisotropy ratio rho(c)/rho(ab) = 525 +/- 49. This is a consequence of the complex bonding scheme of MAX phases with covalent M-X and metallic M-M bonds in the MX planes and predominately covalent, but weaker bonds between the MX and A planes. Published under license by AIP Publishing.
fulltext
• 5.
Linköping University, Department of Physics, Chemistry and Biology. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Toward Structural Optimization of MAX Phases as Epitaxial Thin Films2016In: MATERIALS RESEARCH LETTERS, ISSN 2166-3831, Vol. 4, no 3, p. 152-160Article in journal (Refereed)
Prompted by the increased focus on MAX phase materials and their two-dimensional counterparts MXenes, a brief review of the current state of affairs in the synthesis of MAX phases as epitaxial thin films is given. Current methods for synthesis are discussed and suggestions are given on how to increase the material quality even further as well as arrive at those conditions faster. Samples were prepared to exemplify the most common issues involved with the synthesis, and through suggested paths for resolving these issues we attain samples of a quality beyond what has previously been reported.
fulltext
• 6.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Univ Duisburg Essen, Germany; Univ Duisburg Essen, Germany; Immanuel Kant Baltic Fed Univ, Russia. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Thermally induced substitutional reaction of Fe into Mo2GaC thin films2017In: MATERIALS RESEARCH LETTERS, ISSN 2166-3831, Vol. 5, no 8, p. 533-539Article in journal (Refereed)
The first Fe-based MAX phase is realized by solid-state substitution reaction of an Fe/Au/Mo2GaC thin-film diffusion couple, as determined by X-ray diffraction and scanning transmission electron microscopy. Chemical analysis together with elemental mapping reveals that as much as 50 at.% Fe on the A site can be obtained by thermally induced Au and Fe substitution for Ga atomic layers in Mo2GaC. One-sixth of the original Ga is also replaced by Au atoms. When annealing Mo2GaC thin films covered with Fe only, the Mo2GaC phase remains intact, that is, Au acts as a catalyst for the substitution reaction. [GRAPHICS] .
fulltext
• 7.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Magnetic properties and structural characterization of layered (Cr0.5Mn0.5)(2)AuC synthesized by thermally induced substitutional reaction in (Cr0.5Mn0.5)(2)GaC2018In: APL MATERIALS, ISSN 2166-532X, Vol. 6, no 2, article id 026104Article in journal (Refereed)
The magnetic properties of the new phase (Cr0.5Mn0.5)(2)AuC are compared to the known MAX-phase (Cr0.5Mn0.5)(2)GaC, where the former was synthesized by thermally induced substitution reaction of Au for Ga in (Cr0.5Mn0.5)(2)GaC. The reaction introduced a lattice expansion of similar to 3% along the c-axis, an enhancement of the coercive field from 30 mT to 140 mT, and a reduction of the Curie temperature and the saturation magnetization. Still, (Cr0.5Mn0.5)(2)AuC displays similar features in the magnetic field-and temperature-dependent magnetization curves as previously reported magnetic MAX phases, e.g., (Cr0.5Mn0.5)(2)GaC and (Mo0.5Mn0.5)(2)GaC. Thework suggests a pathway for tuning the magnetic properties of MAX phases. (c) 2018 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license.
fulltext
• 8.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology. University of Iceland, Iceland. Uppsala University, Sweden. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology.
Theoretical stability, thin film synthesis and transport properties of the Mon+1GaCn MAX phase2015In: Physica Status Solidi. Rapid Research Letters, ISSN 1862-6254, E-ISSN 1862-6270, Vol. 9, no 3, p. 197-201Article in journal (Refereed)
The phase stability of Mon +1GaCn has been investigated using ab-initio calculations. The results indicate stability for the Mo2GaC phase only, with a formation enthalpy of 0.4 meV per atom. Subsequent thin film synthesis of Mo2GaC was performed through magnetron sputtering from elemental targets onto Al2O3 [0001], 6H-SiC [0001] and MgO [111] substrates within the temperature range of 500 degrees C and 750 degrees C. High structural quality films were obtained for synthesis on MgO [111] substrates at 590 degrees C. Evaluation of transport properties showed a superconducting behavior with a critical temperature of approximately 7 K, reducing upon the application of an external magnetic field. The results point towards the first superconducting MAX phase in thin film form.
fulltext
• 9.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Finisar Sweden AB, Sweden.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Structural and mechanical properties of amorphous AlMgB14 thin films deposited by DC magnetron sputtering on Si, Al2O3 and MgO substrates2020In: Applied Physics A: Materials Science & Processing, ISSN 0947-8396, E-ISSN 1432-0630, Vol. 126, no 2, article id 133Article in journal (Refereed)
AlMgB14 coatings have been deposited by DC magnetron sputtering from elemental targets on Si (001), Al2O3 (0001) and MgO (001) substrates at temperatures in the range of 25-350 degrees C. The structural and mechanical properties of AlMgB14 films were characterized by X-ray diffraction, scanning electron microscopy, nanoindentation, and analyzed as a function of deposition conditions and substrate materials. The results show that all films are X-ray amorphous, and the mechanical properties of the deposited films depend on the substrate and growth temperature. AlMgB14 thin films deposited at 350 degrees C are found to have smoother surfaces and containing more well-formed B-12 icosahedra than the films deposited at lower temperature, which consequently increase the hardness of the deposited films. The maximum hardness and Youngs modulus of the as-deposited films are about 32.3 GPa and 310 GPa, respectively, for films deposited on Al2O3 substrate at 350 degrees C.
fulltext
• 10.
Faculty of Physics and Center for Nanointegration (CENIDE), University of Duisburg-Essen, 47057, Duisburg, Germany..
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Faculty of Physics and Center for Nanointegration (CENIDE), University of Duisburg-Essen, 47057, Duisburg, Germany.; National University of Science and Technology «MISIS», 119049, Moscow, Russian Federation.. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Grein Research ehf. Dunhaga 5, Reykjavik, Iceland.. Department of Physics, University of Warwick, Coventry, CV4 7AL, UK.. Science Institute, University of Iceland, Dunhaga 3, IS-107, Reykjavik, Iceland.; Division of Materials Physics, Department of Physics and Astronomy, Uppsala University, Box 516, SE-75121, Uppsala, Sweden.. Division of Materials Physics, Department of Physics and Astronomy, Uppsala University, Box 516, SE-75121, Uppsala, Sweden.. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Faculty of Physics and Center for Nanointegration (CENIDE), University of Duisburg-Essen, 47057, Duisburg, Germany.. Faculty of Physics and Center for Nanointegration (CENIDE), University of Duisburg-Essen, 47057, Duisburg, Germany.; Center for Functionalized Magnetic Materials (FunMagMa), Immanuel Kant Baltic Federal University, Kaliningrad, Russian Federation.. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Faculty of Physics and Center for Nanointegration (CENIDE), University of Duisburg-Essen, 47057, Duisburg, Germany. ruslan.salikhov@uni-due.de.; Zavoisky Physical-Technical Institute, Russian Academy of Sciences, 420029, Kazan, Russian Federation. ruslan.salikhov@uni-due.de..
Large uniaxial magnetostriction with sign inversion at the first order phase transition in the nanolaminated Mn2GaC MAX phase2018In: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 8, no 1, article id 2637Article in journal (Refereed)
In 2013, a new class of inherently nanolaminated magnetic materials, the so called magnetic MAX phases, was discovered. Following predictive material stability calculations, the hexagonal Mn2GaC compound was synthesized as hetero-epitaxial films containing Mn as the exclusive M-element. Recent theoretical and experimental studies suggested a high magnetic ordering temperature and non-collinear antiferromagnetic (AFM) spin states as a result of competitive ferromagnetic and antiferromagnetic exchange interactions. In order to assess the potential for practical applications of Mn2GaC, we have studied the temperature-dependent magnetization, and the magnetoresistive, magnetostrictive as well as magnetocaloric properties of the compound. The material exhibits two magnetic phase transitions. The Néel temperature is T N ~ 507 K, at which the system changes from a collinear AFM state to the paramagnetic state. At T t = 214 K the material undergoes a first order magnetic phase transition from AFM at higher temperature to a non-collinear AFM spin structure. Both states show large uniaxial c-axis magnetostriction of 450 ppm. Remarkably, the magnetostriction changes sign, being compressive (negative) above T t and tensile (positive) below the T t . The sign change of the magnetostriction is accompanied by a sign change in the magnetoresistance indicating a coupling among the spin, lattice and electrical transport properties.
fulltext
• 11.
Univ Duisburg Essen, Germany; Univ Duisburg Essen, Germany.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Univ Duisburg Essen, Germany; Univ Duisburg Essen, Germany; Natl Univ Sci and Technol MISIS, Russia. Univ Duisburg Essen, Germany; Univ Duisburg Essen, Germany. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Univ Duisburg Essen, Germany; Univ Duisburg Essen, Germany. Univ Duisburg Essen, Germany; Univ Duisburg Essen, Germany.
Long-term stability and thickness dependence of magnetism in thin (Cr0.5Mn0.5)(2)GaC MAX phase films2019In: MATERIALS RESEARCH LETTERS, ISSN 2166-3831, Vol. 7, no 4, p. 159-163Article in journal (Refereed)
The thickness dependence and long-term stability of the magnetic properties of epitaxial (Cr0.5Mn0.5)(2)GaC MAX phase films on MgO (111) were investigated. For 12.5- to 156-nm-thick films, which corresponds to 10-125 c-axis unit cells, samples were found to be phase pure with negligible c-axis lattice strain of less than 10(-4) nm even for the thinnest films. No influence of the interface layers on the magnetic anisotropy, the magnetization or the para- to ferromagnetic phase transition was observed. All samples remained stable for more than one year in ambient conditions. [GRAPHICS] IMPACT STATEMENT The complex temperature- and magnetic field-dependent magnetism of electrically conducting (Cr0.5Mn0.5)(2)GaC MAX phase films is environmentally robust over one year and independent on interface effects.
fulltext
• 12.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology.
Synthesis and characterization of Ga-containing MAX phase thin films2014Licentiate thesis, comprehensive summary (Other academic)
The study of magnetic Mn+1AXn (MAX) phases (n = 1 − 3, M – a transition metal, A – an A group element, X – C or N) is a recently established research area, fuelled by theoretical predictions and first confirmed experimentally through alloying of Mn into the well-known Cr2AlC and Cr2GeC. Theoretical phase stability investigations suggested a new magnetic MAX phase, Mn2GaC, containing Ga which is liquid close to room temperature. Hence, alternative routes for MAX phase synthesis were needed, motivating a further development of magnetron sputtering from liquid targets.
In this thesis, (Cr1-xMnx)2GaC 0 ≤ x ≤ 1 MAX phase thin films have been synthesized from elemental and/or compound targets, using ultra high vacuum magnetron sputtering. Initial thin film synthesis of Cr2GaC was performed using elemental targets, including liquid Ga. Process optimization ensured optimal target size and crucible geometry for containing the Ga. Films were deposited at 650 °C on MgO(111) substrates. X-ray diffraction and transmission electron microscopy confirms the growth of epitaxial Cr2GaC MAX phase with minor inclusions of Cr3Ga.
To explore the magnetic characteristics upon Mn alloying, synthesis of (Cr0.5Mn0.5)2GaC thin films was performed from elemental Ga and C and a composite Cr/Mn target of 1:1 composition. Films were deposited on MgO(111), Al2O3(0001) (with or without NbN seed layer), and 4° off-cut 4H-SiC(0001) substrates. The films are smooth and of high structural quality as confirmed by X-ray diffraction and transmission electron microscopy. The film composition measured by high resolution energy dispersive X-ray spectroscopy confirms a composition corresponding to (Cr0.5Mn0.5)2GaC. The magnetic response, as measured with vibrating sample magnetometry, displays a ferromagnetic component, however, the temperature dependence of the magnetic moments and saturation fields suggests competing magnetic interaction and possible non-collinear magnetic ordering.
Finally, inspired by theoretical predictions, a new member of the MAX phase family, Mn2GaC, was synthesized. This is the first MAX phase containing Mn as a sole M element. X-ray diffraction and transmission electron microscopy confirms the characteristic MAX phase structure with a 2:1:1 composition. Theoretical work suggests that the magnetic ground state is almost degenerate between ferromagnetic and anti-ferromagnetic. Vibrating sample magnetometry shows ferromagnetic response with a transition temperature Tc of 230 K. However, also for this phase, complex magnetism is suggested. Altogether, the results indicate a new family of magnetic nanolaminates with a rich variation of magnetic ground states.
1. Phase stability of Crn+1GaCn MAX phases from first principles and Cr2GaC thin-film synthesis using magnetron sputtering from elemental targets
Open this publication in new window or tab >>Phase stability of Crn+1GaCn MAX phases from first principles and Cr2GaC thin-film synthesis using magnetron sputtering from elemental targets
2013 (English)In: Physica Status Solidi. Rapid Research Letters, ISSN 1862-6254, E-ISSN 1862-6270, Vol. 7, no 11, p. 971-974Article in journal (Refereed) Published
##### Abstract [en]
Ab-initio calculations have been used to investigate the phase stability and magnetic state of Crn+ 1GaCn MAX phase. Cr2GaC (n = 1) was predicted to be stable, with a ground state corresponding to an antiferromagnetic spin configuration. Thin-film synthesis by magnetron sputtering from elemental targets, including liquid Ga, shows the formation of Cr2GaC, previously only attained from bulk synthesis methods. The films were deposited at 650 degrees C on MgO(111) substrates. X-ray diffraction and high-resolution transmission electron microscopy show epitaxial growth of (000) MAX phase.
##### Place, publisher, year, edition, pages
Wiley-VCH Verlag, 2013
##### Keywords
MAX phases; ab-initio calculations; magnetron sputtering; epitaxial thin films
##### National Category
Engineering and Technology
##### Identifiers
urn:nbn:se:liu:diva-103307 (URN)10.1002/pssr.201308025 (DOI)000328321700009 ()
Available from: 2014-01-16 Created: 2014-01-16 Last updated: 2018-03-15
2. Synthesis and characterization of magnetic (Cr0.5Mn0.5)2GaC thin films
Open this publication in new window or tab >>Synthesis and characterization of magnetic (Cr0.5Mn0.5)2GaC thin films
2015 (English)In: Journal of Materials Science, ISSN 0022-2461, E-ISSN 1573-4803, Vol. 50, no 13, p. 4495-4502Article in journal (Refereed) Published
##### Abstract [en]
Growth of (Cr0.5Mn0.5)2GaC thin films from C, Ga, and compound Cr0.5Mn0.5 targets is reported for depositions on MgO (111), 4H-SiC (0001), and Al2O3 (0001) with and without a NbN (111) seed layer. Structural quality is found to be highly dependent on the choice of substrate with MgO (111) giving the best results as confirmed by X-ray diffraction and transmission electron microscopy. Phase pure, high crystal quality MAX phase thin films are realized, with a Cr:Mn ratio of 1:1. Vibrating sample magnetometry shows a ferromagnetic component from 30 K up to 300 K, with a measured net magnetic moment of 0.67 μB per metal (Cr + Mn) atom at 30 K and 5 T. The temperature dependence of the magnetic response suggests competing magnetic interactions with a resulting non-collinear magnetic ordering.
##### Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2015
##### Keywords
magnetism, thin films, magnetron sputtering, MAX phase
##### National Category
Condensed Matter Physics
##### Identifiers
urn:nbn:se:liu:diva-118837 (URN)10.1007/s10853-015-8999-8 (DOI)000354093500005 ()
##### Note
At the time for thesis presentation publication was in status: Manuscript
Funding Agencies|European Research Council under the European Community [258509]; Swedish Research Council (VR) [642-2013-8020, 621-2012-4425]; KAW Fellowship program; SSF synergy grant FUNCASE; Icelandic University Research fund
Available from: 2015-06-08 Created: 2015-06-04 Last updated: 2018-03-15Bibliographically approved
3. A Nanolaminated Magnetic Phase: Mn2GaC
Open this publication in new window or tab >>A Nanolaminated Magnetic Phase: Mn2GaC
2014 (English)In: Materials Research Letters, ISSN 2166-3831, Vol. 2, no 2, p. 89-93Article in journal (Refereed) Published
##### Abstract [en]
Layered magnetic materials are fascinating from the point of view of fundamental science as well as applications. Discoveries such as giant magnetoresistance (GMR) in magnetic multilayers have revolutionized data storage and magnetic recording, and concurrently initiated the search for new layered magnetic materials. One group of inherently nanolaminated compounds are the so called Mn+1AXn (MAX) phases. Due to the large number of isostructural compositions, researchers are exploring the wide range of interesting properties, and not primarily functionalization through optimization of structural quality. Magnetic MAX phases have been discussed in the literature, though this is hitherto an unreported phenomenon. However, such materials would be highly interesting, based on the attractive and useful properties attained with layered magnetic materials to date. Here we present a new MAX phase, (Cr1–xMnx)2GeC, synthesized as thin film in heteroepitaxial form, showing single crystal material with unprecedented structural MAX phase quality. The material was identified using first-principles calculations to study stability of hypothetical MAX phases, in an eort to identify a potentially magnetic material. The theory predicts a variety of magnetic behavior depending on the Mn concentration and Cr/Mn atomic conguration within the sublattice. The analyzed thin films display a magnetic signal well above room temperature and with partly ferromagnetic ordering. These very promising results open up a field of new layered magnetic materials, with high potential for electronics and spintronics applications.
##### Place, publisher, year, edition, pages
Taylor & Francis, 2014
##### Keywords
MAX phases, sputtering, transmission electron microscopy (TEM), ab initio calculation
##### National Category
Natural Sciences
##### Identifiers
urn:nbn:se:liu:diva-77774 (URN)10.1080/21663831.2013.865105 (DOI)
##### Note
On the day of the defence date the status of this article was previous Manuscript. The original title of the Manuscript was Magnetic nanoscale laminates from first principles and thin film synthesis.
Available from: 2012-05-29 Created: 2012-05-29 Last updated: 2018-03-15Bibliographically approved
Synthesis and characterization of Ga-containing MAX phase thin films
omslag
• 13. Buy this publication >>
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Synthesis and characterization of magnetic nanolaminated carbides2018Doctoral thesis, comprehensive summary (Other academic)
MAX phases are a group of nanolaminated ternary carbides and nitrides, with a composition expressed by the general formula Mn+1AXn (𝑛 = 1 − 3), where M is a transition metal, A is an A-group element, and X is carbon and/or nitrogen. MAX phases have attracted interest due to their unique combination of metallic and ceramic properties, related to their inherently laminated structure of a transition metal carbide (Mn+1Xn) layer interleaved by an A-group metal layer.
This Thesis explores synthesis and characterization of magnetic MAX phases, where the A-group element is gallium (Ga). Due to the low melting point of Ga (T = 30 °C), conventional thin film synthesis methods become challenging, as the material is in liquid form at typical process temperatures. Development of existing methods has therefore been investigated, for reliable/reproducible synthesis routes, including sputtering from a liquid target, and resulting high quality material. Routes for minimizing trial-and-error procedures during optimization of thin film synthesis have also been studied, allowing faster identification of optimal deposition conditions and a simplified transfer of essential deposition parameters between different deposition systems.
A large part of this Thesis is devoted towards synthesis of MAX phase thin films in the Cr-Mn-Ga-C system. First, through process development, thin films of Cr2GaC were deposited by magnetron sputtering. The films were epitaxial, however with small amount of impurity phase Cr3Ga, as confirmed by X-ray diffraction (XRD) measurements. The film structure was confirmed by scanning transmission electron microscopy (STEM) and the composition by energy dispersive X-ray spectroscopy (EDX) inside the TEM.
Inspired by predictive ab initio calculations, the new MAX phase Mn2GaC was successfully synthesized in thin film form by magnetron sputtering. Structural parameters and magnetic properties were analysed. The material was found to have two magnetic transitions in the temperature range 3 K to 750 K, with a first order transition at around 214 K, going from non-collinear antiferromagnetic state at lower temperature to an antiferromagnetic state at higher temperature. The Neél temperature was determined to be 507 K, changing from an antiferromagnetic to a paramagnetic state. Above 800 K, Mn2GaC decomposes. Furthermore, magnetostrictive, magnetoresistive and magnetocaloric properties of the material were iv determined, among which a drastic change in lattice parameters upon the first magnetic transition was observed. This may be of interest for magnetocaloric applications.
Synthesis of both Cr2GaC and Mn2GaC in thin film form opens the possibility to tune the magnetic properties through a solid solution on the transition metal site, by alloying the aforementioned Cr2GaC with Mn, realizing (Cr1-xMnx)2GaC. From a compound target with a Cr:Mn ratio of 1:1, thin films of (Cr0.5Mn0.5)2GaC were synthesized, confirmed by TEM-EDX. Optimized structure was obtained by deposition on MgO substrates at a deposition temperature of 600 ºC. The thin films were phase pure and of high structural quality, allowing magnetic measurements. Using vibrating sample magnetometry (VSM), it was found that (Cr0.5Mn0.5)2GaC has a ferromagnetic component in the temperature range from 30 K to 300 K, with the measured magnetic moment at high field decreasing by increasing temperature. The remanent moment and coercive field is small, 0.036 μB, and 12 mT at 30 K, respectively. Using ferromagnetic resonance spectroscopy, it was also found that the material has pure spin magnetism, as indicated by the determined spectroscopic splitting factor g = 2.00 and a negligible magnetocrystalline anisotropy energy.
Fuelled by the recent discoveries of in-plane chemically ordered quaternary MAX phases, so called i-MAX phases, and guided by ab initio calculations, new members within this family, based on Cr and Mn, were synthesized by pressureless sintering methods, realizing (Cr2/3Sc1/3)2GaC and (Mn2/3Sc1/3)2GaC. Their structural properties were determined. Through these phases, the Mn content is the highest obtained in a bulk MAX phase to date.
This work has further developed synthesis processes for sputtering from liquid material, for an optimized route to achieve thin films of controlled composition and a high structural quality. Furthermore, through this work, Mn has been added as a new element in the family of MAX phase elements. It has also been shown, that alloying with different content of Mn gives rise to varying magnetic properties in MAX phases. As a result of this Thesis, it is expected that the MAX phase family can be further expanded, with more members of new compositions and new properties.
1. Phase stability of Crn+1GaCn MAX phases from first principles and Cr2GaC thin-film synthesis using magnetron sputtering from elemental targets
Open this publication in new window or tab >>Phase stability of Crn+1GaCn MAX phases from first principles and Cr2GaC thin-film synthesis using magnetron sputtering from elemental targets
2013 (English)In: Physica Status Solidi. Rapid Research Letters, ISSN 1862-6254, E-ISSN 1862-6270, Vol. 7, no 11, p. 971-974Article in journal (Refereed) Published
##### Abstract [en]
Ab-initio calculations have been used to investigate the phase stability and magnetic state of Crn+ 1GaCn MAX phase. Cr2GaC (n = 1) was predicted to be stable, with a ground state corresponding to an antiferromagnetic spin configuration. Thin-film synthesis by magnetron sputtering from elemental targets, including liquid Ga, shows the formation of Cr2GaC, previously only attained from bulk synthesis methods. The films were deposited at 650 degrees C on MgO(111) substrates. X-ray diffraction and high-resolution transmission electron microscopy show epitaxial growth of (000) MAX phase.
##### Place, publisher, year, edition, pages
Wiley-VCH Verlag, 2013
##### Keywords
MAX phases; ab-initio calculations; magnetron sputtering; epitaxial thin films
##### National Category
Engineering and Technology
##### Identifiers
urn:nbn:se:liu:diva-103307 (URN)10.1002/pssr.201308025 (DOI)000328321700009 ()
Available from: 2014-01-16 Created: 2014-01-16 Last updated: 2018-03-15
2. A Nanolaminated Magnetic Phase: Mn2GaC
Open this publication in new window or tab >>A Nanolaminated Magnetic Phase: Mn2GaC
2014 (English)In: Materials Research Letters, ISSN 2166-3831, Vol. 2, no 2, p. 89-93Article in journal (Refereed) Published
##### Abstract [en]
Layered magnetic materials are fascinating from the point of view of fundamental science as well as applications. Discoveries such as giant magnetoresistance (GMR) in magnetic multilayers have revolutionized data storage and magnetic recording, and concurrently initiated the search for new layered magnetic materials. One group of inherently nanolaminated compounds are the so called Mn+1AXn (MAX) phases. Due to the large number of isostructural compositions, researchers are exploring the wide range of interesting properties, and not primarily functionalization through optimization of structural quality. Magnetic MAX phases have been discussed in the literature, though this is hitherto an unreported phenomenon. However, such materials would be highly interesting, based on the attractive and useful properties attained with layered magnetic materials to date. Here we present a new MAX phase, (Cr1–xMnx)2GeC, synthesized as thin film in heteroepitaxial form, showing single crystal material with unprecedented structural MAX phase quality. The material was identified using first-principles calculations to study stability of hypothetical MAX phases, in an eort to identify a potentially magnetic material. The theory predicts a variety of magnetic behavior depending on the Mn concentration and Cr/Mn atomic conguration within the sublattice. The analyzed thin films display a magnetic signal well above room temperature and with partly ferromagnetic ordering. These very promising results open up a field of new layered magnetic materials, with high potential for electronics and spintronics applications.
##### Place, publisher, year, edition, pages
Taylor & Francis, 2014
##### Keywords
MAX phases, sputtering, transmission electron microscopy (TEM), ab initio calculation
##### National Category
Natural Sciences
##### Identifiers
urn:nbn:se:liu:diva-77774 (URN)10.1080/21663831.2013.865105 (DOI)
##### Note
On the day of the defence date the status of this article was previous Manuscript. The original title of the Manuscript was Magnetic nanoscale laminates from first principles and thin film synthesis.
Available from: 2012-05-29 Created: 2012-05-29 Last updated: 2018-03-15Bibliographically approved
3. Large uniaxial magnetostriction with sign inversion at the first order phase transition in the nanolaminated Mn2GaC MAX phase
Open this publication in new window or tab >>Large uniaxial magnetostriction with sign inversion at the first order phase transition in the nanolaminated Mn2GaC MAX phase
2018 (English)In: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 8, no 1, article id 2637Article in journal (Refereed) Published
##### Abstract [en]
In 2013, a new class of inherently nanolaminated magnetic materials, the so called magnetic MAX phases, was discovered. Following predictive material stability calculations, the hexagonal Mn2GaC compound was synthesized as hetero-epitaxial films containing Mn as the exclusive M-element. Recent theoretical and experimental studies suggested a high magnetic ordering temperature and non-collinear antiferromagnetic (AFM) spin states as a result of competitive ferromagnetic and antiferromagnetic exchange interactions. In order to assess the potential for practical applications of Mn2GaC, we have studied the temperature-dependent magnetization, and the magnetoresistive, magnetostrictive as well as magnetocaloric properties of the compound. The material exhibits two magnetic phase transitions. The Néel temperature is T N ~ 507 K, at which the system changes from a collinear AFM state to the paramagnetic state. At T t = 214 K the material undergoes a first order magnetic phase transition from AFM at higher temperature to a non-collinear AFM spin structure. Both states show large uniaxial c-axis magnetostriction of 450 ppm. Remarkably, the magnetostriction changes sign, being compressive (negative) above T t and tensile (positive) below the T t . The sign change of the magnetostriction is accompanied by a sign change in the magnetoresistance indicating a coupling among the spin, lattice and electrical transport properties.
##### Place, publisher, year, edition, pages
London: Nature Publishing Group, 2018
##### National Category
Condensed Matter Physics
##### Identifiers
urn:nbn:se:liu:diva-145680 (URN)10.1038/s41598-018-20903-2 (DOI)
Available from: 2018-03-15 Created: 2018-03-15 Last updated: 2018-03-15Bibliographically approved
4. Synthesis and characterization of magnetic (Cr0.5Mn0.5)2GaC thin films
Open this publication in new window or tab >>Synthesis and characterization of magnetic (Cr0.5Mn0.5)2GaC thin films
2015 (English)In: Journal of Materials Science, ISSN 0022-2461, E-ISSN 1573-4803, Vol. 50, no 13, p. 4495-4502Article in journal (Refereed) Published
##### Abstract [en]
Growth of (Cr0.5Mn0.5)2GaC thin films from C, Ga, and compound Cr0.5Mn0.5 targets is reported for depositions on MgO (111), 4H-SiC (0001), and Al2O3 (0001) with and without a NbN (111) seed layer. Structural quality is found to be highly dependent on the choice of substrate with MgO (111) giving the best results as confirmed by X-ray diffraction and transmission electron microscopy. Phase pure, high crystal quality MAX phase thin films are realized, with a Cr:Mn ratio of 1:1. Vibrating sample magnetometry shows a ferromagnetic component from 30 K up to 300 K, with a measured net magnetic moment of 0.67 μB per metal (Cr + Mn) atom at 30 K and 5 T. The temperature dependence of the magnetic response suggests competing magnetic interactions with a resulting non-collinear magnetic ordering.
##### Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2015
##### Keywords
magnetism, thin films, magnetron sputtering, MAX phase
##### National Category
Condensed Matter Physics
##### Identifiers
urn:nbn:se:liu:diva-118837 (URN)10.1007/s10853-015-8999-8 (DOI)000354093500005 ()
##### Note
At the time for thesis presentation publication was in status: Manuscript
Funding Agencies|European Research Council under the European Community [258509]; Swedish Research Council (VR) [642-2013-8020, 621-2012-4425]; KAW Fellowship program; SSF synergy grant FUNCASE; Icelandic University Research fund
Available from: 2015-06-08 Created: 2015-06-04 Last updated: 2018-03-15Bibliographically approved
5. Magnetic Anisotropy in the (Cr0.5Mn0.5)(2)GaC MAX Phase
Open this publication in new window or tab >>Magnetic Anisotropy in the (Cr0.5Mn0.5)(2)GaC MAX Phase
2015 (English)In: MATERIALS RESEARCH LETTERS, ISSN 2166-3831, Vol. 3, no 3, p. 156-160Article in journal (Refereed) Published
##### Abstract [en]
Magnetic MAX phase (Cr0.5Mn0.5)(2)GaC thin films grown epitaxially on MgO(111) substrates were studied by ferromagnetic resonance at temperatures between 110 and 300 K. The spectroscopic splitting factor g = 2.00 +/- 0.01 measured at all temperatures indicates pure spin magnetism in the sample. At all temperatures we find the magnetocrystalline anisotropy energy to be negligible which is in agreement with the identified pure spin magnetism.
##### Place, publisher, year, edition, pages
TAYLOR & FRANCIS INC, 2015
##### Keywords
Magnetic MAX Phase; Ferromagnetic Resonance; g-Factor; Magnetic Anisotropy
##### National Category
Physical Sciences
##### Identifiers
urn:nbn:se:liu:diva-127070 (URN)10.1080/21663831.2015.1036324 (DOI)000372219300006 ()
##### Note
Funding Agencies|EC [280670]; UDE; ERC [258509]; Swedish Research Council (VR) [642-2013-8020]; SSF synergy grant FUNCASE
Available from: 2016-04-13 Created: 2016-04-13 Last updated: 2018-03-15
6. Toward Structural Optimization of MAX Phases as Epitaxial Thin Films
Open this publication in new window or tab >>Toward Structural Optimization of MAX Phases as Epitaxial Thin Films
2016 (English)In: MATERIALS RESEARCH LETTERS, ISSN 2166-3831, Vol. 4, no 3, p. 152-160Article in journal (Refereed) Published
##### Abstract [en]
Prompted by the increased focus on MAX phase materials and their two-dimensional counterparts MXenes, a brief review of the current state of affairs in the synthesis of MAX phases as epitaxial thin films is given. Current methods for synthesis are discussed and suggestions are given on how to increase the material quality even further as well as arrive at those conditions faster. Samples were prepared to exemplify the most common issues involved with the synthesis, and through suggested paths for resolving these issues we attain samples of a quality beyond what has previously been reported.
##### Place, publisher, year, edition, pages
TAYLOR & FRANCIS INC, 2016
##### Keywords
MAX Phase; Thin Films; Reproducible Materials Synthesis; Sample Quality
##### National Category
Inorganic Chemistry
##### Identifiers
urn:nbn:se:liu:diva-132496 (URN)10.1080/21663831.2016.1157525 (DOI)000385011000004 ()
##### Note
Funding Agencies|European Research Council under the European Community Seventh Framework Program (FP7)/ERC Grant [258509]; Swedish Research Council (VR); Knut and Alice Wallenberg (KAW) Fellowship program; SSF synergy grant FUNCASE
Available from: 2016-11-13 Created: 2016-11-12 Last updated: 2018-03-15
Synthesis and characterization of magnetic nanolaminated carbides
omslag
presentationsbild
• 14.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Synthesis of atomically layered and chemically ordered rare-earth (RE) i-MAX phases; (Mo2/3RE1/3)2GaC with RE = Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu2019In: Materials Research Letters, ISSN 2166-3831, Vol. 7, no 11, p. 446-452Article in journal (Refereed)
We report the synthesis of eight new members of the i-MAX family, of the formula (Mo2/3RE1/3)2GaC, where RE = Gd, Tb, Dy, Ho, Er, Tm, Lu, and Yb, the latter not previously incorporated in a MAX phase. The structure and composition of powder samples were investigated by X-ray diffraction, scanning transmission electron microscopy, and energy dispersive X-ray analysis combined with scanning electron microscopy. All phases showed evidence of an orthorhombic (Cmcm) structure, and the phases based on Er and Yb also crystallized in a monoclinic (C2/c) arrangement. The chemical order of the magnetic elements suggests interesting magnetic characteristics, with a high tuning potential through the range of attainable lanthanide elements.
fulltext
attachment
• 15.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Theoretical Prediction and Experimental Verification of the Chemically Ordered Atomic-Laminate i-MAX Phases (Cr2/3Sc1/3)(2)GaC and (Mn2/3Sc1/3)(2)GaC2020In: Crystal Growth & Design, ISSN 1528-7483, E-ISSN 1528-7505, Vol. 20, no 1, p. 55-61Article in journal (Refereed)
We combine predictive ab initio calculations with experimental verification of bulk materials synthesis for exploration of new and potentially magnetic atomically laminated i-MAX phases. Two such phases are discovered: (Cr2/3Sc1/3)(2)GaC and (Mn2/3Sc1/3)(2)GaC synthesized by the solid state reaction from elemental constituents. The latter compound displays a 2-fold increase in Mn content compared to previously reported bulk MAX phases. Both new compounds exhibit the characteristic in-plane chemical order of Cr(Mn) and Sc, and crystallize in an orthorhombic structure, space group Cmcm, as confirmed by scanning transmission electron microscopy. From density functional theory calculations of the magnetic ground state, including the electron-interaction parameter U, we suggest an antiferromagnetic ground state, close to degenerate with the ferromagnetic state.
The full text will be freely available from 2020-12-02 15:15
• 16.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology.
Phase stability of Crn+1GaCn MAX phases from first principles and Cr2GaC thin-film synthesis using magnetron sputtering from elemental targets2013In: Physica Status Solidi. Rapid Research Letters, ISSN 1862-6254, E-ISSN 1862-6270, Vol. 7, no 11, p. 971-974Article in journal (Refereed)
Ab-initio calculations have been used to investigate the phase stability and magnetic state of Crn+ 1GaCn MAX phase. Cr2GaC (n = 1) was predicted to be stable, with a ground state corresponding to an antiferromagnetic spin configuration. Thin-film synthesis by magnetron sputtering from elemental targets, including liquid Ga, shows the formation of Cr2GaC, previously only attained from bulk synthesis methods. The films were deposited at 650 degrees C on MgO(111) substrates. X-ray diffraction and high-resolution transmission electron microscopy show epitaxial growth of (000) MAX phase.
fulltext
• 17.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology. Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden. Science Institute, University of Iceland, Reykjavik, Iceland. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology.
Synthesis and characterization of magnetic (Cr0.5Mn0.5)2GaC thin films2015In: Journal of Materials Science, ISSN 0022-2461, E-ISSN 1573-4803, Vol. 50, no 13, p. 4495-4502Article in journal (Refereed)
Growth of (Cr0.5Mn0.5)2GaC thin films from C, Ga, and compound Cr0.5Mn0.5 targets is reported for depositions on MgO (111), 4H-SiC (0001), and Al2O3 (0001) with and without a NbN (111) seed layer. Structural quality is found to be highly dependent on the choice of substrate with MgO (111) giving the best results as confirmed by X-ray diffraction and transmission electron microscopy. Phase pure, high crystal quality MAX phase thin films are realized, with a Cr:Mn ratio of 1:1. Vibrating sample magnetometry shows a ferromagnetic component from 30 K up to 300 K, with a measured net magnetic moment of 0.67 μB per metal (Cr + Mn) atom at 30 K and 5 T. The temperature dependence of the magnetic response suggests competing magnetic interactions with a resulting non-collinear magnetic ordering.
fulltext
• 18.
University of Duisburg Essen, Germany.
University of Duisburg Essen, Germany; Moscow MV Lomonosov State University, Russia; Helmholtz Zentrum Dresden Rossendorf, Germany. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. University of Duisburg Essen, Germany. University of Duisburg Essen, Germany.
Magnetic Anisotropy in the (Cr0.5Mn0.5)(2)GaC MAX Phase2015In: MATERIALS RESEARCH LETTERS, ISSN 2166-3831, Vol. 3, no 3, p. 156-160Article in journal (Refereed)
Magnetic MAX phase (Cr0.5Mn0.5)(2)GaC thin films grown epitaxially on MgO(111) substrates were studied by ferromagnetic resonance at temperatures between 110 and 300 K. The spectroscopic splitting factor g = 2.00 +/- 0.01 measured at all temperatures indicates pure spin magnetism in the sample. At all temperatures we find the magnetocrystalline anisotropy energy to be negligible which is in agreement with the identified pure spin magnetism.
fulltext
• 19.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Atomically Layered and Ordered Rare-Earth i-MAX Phases: A New Class of Magnetic Quaternary Compounds2019In: Chemistry of Materials, ISSN 0897-4756, E-ISSN 1520-5002, Vol. 31, no 7, p. 2476-2485Article in journal (Refereed)
In 2017, we discovered quaternary i-MAX phases atomically layered solids, where M is an early transition metal, A is an A group element, and X is C-with a ((M2/3M1/32)-M-1)(2)AC chemistry, where the M-1 and M-2 atoms are in-plane ordered. Herein, we report the discovery of a class of magnetic i-MAX phases in which bilayers of a quasi-2D magnetic frustrated triangular lattice overlay a Mo honeycomb arrangement and an Al Kagome lattice. The chemistry of this family is (Mo2/3RE1/3)(2)AlC, and the rare-earth, RE, elements are Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, and Lu. The magnetic properties were characterized and found to display a plethora of ground states, resulting from an interplay of competing magnetic interactions in the presence of magnetocrystalline anisotropy.
fulltext
• 20.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology.
Effect of Ti-Al cathode composition on plasma generation and plasma transport in direct current vacuum arc2014In: Journal of Applied Physics, ISSN 0021-8979, E-ISSN 1089-7550, Vol. 115, no 12, p. 123301-Article in journal (Refereed)
DC arc plasma from Ti, Al, and Ti1-xAlx (x = 0.16, 0.25, 0.50, and 0.70) compound cathodes was characterized with respect to plasma chemistry and charge-state-resolved ion energy. Scanning electron microscopy, X-ray diffraction, and Energy-dispersive X-ray spectroscopy of the deposited films and the cathode surfaces were used for exploring the correlation between cathode-, plasma-, and film composition. Experimental work was performed at a base pressure of 10(-6) Torr, to exclude plasma-gas interaction. The plasma ion composition showed a reduction of Al of approximately 5 at. % compared to the cathode composition, while deposited films were in accordance with the cathode stoichiometry. This may be explained by presence of neutrals in the plasma/vapour phase. The average ion charge states (Ti = 2.2, Al = 1.65) were consistent with reference data for elemental cathodes, and approximately independent on the cathode composition. On the contrary, the width of the ion energy distributions (IEDs) were drastically reduced when comparing the elemental Ti and Al cathodes with Ti0.5Al0.5, going from similar to 150 and similar to 175 eV to similar to 100 and similar to 75 eV for Ti and Al ions, respectively. This may be explained by a reduction in electron temperature, commonly associated with the high energy tail of the IED. The average Ti and Al ion energies ranged between similar to 50 and similar to 61 eV, and similar to 30 and similar to 50 eV, respectively, for different cathode compositions. The attained energy trends were explained by the velocity rule for compound cathodes, which states that the most likely velocities of ions of different mass are equal. Hence, compared to elemental cathodes, the faster Al ions will be decelerated, and the slower Ti ions will be accelerated when originating from compound cathodes. The intensity of the macroparticle generation and thickness of the deposited films were also found to be dependent on the cathode composition. The presented results may be of importance for choice of cathodes for thin film depositions involving compound cathodes.
fulltext
• 21.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. PLANSEE Composite Mat GmbH, Germany. PLANSEE Composite Mat GmbH, Germany. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Vacuum arc plasma generation and thin film deposition from a TiB2 cathode2015In: Applied Physics Letters, ISSN 0003-6951, E-ISSN 1077-3118, Vol. 107, no 18, p. 184103-Article in journal (Refereed)
We have studied the utilization of TiB2 cathodes for thin film deposition in a DC vacuum arc system. We present a route for attaining a stable, reproducible, and fully ionized plasma flux of Ti and B by removal of the external magnetic field, which leads to dissipation of the vacuum arc discharge and an increased active surface area of the cathode. Applying a magnetic field resulted in instability and cracking, consistent with the previous reports. Plasma analysis shows average energies of 115 and 26 eV, average ion charge states of 2.1 and 1.1 for Ti and B, respectively, and a plasma ion composition of approximately 50% Ti and 50% B. This is consistent with measured resulting film composition from X-ray photoelectron spectroscopy, suggesting a negligible contribution of neutrals and macroparticles to the film growth. Also, despite the observations of macroparticle generation, the film surface is very smooth. These results are of importance for the utilization of cathodic arc as a method for synthesis of metal borides. (C) 2015 AIP Publishing LLC.
fulltext
• 22.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. PLANSEE Composite Mat GmbH, Germany. PLANSEE Composite Mat GmbH, Germany. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Effect of Ti-Al cathode grain size on plasma generation and thin film synthesis from a direct current vacuum arc plasma source2019In: AIP Advances, ISSN 2158-3226, E-ISSN 2158-3226, Vol. 9, no 4, article id 045008Article in journal (Refereed)
Herein, we investigate the influence of powder metallurgical manufactured Ti0.5Al0.5 cathode grain size (45-150 mu m) on the properties of a DC arc discharge, for N-2 pressures in the range 10(-5) Torr (base pressure) up to 3x10(-2) Torr. Intermetallic TiAl cathodes are also studied. The arc plasma is characterized with respect to ion composition, ion charge state, and ion energy, and is found to change with pressure, independent on choice of cathode. Scanning electron microscopy, X-ray diffraction, and Energy-dispersive X-ray spectroscopy of the cathode surfaces and the concurrently deposited films are used for exploring the correlation between cathode-, plasma-, and film composition. The plasma has a dominating Al ion content at elevated pressures, while the film composition is consistent with the cathode composition, independent on cathode grain size. Cross-sections of the used cathodes are studied, and presence of a converted layer, up to 10 mu m, is shown, with an improved intermixing of the elements on the cathode surface. This layer is primarily explained by condensation of cathode material from the melting and splashes accompanying the arc spot movement, as well as generated plasma ions being redeposited upon returning to the cathode. The overall lack of dependence on grain size is likely due to similar physical properties of Ti, Al and TiAl grains, as well as the formation of a converted layer. The presented findings are of importance for large scale manufacturing and usage of Ti-Al cathodes in industrial processes. (C) 2019 Author(s).
fulltext
• 23.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. PLANSEE Composite Mat GmbH, Germany. PLANSEE Composite Mat GmbH, Germany. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Generation of super-size macroparticles in a direct current vacuum arc discharge from a Mo-Cu cathode2016In: Applied Physics Letters, ISSN 0003-6951, E-ISSN 1077-3118, Vol. 108, no 5, p. 054103-Article in journal (Refereed)
An inherent property of cathodic arc is the generation of macroparticles, of a typical size ranging from submicrometer up to a few tens of mu m. In this work, we have studied macroparticle generation from a Mo0.78Cu0.22 cathode used in a dc vacuum arc discharge, and we present evidence for super-size macroparticles of up to 0.7mm in diameter. All analyzed particles are found to be rich in Mo (>= 98 at. %). The particle generation is studied by visual observation of the cathode surface during arcing, by analysis of composition and geometrical features of the used cathode surface, and by examination of the generated macroparticles with respect to shape and composition. A mechanism for super-size macroparticle generation is suggested based on observed segregated layers of Mo and Cu identified in the topmost part of the cathode surface, likely due to the discrepancy in melting and evaporation temperatures of Mo and Cu. The results are of importance for increasing the fundamental understanding of macroparticle generation, which in turn may lead to increased process control and potentially provide paths for tuning, or even mitigating, macroparticle generation. (C) 2016 AIP Publishing LLC.
• 24.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Computer and Information Science, ESLAB - Embedded Systems Laboratory. Linköping University, The Institute of Technology.
Effect of cathode composition and nitrogen pressure on macroparticle generation and type of arc discharge in a DC arc source with Ti-Al compound cathodes2015In: Surface & Coatings Technology, ISSN 0257-8972, E-ISSN 1879-3347, Vol. 281, p. 20-26Article in journal (Refereed)
Thin films deposited with unfiltered DC arc plasma from Ti, Ti0.75Al0.25, Ti0.50Al0.50, Ti0.30Al0.70, and Al cathodes were characterized with a scanning electron microscope for quantification of extent of macroparticle incorporation. Depositions were performed in N-2 atmosphere in the pressure range from 10(-6) Torr up to 3 . 10(-2) Torr, and the formation of cathode surface nitride contamination was identified from X-ray diffraction analysis. Visual observation and photographic fixation of the arc spot behavior was simultaneously performed. A reduction in macroparticle generation with decreasing Al content and increasing N-2 pressure was demonstrated. A correlated transformation of the arc from type 2 to the type 1 was visually detected and found to be a function of N-2 pressure and at of Al in the cathode. For the Ti cathode, no arc transformation was detected. These observations can be explained by a comparatively high electrical resistivity and high melting point of Al rich surface nitrides, promoting an arc transformation and a reduction in macropartide generation. (C) 2015 Elsevier B.V. All rights reserved.
• 25.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
PLANSEE Composite Mat GmbH, Germany. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering. PLANSEE Composite Mat GmbH, Germany. Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, Faculty of Science & Engineering.
Effect of Mo-Cu cathode composition on process stability, macroparticle formation, plasma generation, and thin-film deposition in DC arc synthesis2020In: Journal of Applied Physics, ISSN 0021-8979, E-ISSN 1089-7550, Vol. 127, no 1, article id 013301Article in journal (Refereed)
In this work, we present the correlation between cathode composition and features of the arcing process for Mo1-xCux [x = 0.0, 0.07 (0.05), 0.14 (0.10), 0.21 (0.15), 0.40 (0.3), 0.73 (0.63), 0.97 (0.95), and 1.00, atomic fraction (weight fraction)] cathodes used in a DC vacuum-arc deposition system. It is found that the stability of the arcing process crucially depends on the cathode composition. The most stable arc spot and the lowest cathode potential (similar to 19 V) are detected for the Mo0.27Cu0.73 cathode, while the Mo0.93Cu0.07 cathode shows the most unstable arcing process with the highest cathode potential (similar to 28 V). The properties of the generated plasma are also strongly dependent on the relative ratio of the cathode elements. The metal ions from the Mo and Cu cathodes have peak kinetic energies around 136 and 62 eV, respectively, while for a Mo0.79Cu0.21 cathode, the corresponding energies are only 45 and 28 eV. The average charge states decreased from 2.1 to 1.6 for Mo ions and from 2 to 1.2 for Cu ions. The intensity of macroparticle generation and the size of the droplets correlate with the relative fraction of Cu. However, it is shown that, typically for the cathodes with a low amount of Cu, an increased abundance of visually observed macroparticles leads to droplet-free films. The film thicknesses and their compositions also demonstrate dependencies on the elemental composition of the cathode. These results are discussed in the light of no solubility between Mo and Cu and the high temperature of the cathode surface during the arcing process. Published under license by AIP Publishing.
The full text will be freely available from 2021-01-03 13:40
1 - 25 of 25
CiteExportLink to result list
Cite
Citation style
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• oxford
• Other style
More styles
Language
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf
|
{}
|
0
Research Papers: Nuclear Power
# Three Dimensional Modeling of the Hydrodynamics of Oblique Droplet-Hot Wall Interactions During the Reflood Phase After a LOCA
[+] Author and Article Information
D. Chatzikyriakou
Department of Mechanical Engineering, Imperial College London, Exhibition Road, London SW7 2AZ, UKd.chatzikiriakou@imperial.ac.uk
S. P. Walker, B. Belhouachi
Department of Mechanical Engineering, Imperial College London, Exhibition Road, London SW7 2AZ, UK
C. Narayanan, D. Lakehal
ASCOMP GmbH, Technoparkstrasse 1, 8005 Zurich, Switzerland
G. F. Hewitt
Department of Chemical Engineering and Chemical Technology, Imperial College, Prince Consort Road, London SW7 2BY, UK
J. Eng. Gas Turbines Power 132(10), 102914 (Jul 07, 2010) (6 pages) doi:10.1115/1.4000867 History: Received July 29, 2009; Revised August 04, 2009; Published July 07, 2010; Online July 07, 2010
## Abstract
During the reflood phase, following a loss-of-coolant-accident (LOCA), the main mechanism for the precursory cooling of the fuel is by convective heat transfer to the vapor, with the vapor being cooled by the evaporation of the entrained saturated droplets. However, it is believed that the droplets that reach the rod could have an effect on this cooling process. Despite the fact that those droplets do not actually wet the fuel rod due to the formation of a vapor film that sustains them and prevents them from touching the wall, the temperature drop caused by the impingement of such water droplets on a very hot solid surface (whose temperature is beyond the Leidenfrost temperature (1966, “A Track About Some Qualities of Common Water,” Int. J. Heat Mass Transfer, 9, pp. 1153–1166)) is of the order of $30–150°C$ (2008, The Role of Entrained Droplets in Precursory Cooling During PWR Post-LOCA Reflood, TOPSAFE, Dubrovnik, Croatia, 1995, “Heat Transfer During Liquid Contact on Superheated Surfaces,” ASME J. Heat Transfer, 117, pp. 693–697). The associated heat flux is of the order of $105–107 W/m2$ and the heat extracted is in the range of 0.05 J over the time period of the interaction (a few ms) (2008, The Role of Entrained Droplets in Precursory Cooling During PWR Post-LOCA Reflood, TOPSAFE, Dubrovnik, Croatia, 1995, “Heat Transfer During Liquid Contact on Superheated Surfaces,” ASME J. Heat Transfer, 117, pp. 693–697). The hydrodynamic behavior of the droplets upon impingement is reported to affect the heat transfer effectiveness of the droplets. In the dispersed flow regime the droplets are more likely to impinge on the hot surface at a very small angle sliding along the solid wall, still without actually touching it, and remaining in a close proximity for a much larger time period. This changes the heat transfer behavior of the droplet. Here, we investigate numerically the hydrodynamics of the impingement of such droplets on a hot solid surface at various incident angles and various velocities of approach. For our simulations, we use a computational fluid dynamics (CFD), finite-volume computational algorithm (TransAT© ). The level set method is used for the tracking of the interface. We present three-dimensional results of those impinging droplets. The validation of our simulation is done against experimental data already available in the literature. Then, we compare the findings of those results with previous correlations.
<>
## Figures
Figure 1
Qualitative comparison between experimental data (7) and our simulated results (TransAT© ). The droplet size is 140 μm and the droplet velocity is 3 m/s. The approach angle is 30 deg. The Weber number here is 7.
Figure 2
Ratio of normal droplet velocity component after and before the impact against Weber number. Several droplet sizes and velocities were simulated. Good agreement between the predictions using the TransAT© code and the experimental measurements of Anders (7).
Figure 3
2 mm drop, angle of approach is 20 deg, initial velocity 1.2 m/s
Figure 4
200 μm drop, angle of approach is 20 deg, initial velocity 1.2 m/s
Figure 5
Simulated results. Water droplets impinging at various angles on a surface beyond the Leidenfrost threshold. The vertical and the 60 deg impact are similar. When small angles of impingement are considered, then the behavior is different. Here, the Weber numbers are 4, 3, and 0.5 from top to bottom. The droplet diameter is 200 μm.
Figure 6
Spreading of the droplet, time of proximity, and distance it travels close to the wall as a function of angle, for a 200 μm droplet with initial speed 1.2 m/s. These are simulations with TransAT© .
Figure 7
Upper case: droplet with Weber number equal to 35; lower case: droplet with Weber number equal to 0.3
Figure 8
Effect of angle of approach on the disintegration of the droplet. It is obvious that, for small angles of impingement, the droplet disintegrates at a lower Weber number. Good agreement between experiments and our simulated results.
## Discussions
Some tools below are only available to our subscribers or users with an online account.
### Related Content
Customize your page view by dragging and repositioning the boxes below.
Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections
|
{}
|
# All Questions
5,786 questions
Filter by
Sorted by
Tagged with
21 views
### What would I need to be able to calculate the LiDAR confidence score?
According to the definition, the LiDAR confidence score is given by the intensity of light reflection. For example, in one datasheet, they mentioned that white objects within 6m have typical ...
12 views
### Where can I get a driver for the create2?
I just bought a create2 and wanted to connect it with my laptop. Unfortunatly my laptop is not able to recognice the create2. I suppose I need a driver to solve this. Does anyone know where a fitting ...
11 views
### Is there a way to send commands to the Staubli CS9 from remote system via TCP/IP??(like ur_rtde, urx libraries for UR robots)
I am new to ROS development and Staubli robots. Though i have some prior knowledge on UR5e, I am finding it hard to understand the architecture of Staubli and its other programming interfaces (like ...
15 views
### Motion Tracking with Arduino Controlled Camera Slider
I have an Arduino-controlled 3-axis camera slider and I'm thinking of implementing a motion tracker that makes the camera move accordingly on the slider. How feasible is this during a 3-month period? (...
21 views
### Power pack and servo driver for robotic arm?
I have a robotic arm that uses about eight 7.4 volt volt high torque servos. (https://www.servocity.com/2000-series-dual-mode-servo-25-2/) I need to know what Kind of battery system I can use to power ...
24 views
### i want to model the variable distance between two moving vehicles
please i need to model the variable distance between two vehicles, below the code that i'm trying to do , The code ...
8 views
### Having Issues Importing and Using RLGlue locally with Python For Reinforcement Learning
I'm going through an online course on Coursera for Reinforcement Learning that makes use of RLGlue. I want to try to run and adapt the code locally, but am having issues using RLGlue, and not sure why....
43 views
### May I get this robot arm to be controlled via drawing, not programming?
I got an Omron Viper 850 robot arm with a spindle mounted with a cutter. It is controlled via EV+ programming (EV+ is a programming language used in the ACE Adept Omron software to move the robot). ...
12 views
### 3D real-world coordinates detection of an object using Multi camera set up
I have multiple cameras that are stationary and provide a view of a certain area, and I have an object that has some markers on it and I am able to detect it, I want to gather the data from the ...
10 views
### Why reciprocal velocity obstacle generates oscillation free navigation compared to VO
I am tryin to understand this paper about "reciprocal velocity obstacles for real-time multi-agent navigation" and to compare it with the original Velocity Obstacle approach. I can not ...
38 views
### IMU gravity sensing
How are IMUs used to sense the direction of gravity? I have read a number of articles that talk about using IMU for orientation of flying robotics but I do not understand how. Could someone explain ...
22 views
### how to find the kinematic and dynamic model of the mechanism
enter image description here 5 links 4 revolute joints find the kinematic and dynamic model ,link 3 should be horizontal with ground and one end of link 1 and 5 there are sliders enter image ...
24 views
### Simulating a robot in the construction field [closed]
I'm thinking about a research topic that involves robots used in civil engineering specifically dealing with steel structures of buildings. If I choose to simulate the work of the robot in this area, ...
60 views
+100
### FABRIK Inverse Kinematics Convergence Proof For Multiple End-Effector Case
Below, I've linked the FABRIK papers, the first of which is particularly relevant to my question, as it shows the convergence proof for the single end effector case, and this makes sense to me. But I ...
21 views
### time varying gain LQR vs fixed gain LQR, in finite horizon and infinite Horizon
Consider the dynamic system $\dot{x}=Ax+Bu$ and the optimal control formulation of $J = x^TQx + u^TRu$, with optimal linear feedback $u=Kx$ where $K$ is the gain matrix, and I use $k$ to denote time ...
111 views
### Why does ROS2 claim to be “real time”?
ROS2 uses DDS, in the wiki it says that DDS is "The Data Distribution Service (DDS) for real-time systems is an Object Management Group (OMG) machine-to-machine (sometimes called middleware or ...
35 views
### How to design a PID controller for boat?
I have a boat with two trusters and a trajectory planner which is based on the bicycle model. In order to control the boat, the linear velocity of each truster has to be provided. The following ...
28 views
52 views
### Calculating wheel linear velocity from body velocity
A frame {b} is attached to the centre of a robot chassis. The planar configuration is given by $(x,y,\phi)$ where $\phi$ is the angle between the x axis in {b} and the x axis of a fixed reference ...
47 views
### Wheel encoder Tick calculation
Sorry for being a newbie. Can somebody explain me how many ticks a wheel encoder would deliver (based on one complete wheel rotation), if I have a slice with 500 windows? Is the assumption correct, ...
33 views
### ROS2 Stereo View Fails And Stereo Image Proc Doesn't Show Anything
I have set up 2 Monocular Cameras as a stereo camera in ROS2. I successfully published the 2 rectified and calibrated images through the following formats: ...
30 views
### How to reset odom positions of robots while setting initial positions of robots in gazebo simulation through launch file
I'm in the process of creating a coordination system for a multi robot system. For that i currently have created a ROS based simulation in gazebo using Rosbot2.0 (Robot physically available as well). ...
17 views
### Optimization problem of the SPMs design
This article contains section 4. Optimization problem of the SPMs design https://www.sciencedirect.com/science/article/abs/pii/S0921889014001250 Tell me please, are there any special programs for ...
49 views
### Omnidirectional Movement for 3 Wheeled Spherical Omni wheel robot
I was watching James Bruton's video on his spherical omniwheeled robot and he was explaining how to go directly sideways. He explains this from 6:09 to 7:06. I didn't understand how the velocity of ...
75 views
### Jacobian of Euler's rotation equations
I propagate the attitude of a satellite in a free-floating, torque free environment from $t_k$ to $t_{k+1}$ by integrating Euler's equation of motion: \dot{\omega} = [J]^{-1}([\omega]_{\times}[J]\:\...
36 views
### Inverse Kinematics for a 4-DoF Leg
I am beginner in the robotics space and I am trying to apply inverse kinematics to robot leg that has 4 degrees of freedom. I do not know how to think about solving these problems, so any guidance ...
48 views
### Is higher jerk always better for reducing cycle time?
I'm interested in decreasing the cycle time (time to execute a given task) of a robotic arm. As in the title, are there any downsides to maximising the joint jerks of the robot? Naively, increasing ...
52 views
### Multidimensional obstacle avoidance
Artificial potential barriers are known that allow robots to avoid obstacles. They are constructed as follows. https://authors.library.caltech.edu/106548/1/2010.09819.pdf Can you please tell me how ...
14 views
### can't install smach_viewer on ros melodic
I tried installing smach on ROS Melodic with the command: ...
76 views
### Unparable Bluetooth module
I'm doing application in Android Studio that will scan for devices within reach of a phone. What it does exactly is not important. The problem is, that when I scan for devices, I'd get only the ones ...
23 views
### How to control the Dynamixel Motor in PWM mode without having it locked when PWM is zero
I want the motor to be free to move by hand when I set the PWM to zero. Instead, there is a torque that makes the motor still in one position. Is that possible to do?
29 views
### Scale factor of Monocular SLAM (Simultaneous Localization and Mapping )
I am using ORB-SLAM3 with a monocular camera on a drone for Augmented Reality application. I need to know the absolute scale of the map formed by the SLAM. I cannot use a stereo or RBG-D setup. Tthe ...
62 views
### How to use Jacobian Method for path following?
I am currently doing a personal project and get stuck in something as below. In this project, I am going to use the RRT algorithm on the ur5 robot to make it reach the target frame without any ...
15 views
### How to setup ROS and it's GUI tools in local server and connect to local macbook
I recently started learning ROS and I am having Macbook (MacOS Catalina) which is not ideal for running ROS. So, I decided to install ROS in my local home ubuntu 20.04 desktop server and connect it to ...
46 views
### How can I control an Irobot Create using Jetson Nano?
I have an irobot create 4400 model and I'm trying to use a jetson nano to send commands to it. I want to try this example that turns on the play led. I connected the tx and rx and gnd ports from J41 ...
31 views
### Rack and Pinion Gear for CNC
I am trying to build a small 3D printed CNC machine but can't afford lead screws as of now. I need to 3D print a lead screw or use a rack and pinion gear system. I am a little skeptical able the rack ...
15 views
### Ardupilot - Dronekit Setting the Current Location of the Vehicle
hope you are all doing well. I am doing in a project in which I receive GPS data (Longitude, and Latitude) from an Android device via an SQL server. What I am trying to do is to send this Longitude - ...
54 views
### Servo motor vibration problem
I'm working on DIY robotic arm. Robotic arm has 5 servos. The problem is that servo motors are shaking. I found different solutions but none of them works. What happens is that when I connect one PWM ...
41 views
### Relative scale problem
I am doing Monocular Visual Odometry, and I have problem with relative scale. Most of the time its value is between 0.8-1.1, but sometimes it goes crazy and it has value 3,4 and once it had value 25. ...
37 views
### Are there any problems with this design?
https://www.reddit.com/r/robotics/comments/nbqx55/does_this_design_for_a_leg_make_sense_description/?utm_medium=android_app&utm_source=share So essentially I'm trying to make a leg that's able to ...
|
{}
|
# O-direct union
The semi-group obtained from the given family $\{S_\alpha\}$ of semi-groups with zero, pairwise intersecting only at the zero element, by specifying on $\bigcup_\alpha S_\alpha$ the multiplication operation that coincides with the original operation on each semi-group $S_\alpha$ and is such that $S_\alpha S_\beta = 0$ for different $\alpha, \beta$. The $O$-direct union is also called the orthogonal sum. A number of types of semi-groups can be described by decomposing them in an $O$-direct union of known semi-groups (cf., e.g., Maximal ideal; Minimal ideal; Regular semi-group).
|
{}
|
"
BENJAMIN BLUNDELL'S WEBSITE
----------------------------
Setup for the Scarab miniSpartan3 FPGA
20-12-2017
A long time ago, I bought one of the Scarab FPGA development boards which breaks out the Spartan 3 FPGA at a cheap price. Like many nerds, this sat in my box of bits for quite a long time. I've since started a project with my friend Will and although we are looking at a later Xilinx FPGA, I figured it might be worth trying to get this board setup, preferably on Linux. I had some trouble with this so if you've been having trouble getting this older board setup, I might be able to help.
### The miniSpartan3 Scarab
Now Scarab have a custom IDE but this didn't work for me. Indeed, support is very limited for this board now. It's really beenn superceeded by other projects but at the time, it was quite popular and you can still do handy things with it I'd say.
### Vagrant setup
I decided to use a virtual machine, and that Vagrant might be a good way to keep things organised. There are instructions on how to get the software to work on Arch Linux but it seems to be a lot more faff and using virtual machines keeps things neat, so after a lot of messing about and failure, I just decided to use Vagrant.
If you aren't familiar with Vagrant have a look at this link. I decided to go with the Ubuntu Precise Pangolin LTS Vagrant box which seems to work fine. It has all the bits in the right places and it's just a bit easier than messing around with things. Make sure you create a larger hard-disk. The following Vagrant file should work. I went with about 60G of harddisk space. Overkill a little. You might be able to get away with 30G instead. The Xilinx stuff takes up a lot of space.
Vagrant.configure("2") do |config|
config.vm.box = "ubuntu/precise64"
config.vm.provision :shell, path: "bootstrap.sh"
config.vm.provider "virtualbox" do |v|
v.memory = 4096
v.cpus = 2
v.gui = true
v.customize ["modifyhd", "disk id", "--resize", "61440"]
end
config.ssh.forward_x11 = true
end
Now my approach was to do all the building and work inside the VM. This means I need to use Xorg and get away from the headless approach. To that end, one needs install a lot of extra packages. The bootstrap.sh file looks a little like this:
#!/usr/bin/env bash
apt-get update
This is a little overkill - I should probably cut this down but all the packages you need seem to be there.
### Xilinx ISE Webpack
The version I'm using of the Xilinx ISE is 14.7.
The newer program, Vivado is what Xilinx would like you to use now. You can still get this older package from http://www.xilinx.com/support/download/index.html/content/xilinx/en/downloadNav/design-tools.html here.
The Arch Linux page has some good advice on how to install this if you get stuck: https://wiki.archlinux.org/index.php/Xilinx_ISE_WebPACK.
Ultimately, the Xilinx ISE Webpack is freeware, but you will need to download a licence. These are now available from Xilinx for free.
Copy the installation files into your shared vagrant directory and then copy it into your VM. If you are using VirtualBox, you can launch the VirtualBox program itself and see your machine running away. Double click on the machine and you'll get a screen you can interact with - your Xorg window. From here we can run the installer.
tar -xvf Xilinx_ISE_DS_Lin_14.7_1015_1.tar
./xsetup
As we are running in a VM with a head, the visual installer should work fine.
### Launching the IDE
So the first thing to do is make an LED flash right? It is the helloworld of hardware afterall. We need to launch the design tools first though. Assuming you followed the standard install you can do this:
source /opt/Xilinx/14.7/ISE_DS/settings64.sh
ise
### Further steps
From here you have a couple of choices. Start a new project and work it though, or copy the project I've uploaded to git - https://github.com/OniDaito/Scarab3HelloWorld
I'll be writing up this basic LED tutorial in another post, along with a little more about FPGAs in general. For now though, there is a good tutorial you can find at http://users.wpi.edu/~rjduck/Spartan3_Tutorial.pdf. It is a little old but gets across the basics.
|
{}
|
# Multi-party key agreement
I have done a google search for "multi-party key agreement", and there doesn't seem to be anything more recent than about 2005.
Are there any practical multi-party key agreement protocols known?
To be more precise, I want a protocol which:
• Allows multiple individuals to agree a single shared secret
• An adversary cannot tell what the shared secret is by listening to the communications.
• It should be authenticated so an active adversary cannot persuade a participant to communicate with a secret the adversary knows.
Note: I am aware of Multi-party Key Exchange protocol from lattice but a) that doesn't have any answers; b) I am not only interested in lattice cryptography (in fact, I would prefer something based on ECC or factoring).
Edit: Background I want a system for encrypting a conference call. If each caller sends their audio to every other participant with separately agreed keys, then the total amount of work required is $O(n^2)$ (and the work done by each participant is $O(n)$). If everyone agrees a single shared secret, then we might be able to reduce the amount of work required.
• The first part of your question has the same problem as the other question: it is not a specific question and therefore largely off topic. I think generally cryptographers don't care about the date of protocols nor if they are famous or not. Additionally, asking for lists is explicitly off topic. The second part of your question is much better. You fail however to mention why lattice based crypto is not acceptable. Those kind of unexplained exclusions tend to put people off (such as the famous: "but I cannot use any libraries" on StackOverflow). – Maarten Bodewes Aug 1 '18 at 9:55
• I don't need a list - I just need a good one. What I meant about the dates was there were a few papers proposing and knocking down proposals, and then silence. There are no blog posts "this is how you do multi-party key exchange". – Martin Bonner supports Monica Aug 1 '18 at 20:30
• My preference for factoring/ECC is just that those are much better understood systems. If no-one has found a problem with an ECC-based protocol, it probably means it is secure. If no-one has found a problem with a lattice-based protocol, it may just mean that they haven't looked hard enough. – Martin Bonner supports Monica Aug 1 '18 at 20:32
• @MaartenBodewes OTOH, if there is a good lattice-based protocol, I'll take that. – Martin Bonner supports Monica Aug 1 '18 at 20:33
Historically, both the difficulty and the risks involved in securely establishing shared keys in large networks has led to the invention of public-key cryptography. So you might first want to consider using digital signatures/asymmetric encryption instead of sharing the same secret between parties.
If you need all (or some) of the parties to collectively sign or encrypt a message, consider using threshold signature schemes with a Distributed Key Generation protocol. That will produce a key pair that is distributed among $N$ participants such that at least $k$ of them need to collaborate for performing a key operation. For discrete-log cryptosystems there's a paper by Gennaro et al that describes such a setup.
Edit: If you only need to establish a common secret (instead of a key pair) between all the parties, a simpler solution would be to use a generalized Diffie-Hellman key exchange instead. This works for honest participants with insecure communication channels. If the participants can be malicious, a more robust solution is described by Tseng, 2005.
• Thanks. That's a couple of useful links. I think we will stick to pairwise key-agreement. – Martin Bonner supports Monica Aug 8 '18 at 12:51
What ia the problem with doing O(N^2) communication for key exchange. If after that everyone has the same key. The actual data can be sent only once.
A simple option would be: Everybody publishes a public key. Everybody picks a random key and encrypts it with everybody elses public key and shares.
Final key is XOR of all sub keys.
only the setup phase uses multiple communication.
Alternatively appoint a dealer which will coordinate a key among all parties.
• This assumes secure communication channels and honest participants (i.e. issues with man in the middle attacks or participants learning other participants' keys). – Lucian Boca Aug 8 '18 at 16:03
I would recommend looking on the following protocols:
• Burmester Desmedt
• MD+P
• Asynchronous Ratcheting Tree (bleeding edge)
All of them are called Group Key agreements and most of them assume that each participant is in a circle or are applied on a tree. The security of them is based upon Computational Diffie Hellman but in some cases can be used with Elliptic Curve Diffie Hellman.
|
{}
|
# MySQL class to add user/database
I'm creating tool to add new virtualhost on UNIX-box. One of tasks is to add a new user and database to MariaDB (aka MySQL) server. In fact - this my first 'real' attempt to use OOP.
Here is class, which I created for it:
class mysqlUserDb:
warnings.filterwarnings('error')
def __init__(self):
self.root = 'root'
self.host = 'localhost'
self.rootpw = 'p@ss'
try:
print '\nChecking MySQL connection...'
self.db = MySQLdb.connect(self.host, self.root, self.rootpw)
self.cursor = self.db.cursor()
self.cursor.execute('select version()')
print 'Connection OK, proceeding.'
except MySQLdb.Error as error:
print 'Error: %s ' %error + '\nStop.\n'
sys.exit()
def createdb(self, db):
print '\nCreating database...'
try:
self.cursor.execute('create database if not exists ' + db)
self.cursor.execute('show databases like ' + '\'' + db + '\'')
dbs = self.cursor.fetchone()
print 'Database created: %s' %dbs
except Warning as warn:
print 'Warning: %s ' %warn + '\nStop.\n'
sys.exit()
def grants(self, user, userpass, db):
print '\nGrant privilegies... '
try:
self.cursor.execute('grant all on ' + db + '.*' + 'to ' + '\'' + user + '\'' + "@'localhost'" + 'identified by ' + '\'' + userpass + '\'')
self.cursor.execute('select user, db from mysql.db where db=' + '\'' + db + '\'')
grs = self.cursor.fetchall()
print 'Access granted: %r' %grs
except Warning as warn:
print 'Warning: %s ' %warn + '\nStop.\n'
sys.exit()
except MySQLdb.Error as error:
print 'Error: %s ' %error + '\nStop.\n'
sys.exit()
def __del__(self):
print '\nFinishing operations...'
self.cursor.close()
self.db.close()
print 'Done.\n'
Next, in tool it call like:
import createvhostFunctsClass as fun
mysql = fun.mysqlUserDb()
mysql.createdb('db_2')
mysql.grants('user', 'pass', 'db_2')
del mysql
(it's just example, not included yet in tool).
And its works like:
\$ ./myclass.py
Checking MySQL cconnection...
Connection OK, proceeding.
Creating database...
Database created: db_2
Grant privilegies...
Access granted: ('user', 'db_2')
Finishing operations...
Done.
I'm pretty sure, here is lot of stuff, which I missed or did incorrectly (or not the "Python way").
Also, I'm not sure - which way better:
1. create methods for each action (add database, add user) and just call this methods from script (currently done)
2. create one method, which will get needed action ('create database lalala') as argument and call this method several times in script
-
I'm pretty sure, here is lot of stuff, which I missed or did incorrectly (or not the "Python way").
The convention is to use CamelCase for class names. So MysqlUserDb would be better for your class. See PEP8 for more details.
Don't mix string concatenation and formatting expressions like this:
print 'Error: %s ' % error + '\nStop.\n'
Stick to formatting expressions without concatenation:
print 'Error: %s\nStop.\n' % error
You do this a lot. Apply this technique everywhere.
Similarly, you're not using formatting expressions enough. For example in SQL queries like this one:
self.cursor.execute('show databases like ' + '\'' + db + '\'')
With all those quotations and escaping, it's easy to overlook a mistake. It becomes simpler if you use formatting expression, and if you change the outermost quotes to double quotes:
self.cursor.execute("show databases like '%s'" % db)
Your code appears to be for Python 2.x. To be a bit more ready for a possible future migration to Python 3.x, I recommend to start writing your print ... statements as print(...), for example:
print('Connection OK, proceeding.')
Also, I'm not sure - which way better:
1. create methods for each action (add database, add user) and just call this methods from script (currently done)
2. create one method, which will get needed action ('create database lalala') as argument and call this method several times in script
Your current approach is good: use a separate method for each separate action.
### Unused fields
In __init__ you are setting these fields:
self.root = 'root'
self.host = 'localhost'
self.rootpw = 'p@ss'
But then you're not using them anywhere else within the class. So it seems these should not be fields, but perhaps global constants declared at the top of the class. I would also name them a bit differently:
DBROOTUSER = 'root'
DBROOTPASS = 'p@ss'
DBHOST = 'localhost'
### Security
Are you sure you want to store the db's root account password in this script? Make sure the file has restricted permissions (do a chmod 0600 on it).
Needless to say, but better make sure the method parameters are cleaned before reaching your class to avoid SQL injection attacks. Or implement validation inside your methods.
### Naming
def createdb(self, db):
# ...
def grants(self, user, userpass, db):
# ...
I recommend this:
def createdb(self, dbname):
# ...
def grants(self, dbuser, dbpass, dbname):
# ...
This may be a matter of taste though.
-
Thanks a lot. Can't vote up, unfortunately. – setevoy Sep 2 '14 at 19:36
could you pelase explain - what you mean here: "Needless to say, but better make sure the method parameters are cleaned before reaching your class to avoid SQL injection attacks. Or implement validation inside your methods."? P.S. Tool designed for my use only on my only server, that's why I set root pass directly in script (and yes - I'ts owned by OS root too with 0700). Otherway - I'd prefer to set getpass.getpass() and ask pass everytime. – setevoy Sep 3 '14 at 17:19
As long as it's like that, it's fine. Keep it carefully secured. – janos Sep 3 '14 at 20:38
The error handling seems to be problematic.
By convention, a program should exit with a non-zero status to indicate that an error has occurred. By calling sys.exit(), you are indicating that the command completed successfully. Whatever process is calling your script will have a hard time determining whether the database operations succeeded or failed.
Also, warnings are attention-deserving problems that are non-fatal. Your script treats warnings as errors (which are fatal). Either change the vocabulary (tell the user that an error has occurred, not a warning, and exit with a non-zero status) or change the behaviour (print a warning to the user, but continue processing).
-
Thanks, @200. About sys.exit() - yes, will fix. About warnings - MySQL generates 'warning', if database exist and can't be created. Thus - I used 'warning' exceptions as 'erros' to rise error. Also - program can't be continued, if user add database, which currently present. IMHO. – setevoy Sep 2 '14 at 17:27
It's fine to treat warnings from MySQL as errors. Just make sure that what your script reports matches its behaviour. – 200_success Sep 2 '14 at 17:29
I assume in Python, exceptions can propagate up the call stack...right? Would it be better to just let them do so (or throw another exception with a more informative message), and have the caller decide what to do about the problem? (In a decent-sized app, for example, it might want to log the failure rather than just printing to stdout. I'd think it'd have trouble doing so if you just kill the app.) – cHao Sep 2 '14 at 21:40
|
{}
|
# Nuclear Science and Techniques
《核技术》(英文版) ISSN 1001-8042 CN 31-1559/TL 2019 Impact factor 1.556
Nuclear Science and Techniques ›› 2018, Vol. 29 ›› Issue (3): 43
• LOW ENERGY ACCELERATOR, RAY AND APPLICATIONS •
### Improvements to conventional X-ray tube-based cone-beam computed tomography system
Cui Zhang, Xiao-Dong Pan, Hong-Jie Shang, Yan-Hong Luo, Gong-Ping Li
1. School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China
• Contact: Xiao-Dong Pan E-mail:pxd@lzu.edu.cn
• Supported by:
This work was supported by the Fundamental Research Funds for the Central Universities (Nos. lzujbky-2016-208 and lzujbky-2016-32).
PDF ShareIt Export Citation
Cui Zhang, Xiao-Dong Pan, Hong-Jie Shang, Yan-Hong Luo, Gong-Ping Li. Improvements to conventional X-ray tube-based cone-beam computed tomography system.Nuclear Science and Techniques, 2018, 29(3): 43
Citations
Altmetrics
Abstract:
Conventional X-ray tube-based cone-beam computed tomography (CX-CBCT) systems have great potential in industrial applications. Such systems can rapidly obtain a three-dimensional (3D) image of an object. Conventional X-ray tubes fulfill the requirements for industrial applications, because of their high tube voltage and power. Continuous improvements have been made to CX-CBCT systems, such as imaging time shortening, acquisition strategy optimization, and imaging software development, etc. In this study, a CX-CBCT system is developed. Additionally, some improvements to the CXCBCT system are proposed based on the hardware conditions of the X-ray tube and detector. A near-detector (ND) geometry condition is employed to obtain a sharper image and larger detection area. An improved acquisition strategy is proposed to simplify operations and reduce total imaging time. In the ND geometry condition, a simplified method called FBP slice stacking (SS-FBP) is proposed, which can be applied to 3D image reconstruction. SS-FBP is timesaving relative to traditional methods. Furthermore, imaging software for the CX-CBCT system is developed in the MATLAB environment. Several imaging experiments were performed. The results suggest that the CX-CBCT system works properly, and that the above improvements are feasible and practical.
|
{}
|
# OpenGraph DrawingFramework
v. 2022.02 (Dogwood)
ogdf::PQNode< T, X, Y > Class Template Referenceabstract
The class template PQBasicKey is an abstract base class. More...
#include <ogdf/basic/pqtree/PQBasicKey.h>
Inheritance diagram for ogdf::PQNode< T, X, Y >:
## Public Member Functions
PQNode (int count)
The (second) constructor is called, if no information is available or neccessary. More...
PQNode (int count, PQNodeKey< T, X, Y > *infoPtr)
The (first) constructor combines the node with its information and will automatically set the PQBasicKey::m_nodePointer (see basicKey) of the element of type PQNodeKey. More...
virtual ~PQNode ()
The destructor does not delete any accompanying information class as PQLeafKey, PQNodeKey and PQInternalKey. More...
bool changeEndmost (PQNode< T, X, Y > *oldEnd, PQNode< T, X, Y > *newEnd)
The function changeEndmost() replaces the old endmost child oldEnd of the node by a new child newEnd. More...
bool changeSiblings (PQNode< T, X, Y > *oldSib, PQNode< T, X, Y > *newSib)
The function changeSiblings() replaces the old sibling oldSib of the node by a new sibling newSib. More...
int childCount () const
Returns the number of children of a node. More...
void childCount (int count)
Sets the number of children of a node. More...
bool endmostChild () const
The function endmostChild() checks if a node is endmost child of a Q-node. More...
PQNode< T, X, Y > * getEndmost (PQNode< T, X, Y > *other) const
Returns one of the endmost children of node, if node is a Q-node. More...
PQNode< T, X, Y > * getEndmost (SibDirection side) const
Returns one of the endmost children of node, if node is a Q-node. More...
virtual PQInternalKey< T, X, Y > * getInternal () const =0
getInternal() returns a pointer to the PQInternalKey information of a node, in case that the node is supposed to have PQInternalKey information, such as elements of the derived class template PQInternalNode. More...
virtual PQLeafKey< T, X, Y > * getKey () const =0
getKey() returns a pointer to the PQLeafKeyof a node, in case that the node is supposed to have a key, such as elements of the derived class template PQLeaf. More...
PQNode< T, X, Y > * getNextSib (PQNode< T, X, Y > *other) const
The function getNextSib() returns one of the siblings of the node. More...
PQNodeKey< T, X, Y > * getNodeInfo () const
Returns the identification number of a node. More...
PQNode< T, X, Y > * getSib (SibDirection side) const
The function getSib() returns one of the siblings of the node. More...
int identificationNumber () const
Returns the identification number of a node. More...
virtual PQNodeMark mark () const =0
mark() returns the variable PQLeaf::m_mark in the derived class PQLeaf and PQInternalNode. More...
virtual void mark (PQNodeMark)=0
mark() sets the variable PQLeaf::m_mark in the derived class PQLeaf and PQInternalNode. More...
PQNode< T, X, Y > * parent () const
The function parent() returns a pointer to the parent of a node. More...
PQNode< T, X, Y > * parent (PQNode< T, X, Y > *newParent)
Sets the parent pointer of a node. More...
PQNodeType parentType () const
Returns the type of the parent of a node. More...
void parentType (PQNodeType newParentType)
Sets the type of the parent of a node. More...
int pertChildCount () const
Returs the number of pertinent children of a node. More...
void pertChildCount (int count)
Sets the number of pertinent children of a node. More...
SibDirection putSibling (PQNode< T, X, Y > *newSib)
The default function putSibling() stores a new sibling at a free sibling pointer of the node. More...
SibDirection putSibling (PQNode< T, X, Y > *newSib, SibDirection preference)
The function putSibling() with preference stores a new sibling at a free sibling pointer of the node. More...
PQNode< T, X, Y > * referenceChild () const
Returns a pointer to the reference child if node is a P-node. More...
PQNode< T, X, Y > * referenceParent () const
Returns the pointer to the parent if node is a reference child. More...
virtual bool setInternal (PQInternalKey< T, X, Y > *pointerToInternal)=0
virtual bool setKey (PQLeafKey< T, X, Y > *pointerToKey)=0
Sets a specified pointer variable in a derived class to the specified adress of pointerToKey that is of type PQLeafKey. More...
bool setNodeInfo (PQNodeKey< T, X, Y > *pointerToInfo)
Sets the pointer m_pointerToInfo to the specified adress of pointerToInfo. More...
virtual PQNodeStatus status () const =0
Returns the variable PQLeaf::m_status in the derived class PQLeaf and PQInternalNode. More...
virtual void status (PQNodeStatus)=0
Sets the variable PQLeaf::m_status in the derived class PQLeaf and PQInternalNode. More...
virtual PQNodeType type () const =0
Returns the variable PQInternalNode::m_type in the derived class PQLeaf and PQInternalNode. More...
virtual void type (PQNodeType)=0
Sets the variable PQInternalNode::m_type in the derived class PQLeaf and PQInternalNode. More...
## Protected Attributes
List< PQNode< T, X, Y > * > * fullChildren
Stores all full children of a node during a reduction. More...
int m_childCount
int m_debugTreeNumber
Needed for debuging purposes. More...
PQNode< T, X, Y > * m_firstFull
Stores a pointer to the first full child of a Q-node. More...
int m_identificationNumber
Each node that has been introduced once into the tree gets a unique number. More...
PQNode< T, X, Y > * m_leftEndmost
PQNode< T, X, Y > * m_parent
Is a pointer to the parent. More...
PQNodeType m_parentType
Stores the type of the parent which can be either a P- or Q-node. More...
int m_pertChildCount
Stores the number of pertinent children of the node. More...
int m_pertLeafCount
Stores the number of pertinent leaves in the frontier of the node. More...
PQNodeKey< T, X, Y > * m_pointerToInfo
Stores a pointer to the corresponding information of the node. More...
PQNode< T, X, Y > * m_referenceChild
Stores a pointer to one child, the reference child of the doubly linked cirkular list of children of a P-node. More...
PQNode< T, X, Y > * m_referenceParent
Is a pointer to the parent, in case that the parent is a P-node and the node itself is its reference child. More...
PQNode< T, X, Y > * m_rightEndmost
Stores the right endmost child of a Q-node. More...
PQNode< T, X, Y > * m_sibLeft
Stores a pointer ot the left sibling of PQNode. More...
PQNode< T, X, Y > * m_sibRight
Stores a pointer ot the right sibling of PQNode. More...
List< PQNode< T, X, Y > * > * partialChildren
Stores all partial children of a node during a reduction. More...
## Friends
class PQTree< T, X, Y >
All members and member function of PQNode are needed by the class template PQTree. More...
## Detailed Description
### template<class T, class X, class Y> class ogdf::PQNode< T, X, Y >
The class template PQBasicKey is an abstract base class.
It enables the user of the PQ-tree to store different informations at every node of the tree.
The implementation of the PQ-tree provides the storage of three different types of information.
• General information that is stored at P- and Q-nodes and leaves likewise (see also PQNodeKey).
• Information that is only supported for internal nodes (see also internalKey).
• The keys of the leaves (see also leafKey). The keys are constructed to carry the elements of a user defined set of any type, where permissible permutations have to be found. In order to use the datastructure PQ-tree as class template PQTree, the user has to specify a set of arbitrary elements that form the leaves of the PQ-tree. The keys function as storage class of the elements of the set.
All three storage classes are derived class templates of PQBasicKey. The class PQBasicKey has a pointer PQBasicKey::m_nodePointer to a PQNode, beeing either a leaf or an internal PQInternalNode. The base class itself does not provide any storage of the informations, it is hidden in the derived classes. PQBasicKey only declares a few pure virtual functions that are overloaded in the derived classes and which give access to the information stored in the derived classes.
The information stored in an element of a derived class of PQBasicKey is assigned to a unique node in the PQ-tree. This unique node can be identified with the PQBasicKey::m_nodePointer. The maintenance of this pointer is left to the user in the derived concrete classes PQNodeKey and internalKey. By keeping the responsibillity for these classes by the client, nodes with certain informations can be accessed by the client in constant time. This makes the adaption of algorithms fast and easy.
Only the derived concrete class template leafKey is treated in a different way by the class template PQTree. When initializing the PQTree with a set of elements of type leafKey, the class template PQTree sets the pointer PQBasicKey::m_nodePointer of every element. This is due to the fact that a PQ-tree is always defined over some set, whose elements are stored in the leaves. Hence the class PQtree expects such a set and supports its maintainance. Storing extra information at every node may be omitted and makes the PQtree easy applicable.
We now give a short overview of the class template declaration PQBasicKey. The class template PQBasicKey is used as a base class template that specifies three different types of information. The type of information used at a node is depending on the type of the node. These informations have to be specified by the user.
The formal type parameters of the class template PQBasicKey are categorized as follows.
• T is a formal type parameter for the information stored in leafKey.
• X is a formal type parameter for the information stored in PQNodeKey.
• Y is a formal type parameter for the information stored in internalKey.
The class template PQBasicKey contains a few pure virtual member functions that are overloaded in the derived class leafKey, PQNodeKey and internalKey. These functions enable the client to access the information stored at a node.
Definition at line 108 of file PQBasicKey.h.
## ◆ PQNode() [1/2]
template<class T , class X , class Y >
ogdf::PQNode< T, X, Y >::PQNode ( int count, PQNodeKey< T, X, Y > * infoPtr )
The (first) constructor combines the node with its information and will automatically set the PQBasicKey::m_nodePointer (see basicKey) of the element of type PQNodeKey.
Definition at line 571 of file PQNode.h.
## ◆ PQNode() [2/2]
template<class T , class X , class Y >
ogdf::PQNode< T, X, Y >::PQNode ( int count )
explicit
The (second) constructor is called, if no information is available or neccessary.
Definition at line 602 of file PQNode.h.
## ◆ ~PQNode()
template<class T , class X , class Y >
virtual ogdf::PQNode< T, X, Y >::~PQNode ( )
inlinevirtual
The destructor does not delete any accompanying information class as PQLeafKey, PQNodeKey and PQInternalKey.
This has been avoided, since applications may need the existence of these information classes after the corresponding node has been deleted. If the deletion of an accompanying information class should be performed with the deletion of a node, either derive a new class with an appropriate destructor, or make use of the function CleanNode() of the class template PQTree.
Definition at line 85 of file PQNode.h.
## ◆ changeEndmost()
template<class T , class X , class Y >
bool ogdf::PQNode< T, X, Y >::changeEndmost ( PQNode< T, X, Y > * oldEnd, PQNode< T, X, Y > * newEnd )
The function changeEndmost() replaces the old endmost child oldEnd of the node by a new child newEnd.
If the node is a Q-node, then it must have two valid pointers to its endmost children. If one of the endmost children is oldEnd, it is replaced by newEnd. The function changeEndmost() returns 1 if it succeeded in replacing oldEnd by newEnd. Otherwise the function returns 0, leaving with an error message.
Definition at line 521 of file PQNode.h.
## ◆ changeSiblings()
template<class T , class X , class Y >
bool ogdf::PQNode< T, X, Y >::changeSiblings ( PQNode< T, X, Y > * oldSib, PQNode< T, X, Y > * newSib )
The function changeSiblings() replaces the old sibling oldSib of the node by a new sibling newSib.
If the node has oldSib as sibling, then it changes the sibling pointer that references to oldSib and places newSib at its position. The function changeSiblings() returns 1 if it succeeded in replacing oldSib by newSib. Otherwise the function returns 0, leaving with an error message.
Definition at line 549 of file PQNode.h.
## ◆ childCount() [1/2]
template<class T , class X , class Y >
int ogdf::PQNode< T, X, Y >::childCount ( ) const
inline
Returns the number of children of a node.
Definition at line 197 of file PQNode.h.
## ◆ childCount() [2/2]
template<class T , class X , class Y >
void ogdf::PQNode< T, X, Y >::childCount ( int count )
inline
Sets the number of children of a node.
Definition at line 200 of file PQNode.h.
## ◆ endmostChild()
template<class T , class X , class Y >
bool ogdf::PQNode< T, X, Y >::endmostChild ( ) const
inline
The function endmostChild() checks if a node is endmost child of a Q-node.
This is 1 if one of the sibling pointers m_sibLeft or m_sibRight is 0. If the node is endmost child of a Q-node, then it has a valid parent pointer.
Definition at line 121 of file PQNode.h.
## ◆ getEndmost() [1/2]
template<class T , class X , class Y >
PQNode* ogdf::PQNode< T, X, Y >::getEndmost ( PQNode< T, X, Y > * other ) const
inline
Returns one of the endmost children of node, if node is a Q-node.
The function getEndmost() accepts as input a pointer to a PQNode stored in other. The returned endmost child is unequal to the one specified in other. In case that an arbitrary endmost child should be looked up, set other = 0. This makes the function getEndmost() return an arbitrary endmost child (it returns the left endmost child).
Definition at line 134 of file PQNode.h.
## ◆ getEndmost() [2/2]
template<class T , class X , class Y >
PQNode* ogdf::PQNode< T, X, Y >::getEndmost ( SibDirection side ) const
inline
Returns one of the endmost children of node, if node is a Q-node.
The function accepts an integer denoting a direction causing the function to return either the left or the endmost child.
Definition at line 148 of file PQNode.h.
## ◆ getInternal()
template<class T , class X , class Y >
virtual PQInternalKey* ogdf::PQNode< T, X, Y >::getInternal ( ) const
pure virtual
getInternal() returns a pointer to the PQInternalKey information of a node, in case that the node is supposed to have PQInternalKey information, such as elements of the derived class template PQInternalNode.
The internal information is of type PQInternalKey.
Implemented in ogdf::PQInternalNode< T, X, Y >, and ogdf::PQLeaf< T, X, Y >.
## ◆ getKey()
template<class T , class X , class Y >
virtual PQLeafKey* ogdf::PQNode< T, X, Y >::getKey ( ) const
pure virtual
getKey() returns a pointer to the PQLeafKeyof a node, in case that the node is supposed to have a key, such as elements of the derived class template PQLeaf.
The key contains information and is of type PQLeafKey.
Implemented in ogdf::PQInternalNode< T, X, Y >, and ogdf::PQLeaf< T, X, Y >.
## ◆ getNextSib()
template<class T , class X , class Y >
PQNode* ogdf::PQNode< T, X, Y >::getNextSib ( PQNode< T, X, Y > * other ) const
inline
The function getNextSib() returns one of the siblings of the node.
The function getNextSib() accepts as input a pointer to a PQNode stored in other. The returned sibling is unequal to the one specified in other. In case that no sibling has been looked up before, set other = 0. This makes the function getNextSib() return an arbitrary sibling (it returns the left sibling).
Definition at line 183 of file PQNode.h.
## ◆ getNodeInfo()
template<class T , class X , class Y >
PQNodeKey* ogdf::PQNode< T, X, Y >::getNodeInfo ( ) const
inline
Returns the identification number of a node.
Definition at line 158 of file PQNode.h.
## ◆ getSib()
template<class T , class X , class Y >
PQNode* ogdf::PQNode< T, X, Y >::getSib ( SibDirection side ) const
inline
The function getSib() returns one of the siblings of the node.
It accepts an integer denoting a dircetion causing the function to return either the left or the right sibling.
Definition at line 165 of file PQNode.h.
## ◆ identificationNumber()
template<class T , class X , class Y >
int ogdf::PQNode< T, X, Y >::identificationNumber ( ) const
inline
Returns the identification number of a node.
Definition at line 194 of file PQNode.h.
## ◆ mark() [1/2]
template<class T , class X , class Y >
virtual PQNodeMark ogdf::PQNode< T, X, Y >::mark ( ) const
pure virtual
mark() returns the variable PQLeaf::m_mark in the derived class PQLeaf and PQInternalNode.
In a derived class this function has to return the designation used in the first pass of Booth and Luekers algorithm called Bubble(). A node then is either marked BLOCKED, UNBLOCKED or QUEUED (see PQNode).
Implemented in ogdf::PQInternalNode< T, X, Y >, and ogdf::PQLeaf< T, X, Y >.
## ◆ mark() [2/2]
template<class T , class X , class Y >
virtual void ogdf::PQNode< T, X, Y >::mark ( PQNodeMark )
pure virtual
mark() sets the variable PQLeaf::m_mark in the derived class PQLeaf and PQInternalNode.
Implemented in ogdf::booth_lueker::EmbedIndicator.
## ◆ parent() [1/2]
template<class T , class X , class Y >
PQNode* ogdf::PQNode< T, X, Y >::parent ( ) const
inline
The function parent() returns a pointer to the parent of a node.
Warning
After reducing the PQ-tree, some nodes may not have valid parent pointers anymore. This is no fault, the datastructur was designed this way. See also Booth and Lueker.
Definition at line 209 of file PQNode.h.
## ◆ parent() [2/2]
template<class T , class X , class Y >
PQNode* ogdf::PQNode< T, X, Y >::parent ( PQNode< T, X, Y > * newParent )
inline
Sets the parent pointer of a node.
This function is needed in more ellaborated algorithms implemented as derivation of the class template PQTree. Here, the parent pointer probably is always needed and therefore has to be set within special functions, used in a pre-run before applying the bubble Phase of the PQTree.
Definition at line 218 of file PQNode.h.
## ◆ parentType() [1/2]
template<class T , class X , class Y >
PQNodeType ogdf::PQNode< T, X, Y >::parentType ( ) const
inline
Returns the type of the parent of a node.
Definition at line 224 of file PQNode.h.
## ◆ parentType() [2/2]
template<class T , class X , class Y >
void ogdf::PQNode< T, X, Y >::parentType ( PQNodeType newParentType )
inline
Sets the type of the parent of a node.
This does not change the type of the parent!
Definition at line 230 of file PQNode.h.
## ◆ pertChildCount() [1/2]
template<class T , class X , class Y >
int ogdf::PQNode< T, X, Y >::pertChildCount ( ) const
inline
Returs the number of pertinent children of a node.
Definition at line 233 of file PQNode.h.
## ◆ pertChildCount() [2/2]
template<class T , class X , class Y >
void ogdf::PQNode< T, X, Y >::pertChildCount ( int count )
inline
Sets the number of pertinent children of a node.
Definition at line 236 of file PQNode.h.
## ◆ putSibling() [1/2]
template<class T , class X , class Y >
SibDirection ogdf::PQNode< T, X, Y >::putSibling ( PQNode< T, X, Y > * newSib )
inline
The default function putSibling() stores a new sibling at a free sibling pointer of the node.
This is only possible, if the node has at most one sibling. The function then detects a non used sibling pointer and places newSib onto it. putSibling() returns 0 if there have been two siblings detected, occupying the two possible pointers. In this case the new sibling newSib cannot be stored. If there was at a maximum one sibling stored, the function will place newSib on the free pointer and return either LEFT or RIGHT, depending wich pointer has been used.
This function will always scan the pointer to the left brother first.
Definition at line 251 of file PQNode.h.
## ◆ putSibling() [2/2]
template<class T , class X , class Y >
SibDirection ogdf::PQNode< T, X, Y >::putSibling ( PQNode< T, X, Y > * newSib, SibDirection preference )
inline
The function putSibling() with preference stores a new sibling at a free sibling pointer of the node.
This is only possible, if the node has at most one sibling. The function then detects a non used sibling pointer and places newSib onto it. putSibling() returns 0 if there have been two siblings detected, occupying the two possible pointers. In this case the new sibling newSib could not be stored. If there was at a maximum one sibling stored, the function will place newSib on the free pointer and return either LEFT or RIGHT, depending wich pointer has been used.
This function scans the brother first, which has been specified in the preference. If the preference has value LEFT, it scans the pointer to the left brother first. If the value is RIGHT, it scans the pointer to the right brother first.
Definition at line 279 of file PQNode.h.
## ◆ referenceChild()
template<class T , class X , class Y >
PQNode* ogdf::PQNode< T, X, Y >::referenceChild ( ) const
inline
Returns a pointer to the reference child if node is a P-node.
Definition at line 298 of file PQNode.h.
## ◆ referenceParent()
template<class T , class X , class Y >
PQNode* ogdf::PQNode< T, X, Y >::referenceParent ( ) const
inline
Returns the pointer to the parent if node is a reference child.
Definition at line 301 of file PQNode.h.
## ◆ setInternal()
template<class T , class X , class Y >
virtual bool ogdf::PQNode< T, X, Y >::setInternal ( PQInternalKey< T, X, Y > * pointerToInternal )
pure virtual
## ◆ setKey()
template<class T , class X , class Y >
virtual bool ogdf::PQNode< T, X, Y >::setKey ( PQLeafKey< T, X, Y > * pointerToKey )
pure virtual
Sets a specified pointer variable in a derived class to the specified adress of pointerToKey that is of type PQLeafKey.
If a derived class, such as PQInternalNode, is not supposed to store informations of type PQLeafKey, setKey() ignores the informations as long as pointerToKey = 0. The return value then is 1. In case that pointerToKey != 0, the return value is 0.
If a derived class, such as PQLeaf is supposed to store informations of type PQLeafKey, pointerToKey has to be instantiated by the client. The function setKey() does not instantiate the corresponding variable in the derived class. The return value is always 1 unless pointerKey was equal to 0.
Implemented in ogdf::PQInternalNode< T, X, Y >, and ogdf::PQLeaf< T, X, Y >.
## ◆ setNodeInfo()
template<class T , class X , class Y >
bool ogdf::PQNode< T, X, Y >::setNodeInfo ( PQNodeKey< T, X, Y > * pointerToInfo )
inline
Sets the pointer m_pointerToInfo to the specified adress of pointerToInfo.
Definition at line 304 of file PQNode.h.
## ◆ status() [1/2]
template<class T , class X , class Y >
virtual PQNodeStatus ogdf::PQNode< T, X, Y >::status ( ) const
pure virtual
Returns the variable PQLeaf::m_status in the derived class PQLeaf and PQInternalNode.
Its objective is to manage status of a node in the PQ-tree. A status is any kind of information of the current situation in the frontier of a node (the frontier of a node are all descendant leaves of the node). A status is anything such as EMPTY, FULL or PARTIAL (see PQNode). Since there might be more than those three possibilities, (e.g. in computing planar subgraphs this function probably has to be overloaded by the client.
Implemented in ogdf::PQInternalNode< T, X, Y >, and ogdf::PQLeaf< T, X, Y >.
## ◆ status() [2/2]
template<class T , class X , class Y >
virtual void ogdf::PQNode< T, X, Y >::status ( PQNodeStatus )
pure virtual
Sets the variable PQLeaf::m_status in the derived class PQLeaf and PQInternalNode.
Implemented in ogdf::booth_lueker::EmbedIndicator.
## ◆ type() [1/2]
template<class T , class X , class Y >
virtual PQNodeType ogdf::PQNode< T, X, Y >::type ( ) const
pure virtual
Returns the variable PQInternalNode::m_type in the derived class PQLeaf and PQInternalNode.
Its objective it to manage the type of a node. node the current node is. The type of a node in the class template PQTree is either PNode, QNode or leaf (see PQNode). There may be of course more types such as sequence indicators.
Observe that the derived class template PQLeaf does not have a variable PQInternalNode::m_type, since it obviously is of type leaf.
Implemented in ogdf::PQInternalNode< T, X, Y >, and ogdf::PQLeaf< T, X, Y >.
## ◆ type() [2/2]
template<class T , class X , class Y >
virtual void ogdf::PQNode< T, X, Y >::type ( PQNodeType )
pure virtual
Sets the variable PQInternalNode::m_type in the derived class PQLeaf and PQInternalNode.
Implemented in ogdf::booth_lueker::EmbedIndicator.
## ◆ PQTree< T, X, Y >
template<class T , class X , class Y >
friend class PQTree< T, X, Y >
friend
All members and member function of PQNode are needed by the class template PQTree.
Therefore the class PQTree was made friendof PQNode, since this prevents the use of a large amount of extra public functions.
Definition at line 58 of file PQNode.h.
## ◆ fullChildren
template<class T , class X , class Y >
List*>* ogdf::PQNode< T, X, Y >::fullChildren
protected
Stores all full children of a node during a reduction.
Definition at line 502 of file PQNode.h.
## ◆ m_childCount
template<class T , class X , class Y >
int ogdf::PQNode< T, X, Y >::m_childCount
protected
Definition at line 416 of file PQNode.h.
## ◆ m_debugTreeNumber
template<class T , class X , class Y >
int ogdf::PQNode< T, X, Y >::m_debugTreeNumber
protected
Needed for debuging purposes.
The PQ-trees can be visualized with the help of the Tree Interface and the m_debugTreeNumber is needed to print out the tree in the correct file format.
Definition at line 424 of file PQNode.h.
## ◆ m_firstFull
template<class T , class X , class Y >
PQNode* ogdf::PQNode< T, X, Y >::m_firstFull
protected
Stores a pointer to the first full child of a Q-node.
Definition at line 449 of file PQNode.h.
## ◆ m_identificationNumber
template<class T , class X , class Y >
int ogdf::PQNode< T, X, Y >::m_identificationNumber
protected
Each node that has been introduced once into the tree gets a unique number.
If the node is removed from the tree during a reduction or with the help of one of the functions that is provided by the class template PQtree, its number is not reused. This always allows exact identification of nodes during any process that is envoked on the PQ-tree. We strongly recommend users who construct the tree with the help of the construction functions and who instantiate the nodes by them selves to do the same.
Definition at line 437 of file PQNode.h.
## ◆ m_leftEndmost
template<class T , class X , class Y >
PQNode* ogdf::PQNode< T, X, Y >::m_leftEndmost
protected
Definition at line 451 of file PQNode.h.
## ◆ m_parent
template<class T , class X , class Y >
PQNode* ogdf::PQNode< T, X, Y >::m_parent
protected
Is a pointer to the parent.
Observe that this pointer may not be up to date after a few applications of the reduction.
Definition at line 458 of file PQNode.h.
## ◆ m_parentType
template<class T , class X , class Y >
PQNodeType ogdf::PQNode< T, X, Y >::m_parentType
protected
Stores the type of the parent which can be either a P- or Q-node.
Definition at line 440 of file PQNode.h.
## ◆ m_pertChildCount
template<class T , class X , class Y >
int ogdf::PQNode< T, X, Y >::m_pertChildCount
protected
Stores the number of pertinent children of the node.
Definition at line 443 of file PQNode.h.
## ◆ m_pertLeafCount
template<class T , class X , class Y >
int ogdf::PQNode< T, X, Y >::m_pertLeafCount
protected
Stores the number of pertinent leaves in the frontier of the node.
Definition at line 446 of file PQNode.h.
## ◆ m_pointerToInfo
template<class T , class X , class Y >
PQNodeKey* ogdf::PQNode< T, X, Y >::m_pointerToInfo
protected
Stores a pointer to the corresponding information of the node.
Definition at line 498 of file PQNode.h.
## ◆ m_referenceChild
template<class T , class X , class Y >
PQNode* ogdf::PQNode< T, X, Y >::m_referenceChild
protected
Stores a pointer to one child, the reference child of the doubly linked cirkular list of children of a P-node.
With the help of this pointer, it is possible to access the children of the P-node
Definition at line 466 of file PQNode.h.
## ◆ m_referenceParent
template<class T , class X , class Y >
PQNode* ogdf::PQNode< T, X, Y >::m_referenceParent
protected
Is a pointer to the parent, in case that the parent is a P-node and the node itself is its reference child.
The pointer is needed in order to identify the reference child among all children of a P-node.
Definition at line 474 of file PQNode.h.
## ◆ m_rightEndmost
template<class T , class X , class Y >
PQNode* ogdf::PQNode< T, X, Y >::m_rightEndmost
protected
Stores the right endmost child of a Q-node.
Definition at line 477 of file PQNode.h.
## ◆ m_sibLeft
template<class T , class X , class Y >
PQNode* ogdf::PQNode< T, X, Y >::m_sibLeft
protected
Stores a pointer ot the left sibling of PQNode.
If PQNode is child of a Q-node and has no left sibling, m_sibLeft is set to 0. If PQNode is child of a P-node, all children of the P-node are linked in a circular list. In the latter case, m_sibLeft is never 0.
Definition at line 486 of file PQNode.h.
## ◆ m_sibRight
template<class T , class X , class Y >
PQNode* ogdf::PQNode< T, X, Y >::m_sibRight
protected
Stores a pointer ot the right sibling of PQNode.
If PQNode is child of a Q-node and has no right sibling, m_sibRight is set to 0. If PQNode is child of a P-node, all children of the P-node are linked in a circular list. In the latter case, m_sibRight is never 0.
Definition at line 495 of file PQNode.h.
## ◆ partialChildren
template<class T , class X , class Y >
List*>* ogdf::PQNode< T, X, Y >::partialChildren
protected
Stores all partial children of a node during a reduction.
Definition at line 505 of file PQNode.h.
The documentation for this class was generated from the following files:
|
{}
|
×
# Weird answers !!
In this Problem he solved it by breaking the question into brackets !! but even then each bracket will equal zero and by summing or subtracting those brackets we get 0 !!! how could he come up with that 23!!
Note by Eman Abulmagd
3 years, 8 months ago
## Comments
Sort by:
Top Newest
Note that there is a minus sign before $$(-1)^{a}$$ for odd values of $$a$$. · 3 years, 8 months ago
Log in to reply
The final answer is 26 (not 23 like you mentioned).
As pointed out, each of the terms contribute a value of 1 to the sum, and there are 26 terms. Staff · 3 years, 8 months ago
Log in to reply
×
Problem Loading...
Note Loading...
Set Loading...
|
{}
|
2020
Activity report
Project-Team
CAMBIUM
RNSR: 201923244M
Research center
In partnership with:
Collège de France
Team name:
Programming languages: type systems, concurrency, proofs of programs
Domain
Algorithmics, Programming, Software and Architecture
Theme
Proofs and Verification
Creation of the Project-Team: 2019 August 01
# Keywords
• A1.1.1. Multicore, Manycore
• A1.1.3. Memory models
• A2.1. Programming Languages
• A2.1.1. Semantics of programming languages
• A2.1.3. Object-oriented programming
• A2.1.4. Functional programming
• A2.1.6. Concurrent programming
• A2.1.11. Proof languages
• A2.2. Compilation
• A2.2.1. Static analysis
• A2.2.2. Memory models
• A2.2.4. Parallel architectures
• A2.2.5. Run-time systems
• A2.4. Formal method for verification, reliability, certification
• A2.4.1. Analysis
• A2.4.3. Proofs
• A2.5.4. Software Maintenance & Evolution
• A7.1.2. Parallel algorithms
• A7.2. Logic in Computer Science
• A7.2.2. Automated Theorem Proving
• A7.2.3. Interactive Theorem Proving
• B5.2.3. Aviation
• B6.1. Software industry
• B6.6. Embedded systems
• B9.5.1. Computer science
# 1 Team members, visitors, external collaborators
## Research Scientists
• François Pottier [Team leader, Inria, Senior Researcher, HDR]
• Damien Doligez [Inria, Researcher]
• Ioannis Filippidis [Inria, Starting Research Position, until Mar 2020]
• Xavier Leroy [Collège de France, Senior Researcher]
• Luc Maranget [Inria, Researcher]
• Gabriel Radanne [Inria, Starting Research Position, until Nov 2020]
• Didier Rémy [Inria, Senior Researcher, HDR]
## PhD Students
• Frédéric Bour [Tarides, CIFRE]
• Basile Clement [Inria]
• Nathanaël Courant [École Normale Supérieure de Paris]
• Paulo Emílio De Vilhena [Inria]
• Glen Mével [Inria]
• Thomas Refis [Tarides, CIFRE, from Feb 2020]
• Léo Stefanesco [Collège de France, from Oct 2020]
## Technical Staff
• Florian Angeletti [Inria, Engineer]
• Sébastien Hinderer [Inria, Engineer, from Mar 2020]
## Interns and Apprentices
• Antoine Hacquard [Inria, until Jan 2020]
• Hélène Milome [Inria]
## Visiting Scientist
• Jacques Garrigue [Université de Nagoya, until Jul 2020]
# 2 Overall objectives
The research conducted in the Cambium team aims at improving the safety, reliability and security of software through advances in programming languages and in formal program verification. Our work is centered on the design, formalization, and implementation of programming languages, with particular emphasis on type systems and type inference, formal program verification, shared-memory concurrency and weak memory models. We are equally interested in theoretical foundations and in applications to real-world problems. The OCaml programming language and the CompCert C compiler embody many of our research results.
## 2.1 Software reliability and reusability
Software nowadays plays a pervasive role in our environment: it runs not only on general-purpose computers, as found in homes, offices, and data centers, but also on mobile phones, credit cards, inside transportation systems, factories, and so on. Furthermore, whereas building a single isolated software system was once rightly considered a daunting task, today, tens of millions of developers throughout the world collaborate to develop software components that have complex interdependencies. Does this mean that the “software crisis” of the early 1970s, which Dijkstra described as follows, is over?
By now it is generally recognized that the design of any large sophisticated system is going to be a very difficult job, and whenever one meets people responsible for such undertakings, one finds them very much concerned about the reliability issue, and rightly so. – Edsger W. Dijkstra
To some extent, the crisis is indeed over. In the past five decades, strong emphasis has been put on modularity and reusability. It is by now well-understood how to build reusable software components, thus avoiding repeated programming effort and reducing costs. The availability of hundreds of thousands of such components, hosted in collaborative repositories, has allowed the software industry to bloom in a manner that was unimaginable a few decades ago.
As pointed out by Dijkstra, however, the problem is not just to build software, but to ensure that it works. Today, the reliability of most software leaves a lot to be desired. Consumer-grade software, including desktop, Web, and mobile phone applications, often crashes or exhibits unexpected behavior. This results in loss of time, loss of data, and also can often be exploited for malicious purposes by attackers. Reliability includes safety—exhibiting appropriate behavior under normal usage conditions—and security—resisting abuse in the hands of an attacker.
Today, achieving very high levels of reliability is possible, albeit at a tremendous cost in time and money. In the aerospace industry, for instance, high reliability is obtained via meticulous development processes, extensive testing efforts, and external reviewing by independent certification authorities. There and elsewhere, formal verification is also used, instead of or in addition to the above methods. In the hardware industry, model-checking is used to verify microprocessor components. In the critical software industry, deductive program verification has been used to verify operating system kernels, file systems, compilers, and so on. Unfortunately, these methods are difficult to apply in industries that have strong cost and time-to-market constraints, such as the automotive industry, let alone the general software industry.
Today, thus, we arguably still are experiencing a “reliable-software crisis”. Although we have become pretty good at producing and evolving software, we still have difficulty producing cheap reliable software.
How to resolve this crisis remains, to a large extent, an open question. Modularity and reusability seem needed now more than ever, not only in order to avoid repeated programming effort and reduce the likelihood of errors, but also and foremost to avoid repeated specification and verification effort. Still, apparently, the languages that we use to write software are not expressive enough, and the logics and tools that we use to verify software are not mature enough, for this crisis to be behind us.
## 2.2 Qualities of a programming language
A programming language is the medium through which an intent (software design) is expressed (program development), acted upon (program execution), and reasoned about (verification). It would be a mistake to argue that, with sufficient dedication, effort, time and cleverness, good software can be written in any programming language. Although this may be true in principle, in reality, the choice of an adequate programming language can be the deciding factor between software that works and software that does not, or even cannot be developed at all.
We believe, in particular, that it is crucial for a programming language to be safe, expressive, to encourage modularity, and to have a simple, well-defined semantics.
• Safety. The execution of a program must not ever be allowed to go wrong in an unpredictable way. Examples of behaviors that must be forbidden include
reading or writing data outside of the memory area assigned by the operating system to the process and executing arbitrary data as if it were code. A programming language is safe if every safety violation is gracefully detected either at compile time or at runtime.
• Expressiveness. The programming language should allow programmers to think in terms of concise, high-level abstractions—including the concepts and entities of the application domain—as opposed to verbose, low-level representations or encodings of these concepts.
• Modularity. The programming language should make it easy to develop a software component in isolation, to describe how it is intended to be composed with other components, and to check at composition time that this intent is respected.
• Semantics. The programming language should come with a mathematical definition of the meaning of programs, as opposed to an informal, natural-language description. This definition should ideally be formal, that is, amenable to processing by a machine. A well-defined semantics is a prerequisite for proving that the language is safe (in the above sense) and for proving that a specific program is correct (via model-checking, deductive program verification, or other formal methods).
The safety of a programming language is usually achieved via a combination of design decisions, compile-time type-checking, and runtime checking. As an example design decision, memory deallocation, a dangerous operation, can be placed outside of the programmer's control. As an example of compile-time type-checking, attempting to use an integer as if it were a pointer can be considered a type error; a program that attempts to do this is then rejected by the compiler before it is executed. Finally, as an example of runtime checking, attempting to access an array outside of its bounds can be considered a runtime error: if a program attempts to do this, then its execution is aborted.
Type-checking can be viewed as an automated means of establishing certain correctness properties of programs. Thus, type-checking is a form of “lightweight formal methods” that provides weak guarantees but whose burden seems acceptable to most programmers. However, type-checking is more than just a program analysis that detects a class of programming errors at compile time. Indeed, types offer a language in which the interaction between one program component and the rest of the program can be formally described. Thus, they can be used to express a high-level description of the service provided by this component (i.e., its API), independently of its implementation. At the same time, they protect this component against misuse by other components. In short, “type structure is a syntactic discipline for enforcing levels of abstraction”. In other words, types offer basic support for expressiveness and modularity, as described above.
For this reason, types play a central role in programming language design. They have been and remain a fundamental research topic in our group. More generally, the design of new programming languages and new type systems and the proof of their safety has been and remains an important theme. The continued evolution of OCaml, as well as the design and formalization of Mezzo 2, are examples.
## 2.3 Design, implementation, and evolution of OCaml
Our group's expertise in programming language design, formalization and implementation has traditionally been focused mainly on the programming language OCaml 26. OCaml can be described as a high-level statically-typed general-purpose programming language. Its main features include first-class functions, algebraic data structures and pattern matching, automatic memory management, support for traditional imperative programming (mutable state, exceptions), and support for modularity and encapsulation (abstract types; modules and functors; objects and classes).
OCaml meets most of the key criteria that we have put forth above. Thanks to its static type discipline, which rejects unsafe programs, it is safe. Because its type system is equipped with powerful features, such as polymorphism, abstract types, and type inference, it is expressive, modular, and concise. Although OCaml as a whole does not have a formal semantics, many fragments of it have been formally studied in isolation. As a result, we believe that OCaml is a good language in which to develop complex software components and software systems and (possibly) to verify that they are correct.
OCaml has long served a dual role as a vehicle for our programming language research and as a mature real-world programming language. This remains true today, and we wish to preserve this dual role. On the research side, there are many directions in which the language could be extended. On the applied side, OCaml is used within academia (for research and for teaching) and in the industry. It is maintained by a community of active contributors, which extends beyond our team at Inria. It comes with a package manager, opam, a rich ecosystem of libraries, and a set of programming tools, including an IDE (Merlin), support for debugging and performance profiling, etc.
OCaml has been used to develop many complex systems, such as proof assistants (Coq, HOL Light), automated theorem provers (Alt-Ergo, Zenon), program verification tools (Why3), static analysis engines (Astrée, Frama-C, Infer, Flow), programming languages and compilers (SCADE, Reason, Hack), Web servers (Ocsigen), operating systems (MirageOS, Docker), financial systems (at companies such as Jane Street, LexiFi, Nomadic Labs), and so on.
## 2.4 Software verification
We have already mentioned the importance of formal verification to achieve the highest levels of software quality. One of our major contributions to this field has been the verification of programming tools, namely the CompCert optimizing compiler for the C language 34 and the Verasco abstract interpretation-based static analyzer 7. Technically, this is deductive verification of purely functional programs, using the Coq proof assistant both as the prover and the programming language. Scientifically, CompCert and Verasco are milestones in the area of program proof, due to the complexity and realism of the code generation, optimization, and static analysis techniques that are verified. Practically, these formally-verified tools strengthen the guarantees that can be obtained by formal verification of critical software and reduce the need for other verification activities, attracting the interest of Airbus and other companies that develop critical embedded software.
CompCert is implemented almost entirely in Gallina, the purely functional programming language that lies at the heart of Coq. Extraction, a whole-program translation from Gallina to OCaml, allows Gallina programs to be compiled to native code and efficiently executed. Unfortunately, Gallina is a very restrictive language: it rules out all side effects, including nontermination, mutable state, exceptions, delimited control, nondeterminism, input/output, and concurrency. In comparison, most industrial programming languages, including OCaml, are vastly more expressive and convenient. Thus, there is a clear need for us to also be able to verify software components that are written in OCaml and exploit side effects.
To reason about the behavior of effectful programs, one typically uses a “program logic”, that is, a system of deduction rules that are tailor-made for this purpose, and can be built into a verification tool. Since the late 1960s, program logics for imperative programming languages with global mutable state have been in wide use. A key advance was made in the 2000s with the appearance of Separation Logic, which emphasizes local reasoning and thereby allows reasoning about a callee independently of its caller, about one heap fragment independently of the rest of the heap, about one thread independently of all other threads, and so on. Today, this field is extremely active: the development of powerful program logics for rich effectful programming languages, such as OCaml or Multicore OCaml, is a thriving and challenging research area.
Our team has expertise in this field. For several years, François Pottier has been investigating the theoretical foundations and applications of several features of modern Separation Logics, such as “hidden state” and “monotonic state”. Jean-Marie Madiot has contributed to the Verified Software Toolchain, which includes a version of Concurrent Separation Logic for a subset of C. Arthur Charguéraud 1 has developed CFML, an implementation of Separation Logic for a subset of OCaml. Armaël Guéneau has extended CFML with the ability to simultaneously verify the correctness and the time complexity of an OCaml component. Glen Mével and Paulo de Vilhena are currently investigating the use of Iris, a descendant of Concurrent Separation Logic, to carry out proofs of Multicore OCaml programs.
We envision several ways of using OCaml components that have been verified using a program logic. In the simplest scenario, some key OCaml components, such as the standard library, are verified, and are distributed for use in unverified applications. This increases the general trustworthiness of the OCaml system, but does not yield strong guarantees of correctness. In a second scenario, a fully verified application is built out of verified OCaml components, therefore it comes with an end-to-end correctness guarantee. In a third scenario, while some components are written and verified directly at the level of OCaml, others are first written and verified in Gallina, then translated down to verified OCaml components by an improved version of Coq's extraction mechanism. In this scenario, it is possible to fully verify an application that combines effectful OCaml code and side-effect-free Gallina code. This scenario represents an improvement over the current state of the art. Today, CompCert includes several OCaml components, which cannot be verified in Coq. As a result, the data produced by these components must be validated by verified checkers.
## 2.5 Shared-memory concurrency
Concurrent shared-memory programming seems required in order to extract maximum performance out of the multicore general-purpose processors that have been in wide use for more than a decade. (GPUs and other special-purpose processors offer even greater raw computing power, but are not easily exploited in the symbolic computing applications that we are usually interested in.) Unfortunately, concurrent programming is notoriously more difficult than sequential programming. This can be attributed to a “state-space explosion problem”: the number of permitted program executions grows exponentially with the number of concurrent agents involved. Shared memory introduces an additional, less notorious, difficulty: on a modern multicore processor, execution does not follow the strong model where the instructions of one thread are interleaved with the instructions of other threads, and where reads and writes to memory instantaneously take effect. To properly understand and analyze a program, one must first formally define the semantics of the programming language, or of the device that is used to execute the program. The aspect of the semantics that governs the interaction of threads through memory is known as a memory model. Most modern memory models are weak in the sense that they offer fewer guarantees than the strong model sketched above.
Describing a memory model in precise mathematical language, in a manner that is at the same time faithful with respect to real-world machines and exploitable as a basis for reasoning about programs, is a challenging problem and a domain of active research, where thorough testing and verification are required.
Luc Maranget and Jean-Marie Madiot have acquired an expertise in the domain of weak memory models, including so-called axiomatic models and event-structure-based models. Moreover, Luc Maranget develops diy-herd-litmus, a unique software suite for defining, simulating and testing memory models. In short, diy generates so-called litmus tests from concise specifications; herd simulates litmus tests with respect to memory models expressed in the domain-specific language Cat; litmus executes litmus tests on real hardware. These tools have been instrumental in finding bugs in the deployed processors IBM Power5 and ARM Cortex-A9. Moreover, within industry, some models are now written in Cat, either for internal use, such as the AArch64 model by Will Deacon (ARM), or for publication, such as the RISC-V model by Luc Maranget and the HSA model by Jade Alglave and Luc Maranget.
For a long time, the OCaml language and runtime system have been restricted to sequential execution, that is, execution of a single computation thread on a single processor core. Yet, since 2014 approximately, the Multicore OCaml project at OCaml Labs (Cambridge, UK) is preparing a version of OCaml where multiple threads execute concurrently and communicate with each other via shared memory.
In principle, it seems desirable for Multicore OCaml to become the standard version of OCaml. Integrating Multicore OCaml into mainstream OCaml, however, is a major undertaking. The runtime system is deeply impacted: in particular, OCaml's current high-performance garbage collector must be replaced with an entirely new concurrent collector. The memory model and operational semantics of the language must be clearly defined. At the programming-language level, several major extensions are proposed, including effect handlers (a generalization of exception handlers, introducing a form of delimited control) and a new type-and-effect-discipline that statically detects and rejects unhandled effects.
# 3 Research program
Our research proposal is organized along three main axes, namely programming language design and implementation, concurrency, and program verification. These three areas have strong connections. For instance, the definition and implementation of Multicore OCaml intersects the first two axes, whereas creating verification technology for Multicore OCaml programs intersects the last two.
In short, the “programming language design and implementation” axis includes:
• The search for richer type disciplines, in an effort to make our programming languages safer and more expressive. Two domains, namely modules and effects, appear of particular interest. In addition, we view type inference as an important cross-cutting concern.
• The continued evolution of OCaml. The major evolutions that we envision in the medium term are the integration of Multicore OCaml, the addition of modular implicits, and a redesign of the type-checker.
• Research on refactoring and program transformations.
The “concurrency” axis includes:
• Research on weak memory models, including axiomatic models, operational models, and event-structure models.
• Research on the Multicore OCaml memory model. This might include proving that the axiomatic and operational presentations of the model agree; testing the Multicore OCaml implementation to ensure that it conforms to the model; and extending the model with new features, should the need arise.
The “program verification” axis includes:
• The continued evolution of CompCert.
• Building new verified tools, such as verified compilers for domain-specific languages, verified components for the Coq type-checker, and so on.
• Verifying algorithms and data structures implemented in OCaml and in Multicore OCaml and enriching Separation Logic with new features, if needed, to better support this activity.
• The continued development of tools for TLA+.
# 4 Application domains
## 4.1 Formal methods
We develop techniques and tools for the formal verification of critical software:
• program logics based on CFML and Iris for the deductive verification of software, including concurrency and algorithmic complexity aspects;
• verified development tools such as the CompCert verified C compiler, which extends properties established by formal verification at the source level all the way to the final executable code.
Some of these techniques have already been used in the nuclear industry (MTU Friedrichshafen uses CompCert to develop emergency diesel generators) and are under evaluation in the aerospace industry.
## 4.2 High-assurance software
Software that is not critical enough to undergo formal verification can still benefit greatly, in terms of reliability and security, from a functional, statically-typed programming language. The OCaml type system offers several advanced tools (generalized algebraic data types, abstract types, extensible variant and object types) to express many data structure invariants and safety properties and have them automatically enforced by the type-checker. This makes OCaml a popular language to develop high-assurance software, in particular in the financial industry. OCaml is the implementation language for the Tezos blockchain and cryptocurrency. It is also used for automated trading at Jane Street and for modeling and pricing of financial contracts at Bloomberg, Lexifi and Simcorp. OCaml is also widely used to implement code verification and generation tools at Facebook, Microsoft, CEA, Esterel Technologies, and many academic research groups, at Inria and elsewhere.
## 4.3 Design and test of microprocessors
The diy tool suite and the underlying methodology is in use at ARM Ltd to design and test the memory model of ARM architectures. In particular, the internal reference memory model of the ARMv8 (or AArch64) architecture has been written “in house” in Cat, our domain-specific language for specifying and simulating memory models. Moreover, our test generators and runtime infrastructure are used routinely at ARM to test various implementations of their architectures.
## 4.4 Teaching programming
Our work on the OCaml language family has an impact on the teaching of programming. OCaml is one of the programming languages selected by the French Ministry of Education for teaching Computer Science in classes préparatoires scientifiques. OCaml is also widely used for teaching advanced programming in engineering schools, colleges and universities in France, the USA, and Japan. The MOOC “Introduction to Functional Programming in OCaml”, developed at University Paris Diderot, is available on the France Université Numérique platform and comes with an extensive platform for self-training and automatic grading of exercises, developed in OCaml itself.
# 5 New software and platforms
## 5.1 Software
### 5.1.1 The CompCert verified compiler
Participants: Xavier Leroy, Michael Schmidt, Bernhard Schommer.
Since 2005, in the context of our work on compiler verification, we have been developing and formally verifying CompCert, a moderately-optimizing compiler for a large subset of the C programming language. CompCert generates assembly code for the ARM, PowerPC, RISC-V and x86 architectures 34. It comprises a back-end, which translates the Cminor intermediate language to PowerPC assembly and which can be reused for source languages other than C 32, and a front-end, which translates the “CompCert C” subset of C to Cminor. The compiler is written mostly within the specification language of the Coq proof assistant, out of which Coq's extraction facility generates executable OCaml code. The compiler comes with a 100000-line machine-checked proof of semantic preservation, establishing that the generated assembly code executes exactly as prescribed by the semantics of the source C program.
This year, we improved the CompCert C compiler and tools in several directions:
• Conformance with the ISO C 11 standard was improved: the _Static_assert construct is now supported, and several discrepancies were fixed.
• We introduced mechanisms to specify the semantics of built-in functions. We used them to provide semantics for a growing number of built-in functions, making them amenable to optimizations such as constant propagation and common subexpression elimination.
• The x86 code generator was updated to support Cygwin 64 as a target platform, making it easier to use CompCert under Windows.
• Conformance with the Application Binary Interfaces (ABI) for AArch64, PowerPC, RISC-V, and x86 was improved.
• The clightgen tool, which integrates CompCert in the Verified Software Toolchain developed by Andrew Appel's team at Princeton University 28, was improved so as to simplify the verification of C programs composed of multiple source files.
We released two versions of CompCert incorporating these improvements: version 3.7 in March 2020 and version 3.8 in November 2020.
### 5.1.2 The OCaml system
Participants: Florian Angeletti, Frédéric Bour, Damien Doligez, Jacques Garrigue, Sébastien Hinderer, Xavier Leroy, Luc Maranget, Thomas Refis, David Allsop, Stephen Dolan, Alain Frisch, Jacques-Henri Jourdan, Nicolás Ojeda Bär, Gabriel Scherer, Mark Shinwell, Leo White, Jeremy Yallop.
This year, we released two major versions of the OCaml system: version 4.10.0 in February and version 4.11.0 in August. We also released four minor versions (4.09.1, 4.10.1, 4.10.2, 4.11.1) with bug fixes and backports of new features. The main novelties in these releases are:
• The language has been extended to allow users to define their own multidimensional array-like indexing operators.
• A new memory profiler, statmemprof, is now available. It is based on statistical sampling of allocations, resulting in much lower run-time overhead than the earlier memory profiler, Spacetime.
• OCaml now fully supports the MacOS system running on ARM 64-bit processors, including the latest Macintosh models with “Apple silicon”.
• A native-code generator for the RISC-V processor architecture has been added.
• A new memory allocator for the major heap is now available. It is based on a best-fit strategy and causes less heap fragmentation than the previous allocator.
• The exhaustiveness check has been made more precise for case analyses that involve GADTs or empty types.
• The runtime system can now record statistics and events in the standard CTF format.
• The integration of the Multicore OCaml project has begun, with a number of internal changes to the runtime system that will be required for full multicore support.
• More than one hundred usability improvements have been implemented, ranging from more readable stack backtraces through improved error messages to new standard library functions.
• About 80 bugs have been fixed.
### 5.1.3 The Menhir parser generator
Participants: François Pottier.
Since 2005, François Pottier has been developing Menhir, an LR(1) parser generator for OCaml. Menhir is used both within our group (where it is exploited, in particular, by the OCaml and CompCert compilers) and by many users in the OCaml community. This year, a number of improvements and bug fixes have been performed:
• The algorithms for constructing LR automata have been re-implemented in a style that is more concise, more elegant and more efficient. A bug in our implementation of Pager's construction algorithm has been fixed. Our new implementation operates in two phases: first compute the automaton's states, then compute its transitions. It is significantly easier to describe and understand than our earlier implementation.
• A simplified error-handling strategy has been introduced. It removes a couple undesirable features of the traditional error-handling strategy inherited from yacc.
• Several “bit set” data structures have been improved, for greater speed.
• The test that determines whether macro-expansion will terminate has been re-implemented. The old test was discovered to be neither sound nor complete. The new test is hopefully both sound and complete.
• The manner in which Menhir performs type inference has been slightly modified so as to avoid certain (infrequent) situations in which incorrect types could be inferred.
• Menhir is now built using dune instead of ocamlbuild. This allows taking advantage of parallelism while building and testing Menhir.
### 5.1.4 The odoc documentation tool
Participants: Jon Ludlam, Gabriel Radanne, Florian Angeletti, Leo White.
Rendering the documentation of a piece of OCaml code is a difficult task. Indeed, the OCaml module system allows setting up complex inter-dependencies that are difficult to compute and difficult to render in a concise document. odoc is our latest attempt at creating a documentation tool that handles the full complexity of the OCaml language.
This year, Gabriel Radanne rewrote a significant portion of odoc to provide improved HTML output, make it possible to produce other document formats, and introduce the ability to produce man pages. Florian Angeletti then implemented PDF output and integrated the usage of odoc in the official OCaml distribution. Concurrently, Jon Ludlam and Leo White rewrote the resolution mechanism of odoc, which led to a joint presentation at the OCaml workshop.
### 5.1.5 The diy tool suite
The diy suite provides a set of tools for testing shared memory models: the litmus tool for running tests on hardware, various generators for producing tests from concise specifications, and herd, a memory model simulator. Tests are small programs written in x86, Power, ARM, generic (LISA) assembler, or a subset of the C language that can thus be generated from concise specifications, run on hardware, or simulated on top of memory models. Test results can be handled and compared using additional tools. On distinctive feature of our system is Cat, a domain-specific language for memory models.
This year, a feature branch for handling virtual memory was created, of which Jade Alglave and Luc Maranget are (almost) the exclusive authors. It is the backbone of our current research. Moreover, many authors (most of whom work at ARM Ltd.) have been contributing in various manners:
• Test and build infrastructure.
• Extension of the simulated instruction set.
• Architectural extensions: capabilities (ARM Morello), SIMD (ARM Neon; work in progress).
### 5.1.6 The TLAPS proof system
Participants: Damien Doligez, Leslie Lamport, Ioannis Filippidis, Stephan Merz.
Damien Doligez heads the “Tools for Proofs” team in the Microsoft-Inria Joint Centre. The aim of this project is to extend the TLA+ language with a formal language for hierarchical proofs, formalizing Lamport's ideas 31, and to build tools for writing TLA+ specifications and mechanically checking the proofs.
This year, we made a bug-fix release of TLAPS (version 1.4.5). We have also been testing the new support for the enabled operator and the action composition operator in TLA+ proofs. We hope to release version 1.5.0 with this support very soon.
We also made a maintenance release of Zenon (version 0.8.5) to make it compatible with the latest version of OCaml.
### 5.1.7 Sek, an efficient sequence library for OCaml
Participants: Arthur Charguéraud, François Pottier.
This year, Arthur Charguéraud and François Pottier developed Sek, a library that offers efficient implementations of ephemeral sequences, persistent sequences, and ephemeral iterators on both kinds of sequences. Sek publishes 4 abstract types and over 150 operations. Its data structures involve complex balancing invariants, shared mutable state, and a subtle ownership policy that determines when an object can be updated in place and when it must be copied. It is intended to offer very good performance, in terms of both space and time, in most usage scenarios; thus, it should remove the need for more specialized data structures, such as stacks, queues, deques, catenable deques, and so on. The library has been published and is available via OCaml's package manager, opam. No paper about Sek has been published at this time. It is worth noting that testing Sek was our main motivation for developing Monolith (§5.1.8).
### 5.1.8 Monolith, a library for testing OCaml libraries
Participants: François Pottier.
This year, François Pottier developed Monolith, an OCaml library whose purpose is to facilitate black-box testing of other OCaml libraries. Monolith provides a rich specification language, which allows the user to describe her library's API, and an engine, which generates clients of this API and executes them. This reduces the problem of testing a library to the simpler problem of testing a complete program. Testing can then be performed either in a purely random manner or with the help of an off-the-shelf fuzzer, such as AFL. This work is described in a paper that will be presented at JFLA 2021 20. Monolith has been used to test and debug Sek (§5.1.7).
## 5.2 New software
### 5.2.1 OCaml
• Keywords: Functional programming, Static typing, Compilation
• Functional Description: The OCaml language is a functional programming language that combines safety with expressiveness through the use of a precise and flexible type system with automatic type inference. The OCaml system is a comprehensive implementation of this language, featuring two compilers (a bytecode compiler, for fast prototyping and interactive use, and a native-code compiler producing efficient machine code for x86, ARM, PowerPC and System Z), a debugger, a documentation generator, a compilation manager, a package manager, and many libraries contributed by the user community.
• URL:
• Publications:
• Contacts: Xavier Leroy, Damien Doligez
• Participants: Damien Doligez, Xavier Leroy, Fabrice Le Fessant, Luc Maranget, Gabriel Scherer, Alain Frisch, Jacques Garrigue, Marc Shinwell, Jeremy Yallop, Leo White
### 5.2.2 Compcert
• Name: The CompCert formally-verified C compiler
• Keywords: Compilers, Formal methods, Deductive program verification, C, Coq
• Functional Description: CompCert is a compiler for the C programming language. Its intended use is the compilation of life-critical and mission-critical software written in C and meeting high levels of assurance. It accepts most of the ISO C 99 language, with some exceptions and a few extensions. It produces machine code for the ARM, PowerPC, RISC-V, and x86 architectures. What sets CompCert C apart from any other production compiler, is that it is formally verified to be exempt from miscompilation issues, using machine-assisted mathematical proofs (the Coq proof assistant). In other words, the executable code it produces is proved to behave exactly as specified by the semantics of the source C program. This level of confidence in the correctness of the compilation process is unprecedented and contributes to meeting the highest levels of software assurance. In particular, using the CompCert C compiler is a natural complement to applying formal verification techniques (static analysis, program proof, model checking) at the source code level: the correctness proof of CompCert C guarantees that all safety properties verified on the source code automatically hold as well for the generated executable.
• Release Contributions: Novelties include a formally-verified type checker for CompCert C, a more careful modeling of pointer comparisons against the null pointer, algorithmic improvements in the handling of deeply nested struct and union types, much better ABI compatibility for passing composite values, support for GCC-style extended inline asm, and more complete generation of DWARF debugging information (contributed by AbsInt).
• URL:
• Authors: Xavier Leroy, Bernhard Schommer, Guillaume Melquiond, Jacques-Henri Jourdan, Sylvie Boldo
• Contact: Xavier Leroy
• Participants: Xavier Leroy, Sandrine Blazy, Jacques-Henri Jourdan, Sylvie Boldo, Guillaume Melquiond
• Partner: AbsInt Angewandte Informatik GmbH
### 5.2.3 Diy
• Name: Do It Yourself
• Keyword: Parallelism
• Functional Description: The diy suite provides a set of tools for testing shared memory models: the litmus tool for running tests on hardware, various generators for producing tests from concise specifications, and herd, a memory model simulator. Tests are small programs written in x86, Power or ARM assembler that can thus be generated from concise specification, run on hardware, or simulated on top of memory models. Test results can be handled and compared using additional tools.
• URL:
• Authors: Jade Alglave, Luc Maranget
• Contact: Luc Maranget
• Participants: Jade Alglave, Luc Maranget
• Partner: University College London UK
### 5.2.4 Menhir
• Keywords: Compilation, Context-free grammars, Parsing
• Functional Description: Menhir is a LR(1) parser generator for the OCaml programming language. That is, Menhir compiles LR(1) grammar specifications down to OCaml code. Menhir was designed and implemented by François Pottier and Yann Régis-Gianas.
• Publications:
• Contact: François Pottier
### 5.2.5 CFML
• Name: Interactive program verification using characteristic formulae
• Keywords: Coq, Software Verification, Deductive program verification, Separation Logic
• Functional Description: The CFML tool supports the verification of OCaml programs through interactive Coq proofs. CFML proofs establish the full functional correctness of the code with respect to a specification. They may also be used to formally establish bounds on the asymptotic complexity of the code. The tool is made of two parts: on the one hand, a characteristic formula generator implemented as an OCaml program that parses OCaml code and produces Coq formulae, and, on the other hand, a Coq library that provides notations and tactics for manipulating characteristic formulae interactively in Coq.
• URL:
• Contact: Arthur Charguéraud
• Participants: Arthur Charguéraud, Armaël Guéneau, François Pottier
### 5.2.6 TLAPS
• Name: TLA+ proof system
• Keyword: Proof assistant
• Functional Description: TLAPS is a platform for developing and mechanically verifying proofs about TLA+ specifications. The TLA+ proof language is hierarchical and explicit, allowing a user to decompose the overall proof into proof steps that can be checked independently. TLAPS consists of a proof manager that interprets the proof language and generates a collection of proof obligations that are sent to backend verifiers. The current backends include the tableau-based prover Zenon for first-order logic, Isabelle/TLA+, an encoding of TLA+ set theory as an object logic in the logical framework Isabelle, an SMT backend designed for use with any SMT-lib compatible solver, and an interface to a decision procedure for propositional temporal logic.
• News of the Year: In 2020, we published a minor release, fixing some issues notably for the SMT back-end. Substantial work was devoted to supporting liveness reasoning, in particular proofs about the enabled and action composition constructions of TLA+. We also prepared support for current versions of the Isabelle back-end prover.
• URL:
• Contacts: Stephan Merz, Damien Doligez
• Participants: Damien Doligez, Stephan Merz, Ioannis Filippidis
• Partner: Microsoft
### 5.2.7 ZENON
• Name: The Zenon automatic theorem prover
• Keywords: Automated theorem proving, First-order logic
• Functional Description:
Zenon is an automatic theorem prover based on the tableaux method. Given a first-order statement as input, it outputs a fully formal proof in the form of a Coq or Isabelle proof script. It has special rules for efficient handling of equality and arbitrary transitive relations. Although still in the prototype stage, it already gives satisfying results on standard automatic-proving benchmarks.
Zenon is designed to be easy to interface with front-end tools (for example integration in an interactive proof assistant) and also to retarget to output scripts for different frameworks (for example Dedukti).
• URL:
• Publications:
• Author: Damien Doligez
• Contact: Damien Doligez
• Participant: Damien Doligez
### 5.2.8 hevea
• Name: hevea is a fast latex to html translator.
• Keywords: LaTeX, Web
• Functional Description:
HEVEA is a LATEX to html translator. The input language is a fairly complete subset of LATEX 2 (old LATEX style is also accepted) and the output language is html that is (hopefully) correct with respect to version 5. HEVEA understands LATEX macro definitions. Simple user style files are understood with little or no modifications. Furthermore, HEVEA customisation is done by writing LATEX code.
HEVEA is written in Objective Caml, as many lexers. It is quite fast and flexible. Using HEVEA it is possible to translate large documents such as manuals, books, etc. very quickly. All documents are translated as one single html file. Then, the output file can be cut into smaller files, using the companion program HACHA. HEVEA can also be instructed to output plain text or info files.
Information on HEVEA is available at http://hevea.inria.fr/.
• URL:
• Author: Luc Maranget
• Contact: Luc Maranget
# 6 New results
## 6.1 Programming language design and implementation
### 6.1.1 Evolution of the OCaml type system
Participants: Florian Angeletti, Jacques Garrigue, Thomas Refis, Didier Rémy, Leo White, Gabriel Scherer.
Throughout this year, taking advantage of Jacques Garrigue's visit, we have worked to improve the type system, its robustness, and its implementation. This includes:
• Giving a proper formalization of the typing of generalized algebraic data types (GADTs) and pattern matching on GADTs, including making progress towards their formalization in Coq.
• Introducing notions of injective and nominal types, which allow a more complete typing of GADTs. These features have been presented by Jacques Garrigue at the 2020 ML Family Workshop.2 Injective types will be part of OCaml 4.12.
• Adding support for naming existential type variables in pattern matching constructs.
• Improving the readability of the type-checker's code.
### 6.1.2 Refactoring with ornaments in ML
Participants: Didier Rémy, Ambre Williams.
Ambre Williams and Didier Rémy have been working on ornaments for ML, a technique that allows code refactoring and evolution based on the transformations of datatypes. Ornaments have been introduced as a way of describing changes in data type definitions that can reorganize or add pieces of data. After a new data structure has been described as an ornament of an older one, the functions that operate on the bare structure can be partially or sometimes totally lifted into functions that operate on the ornamented structure.
This year, Williams improved and completed the formalization of ornaments, which she presented in her PhD dissertation in December 22.
### 6.1.3 Linear types
Participants: Gabriel Radanne, Hannes Saffrich, Peter Thiemann.
Linear types, recently made popular by the Rust programming language, allow to statically check the usage of resources such as file descriptors, network connections, or dynamically allocated memory.
In 2019, Peter Thiemann, Hannes Saffrich and Gabriel Radanne developed the language Affe, which combines Rust's flagship features, namely linear types and ownership, with the ease of use of the programming languages of the ML family, thanks to support for functional programming, GC-by-default, and full type inference.
This year, they wrote a paper that describes Affe and its inner workings and demonstrates its soundness 14. This paper was presented at ICFP 2020 by Gabriel Radanne.
### 6.1.4 An incremental type-checker for OCaml modules
Participants: Gabriel Radanne, Didier Rémy, Jacques Garrigue, Thomas Refis.
Modules are a core feature of ML languages, allowing to assemble pieces of software in a high-level and composable fashion. OCaml benefits from a particularly rich module system which was originally described more than two decades ago 35, 33, but has significantly grown since.
This year, Gabriel Radanne, in collaboration with Didier Rémy and Jacques Garrigue, started formalizing a new module system which combines all of the features that have been introduced since the last formalization effort by Xavier Leroy. This new system also improves inference and provides a solid basis for further experiments, such as the “modular implicits” that are currently being investigated by Thomas Refis and Didier Rémy (§6.1.5). Gabriel Radanne started a “clean room” implementation of a prototype type-checker for this new module system.
### 6.1.5 Designing and formalizing modular implicits
Participants: Thomas Refis, Didier Rémy, Gabriel Radanne, Leo White.
A few years ago, White et al. suggested a way to add ad-hoc polymorphism to OCaml, in the form of modular implicits 37. This new language feature can in fact be viewed as the combination of two independent parts. The first component, modular explicits, is an extension to ML's core language with a seemingly dependent arrow type. The second component, an implicit resolution mechanism, finds suitable values for omitted arguments in function applications, based on the type constraints that apply to these missing arguments.
In 2020, Thomas Refis started a PhD under the supervision of Didier Rémy. He aims to revive this project and eventually to merge it into mainline OCaml.
This year, Thomas and Didier worked on formalizing the semantics of modular explicits, which can be seen as syntactic sugar for first-class functors. They also started studying the resolution mechanism implemented in the earlier prototype of modular implicits, so as to understand its limitations and its interaction with the OCaml type-checker.
### 6.1.6 Partial type inference with second-order types
Participants: Didier Rémy.
Adding second-order types to ML in a way that smoothly integrates with ML-style type inference for first-order types has been a challenge for many years. In 2007, Le Botlan and Rémy proposed a solution to this problem, named MLF, that is still the state of the art today. Unfortunately, this solution has not been adopted, as it is a bit involved and goes beyond System F, which is the reference system for second-order types. As a result, partial type inference in the presence of second-order types remains a topic of research, and researchers continue to propose ad hoc solutions.
Didier Rémy has been investigating a new approach using the powerful inference engine of MLF to infer a typing derivation in MLF, which is then lowered to a derivation of System F. This process fails if no System F derivation exists. Preliminary investigations are promising.
### 6.1.7 Automatic synthesis of high-performance numerical libraries
Participants: Basile Clement.
Basile Clement has been working on developing a domain-specific language and a machine-learning-based compiler for the synthesis of high-performance numerical libraries, with a focus on GPUs.
One of the key challenges is to design a language that is expressive enough to capture complex loop-based code transformations while keeping the proof of semantic preservation simple. Another challenge is to accurately capture the potential peculiarities of the hardware, so as to expose the relation between the program and its performance, as far as possible, to the learning component.
This year, Basile worked on a formal semantics for an array language with explicit loops and an equational semantics. He wrote a small prototype verifier in OCaml to test the equivalence of a generated implementation with a given specification, as well as a specification in Coq for a subset of the language.
### 6.1.8 Analysis of an LR parser's stack
Participants: Frédéric Bour.
A few years ago, building on prior work by Jeffery, François Pottier implemented in the Menhir parser generator a principled method for producing good syntax error messages 36. This method chooses an error message based solely on the state in which a syntax error was detected by the LR automaton.
This year, Frédéric Bour investigated a more ambitious approach, with the aim of providing messages that are better suited to certain specific situations. This approach is able to exploit not only the current state of the LR automaton, but also to analyze the shape of its stack, thanks to a novel form of regular expressions.
### 6.1.9 Formalization of equational monadic reasoning for combined choice
Participants: Jacques Garrigue, Reynald Affeldt, David Nowak, Takafumi Saikawa.
Following work by Affeldt, Nowak and Saikawa on formalized equational monadic reasoning for programs with a variety of effects, we tackled the problem of providing a concrete model for a monad that combines nondeterministic choice with probabilistic choice. The resulting monad is fully formalized in Coq, and relies on a formalization of discrete probabilities and convex distributions. A report has been submitted for publication. This also required a formalization of axiomatic convex spaces, which was separately published at CICM 2020.3
## 6.2 Shared-memory concurrency
### 6.2.1 Axiomatic memory models
Participants: Jade Alglave, Will Deacon, Antoine Hacquard, Luc Maranget.
Modern multi-core and multi-processor computers do not follow the intuitive “Sequential Consistency” model that would define a concurrent execution as the interleaving of the executions of its constituent threads and that would command instantaneous writes to the shared memory. This situation is due both to in-core optimizations such as speculative and out-of-order execution of instructions, and to the presence of sophisticated (and cooperating) caching devices between processors and memory.
Jade Alglave and Luc Maranget have been collaborating in this domain for a decade. This year, they submitted a paper entitled “Armed cats: formal concurrency modeling at Arm” to the journal Transaction on Programming Languages and Systems (TOPLAS). The article has been accepted modulo revisions, and a revised version has been submitted in December. The paper presents an extension of the AArch64 (ARMv8) and x86 (TSO) models to mixed-size accesses. This extension is of practical interest, as many programs, in particular system programs, access memory using different sizes—e.g. by mixing byte and word accesses—which may overlap. Our work introduces a general treatment of memory model extensions, producing two provably equivalent alternative formulations. Our results have been confirmed via vast experimental campaigns, synthesized at http://diy.inria.fr/mixed/. The paper includes work by Antoine Hacquard, who was an intern at Cambium in 2019.
Concurrently, Jade Alglave and Luc Maranget are designing another extension to the ARM memory model, namely virtual memory. This work in progress aims to account for the interaction of the memory model and of virtual memory. Understanding this interaction is an absolute necessity in order to implement correct operating systems. Luc Maranget is specifically in charge of software development and of experiments. We already have interesting experimental results, having experimentally demonstrated the necessity of systems programming idioms recommended by ARM's official documentation.
### 6.2.2 Unifying axiomatic and operational weak memory models
Modern multi-processors optimize the running speed of programs using a variety of techniques, including caching, instruction reordering, and branch speculation. While those techniques are perfectly invisible to sequential programs, such is not the case for concurrent programs that execute several threads and share memory: threads do not share at every point in time a single consistent view of memory. A weak memory model offers only weak consistency guarantees when reasoning about the permitted behaviors of a program. Until now, there have been two kinds of such models, based on different mathematical foundations: axiomatic models and operational models.
Axiomatic models explicitly represent the dependencies between the program and memory actions. These models are convenient for causal reasoning about programs. They are also well-suited to the simulation and testing of hardware microprocessors.
Operational models represent program states directly, thus can be used to reason on programs: program logics become applicable, and the reasoning behind nondeterministic behavior is much clearer. This makes them preferable for reasoning about software.
Jean-Marie Madiot has been collaborating with weak memory model expert Jade Alglave and concurrent game semantics researcher Simon Castellan in order to unify these styles, in a way that attempts to combine the best of both approaches. The first results are a formalization of TSO-style architectures using partial-order techniques similar to the ones used in game semantics, and a proof of a stronger-than-state-of-art “data-race freedom” theorem: well-synchronized programs can assume a strong memory model.
This year, Jean-Marie Madiot also started developing a tool that transforms models written in the format of the memory model simulator herd into models that can be reasoned about in the Coq proof assistant. This allowed him to build mechanized proofs of properties of existing models: inclusion of models, equivalence of models, and equivalence of different acyclicity conditions. Quentin Ladeveze's formalization of the DRF-SC property of C/C++11 programs (§6.2.3) fits inside the same framework.
### 6.2.3 A mechanized proof of DRF-SC for the RC11 memory model
Quentin Ladeveze, who is co-advised by Luc Maranget and Jean-Marie Madiot, has been working on a proof of the DRF-SC property that is independent of the memory model.
DRF-SC is a well-known property that most memory models are intended to satisfy. In a weak memory model that satisfies this property, if all of the executions of a program under the sequentially consistent (SC) model are data-race-free (DRF), then all executions of the program under the weak memory model are also consistent with SC. In practice, this property allows a programmer to completely ignore the possible weak behaviors of her program, provided she writes a data-race-free program. Proofs of this property exist for some weak memory models. Our goal is to design a generic proof, by relying on properties that are shared by all of the models that satisfy this property.
This year, Quentin Ladeveze formalized in the Coq proof assistant a memory model that describes the behavior of C/C++11 programs and a proof that this model enjoys the DRF-SC property.
A paper that describes this formalization has been accepted for presentation at JFLA 2021 19.
## 6.3 Software specification and verification
### 6.3.1 Verified code generation in the polyhedral model
Participants: Nathanaël Courant, Xavier Leroy.
The polyhedral model is a high-level intermediate representation for loop nests iterating over arrays and matrices, as found in numerical code. It supports a great many loop optimizations (fusion, splitting, interchange, blocking, etc) in a uniform, mathematically-elegant manner.
In 2018, Nathanaël Courant, under Xavier Leroy's supervision, developed a Coq formalization of the polyhedral model. He implemented and verified a code generator that produces efficient sequential code out of an optimized polyhedral representation.
This year, Nathanaël Courant and Xavier Leroy wrote a paper that describes this verification work 11. This paper has been published and presented at the conference POPL 2021.
### 6.3.2 A separation logic for effect handlers
Participants: Paulo Emílio de Vilhena, François Pottier.
Paulo Emílio de Vilhena is a second-year PhD student, advised by François Pottier. His aim is to devise a separation logic with support for verifying programs that exploit effect handlers.
This year, Paulo made considerable progress towards that goal. He defined a calculus with support for effect handlers, formalized its operational semantics in Coq, and proposed a new separation logic, based on Iris 30, for this calculus. To demonstrate the usability of this logic, he carried out two short yet nontrivial case studies. A paper on this topic has been published and presented at the conference POPL 2021 5.
### 6.3.3 A program logic for Multicore Ocaml
Participants: Glen Mével, Jacques-Henri Jourdan, François Pottier.
Glen Mével, who is co-advised by Jacques-Henri Jourdan and François Pottier, has been working on designing a mechanized program logic for Multicore OCaml.
One of the key challenges is to enable deductive reasoning under a weak memory model. In such a model, the behaviors of a program are no longer described by a naive interleaving semantics. Thus, the operational semantics that describes a weak memory model often feels unnatural to the programmer, and is difficult to reason about.
At the beginning of this year, we proposed a program logic for Multicore OCaml, named Cosmo. Cosmo extends Iris 30 with a notion of “view” that allows the programmer to reason in an explicit (yet abstract) manner about the current thread's view of memory, and about the manner in which views are transferred from one thread to another via reads and writes of atomic memory locations. This work has been published and presented by Glen at ICFP 2020 13.
Since then, Glen extended Cosmo with support for arrays. This extension allows reasoning on a wider variety of programs. Using this extended logic, Glen proved the functional correctness of a concurrent first-in first-out queue, whose invariant is nontrivial.
### 6.3.4 Algebraically closed fields in Isabelle/HOL
Participants: Paulo Emílio de Vilhena, Lawrence Paulson.
During the summer of 2018, Paulo Emílio de Vilhena did a research internship under the supervision of Lawrence Paulson at the University of Cambridge. The topic was the formalization of mathematics in the proof assistant Isabelle/HOL. Paulo and Lawrence verified in Isabelle/HOL the fundamental theorem of algebra, which states that every field has an algebraic closure.
Although the majority of this work was complete by the end of the internship, the results were published only this year at the conference IJCAR 2020 17.
### 6.3.5 Towards an efficient, verified proof checker for Coq
Participants: Nathanaël Courant.
Nathanaël Courant, who is advised by Xavier Leroy, has been working on writing a formally verified and efficient convertibility test for Coq.
One of the key challenges is to perform strong reduction, whereas computers are better suited to weak reduction. Strong reduction is a form of computation that involves both concrete values and symbolic variables, and where it is permitted to perform reductions in the body of a function before this function is actually called. Weak reduction, in contrast, involves concrete values only, and does not evaluate a function until it is invoked. With strong reduction, care must be taken not to evaluate too much, and to avoid reducing the body of functions that will not appear in the final term. Besides, another difficult problem is to compare reduced terms, or even to combine the convertibility test with reduction itself.
This year, Nathanaël worked on defining a big-step semantics for strong call-by-need $\lambda$-calculus. He also wrote a Coq proof that such a semantics is compatible with standard small-step reduction for the $\lambda$-calculus, and extended this result to show that it still holds in the presence of data constructors and pattern matching.
### 6.3.6 An interactive, modular proof environment for OCaml
Participants: Frédéric Bour, François Pottier.
Frédéric Bour aims to design and implement a tool that allows verifying simple properties of OCaml programs. As a starting point, he is adapting the methodology of the VeriFast verifier 29 to OCaml programs.
This year, Frédéric worked on the translation of a subset of OCaml to a custom verification language. Verification is then handled by two different layers: an ad-hoc verifier based on separation logic for modeling effects and the Z3 theorem prover for first-order properties.
# 7 Bilateral contracts and grants with industry
## 7.1 Bilateral contracts with industry
### 7.1.1 The Caml Consortium
Participants: Damien Doligez.
The Caml Consortium is a formal structure where industrial and academic users of OCaml can support the development of the language and associated tools, express their specific needs, and contribute to the long-term stability of OCaml. Membership fees are used to fund specific developments targeted towards industrial users. Members of the Consortium automatically benefit from very liberal licensing conditions on the OCaml system, allowing for instance the OCaml compiler to be embedded within proprietary applications.
Damien Doligez chairs the Caml Consortium.
The Consortium currently has 9 member companies:
• Aesthetic Integration
• Citrix
• Docker
• Esterel / ANSYS
• Jane Street
• LexiFi
• Microsoft
• SimCorp
In the future, we would like to replace the Caml Consortium with the OCaml Software Foundation, discussed below. For the moment, however, the Caml Consortium remains alive, because the licensing conditions that it offers are unique.
### 7.1.2 Tarides
Participants: Frédéric Bour, Thomas Refis, François Pottier, Didier Rémy.
Two of our PhD students, Frédéric Bour and Thomas Refis, are employed by Tarides and carry out a PhD under a CIFRE agreement. Tarides is a small high-tech software company, with a strong expertise in virtualization, distributed systems, and programming languages. Several of their key products, such as MirageOS, are developed using OCaml.
## 7.2 Bilateral grants with industry
### 7.2.1 The OCaml Software Foundation
Participants: Damien Doligez, Xavier Leroy.
The OCaml Software Foundation, established in 2018 under the umbrella of the Inria Foundation, aims to promote, protect, and advance the OCaml programming language and its ecosystem, and to support and facilitate the growth of a diverse and international community of OCaml users.
Damien Doligez and Xavier Leroy serve as advisors on the foundation's Executive Committee.
We receive substantial basic funding from the OCaml Software Foundation in order to support research activity related to OCaml.
### 7.2.2 Funding from Nomadic Labs
Nomadic Labs, a Paris-based company, has implemented the Tezos blockchain and cryptocurrency entirely in OCaml. This year, Nomadic Labs and Inria have signed a framework agreement (“contrat-cadre”) that allows Nomadic Labs to fund multiple research efforts carried out by Inria groups. Within this framework, we have received three 3-year grants:
• “Évolution d'OCaml”. This grant is intended to fund a number of improvements to OCaml, including the addition of new features and a possible re-design of the OCaml type-checker. This grant has allowed us to fund Jacques Garrigue's visit (10 months, from September 2019 to June 2020) and to hire Gabriel Radanne on a Starting Research Position (14 months, from October 2019 to November 2020).
• “Maintenance d'OCaml”. This grant is intended to fund the day-to-day maintenance of OCaml as well as the considerable work involved in managing the release cycle. This grant has allowed us to hire Florian Angeletti as an engineer for 3 years.
• “Multicore OCaml”. This grant is intended to encourage research work on Multicore OCaml within our team. This grant has allowed us to fund Glen Mével's PhD thesis (3 years).
### 7.2.3 Funding from the Microsoft-Inria joint lab
Funding from the Microsoft-Inria joint lab has allowed us to hire Ioannis Filippidis on a Starting Research Position (until March 2020) to work on the TLAPS system.
# 8 Partnerships and cooperations
## 8.1 International research visitors
### 8.1.1 Visits of international scientists
Jacques Garrigue (Nagoya University) visited us in Paris from September 2019 to June 2020. He has long been one of the key designers and implementors of the OCaml type system. During his visit, we have collaborated on the design of new language features and on a possible re-design of the type-checker implementation.
# 9 Dissemination
## 9.1 Promoting scientific activities
### 9.1.1 Scientific events: organisation
François Pottier is a member of the ICFP steering committee.
### 9.1.2 Scientific events: selection
Xavier Leroy was a member of the program committee of CC 2021, the 30th International Conference on Compiler Construction, and of PriSC 2021, the Workshop on Principles of Secure Compilation.
Luc Maranget was a member of the program committee of POPL 2021, the 48th ACM SIGPLAN Symposium on Principles of Programming Languages.
Didier Rémy was a member of the program committee of FLOPS 2020, the 15th International Symposium on Functional and Logic Programming.
### 9.1.3 Journals
Xavier Leroy is an area editor for the Journal of the ACM, in charge of the Programming Languages area. He is also a member of the editorial board of Journal of Automated Reasoning.
François Pottier is a member of the editorial boards of the Journal of Functional Programming and the Proceedings of the ACM on Programming Languages.
Damien Doligez chairs the Caml Consortium.
Luc Maranget is member of Inria Commission d'évaluation. He was a member of two Chargé de Recherche hiring committees.
François Pottier is a member of Inria Paris' Commission de Développement Technologique and the president of Inria Paris' Comité de Suivi Doctoral.
Didier Rémy is a co-chair of the steering committee of the Inria-Nomadic Labs partnership. He is Inria's delegate in the pedagogical team and management board of MPRI.
## 9.2 Teaching - Supervision - Juries
### 9.2.1 Teaching
In 2020, the members of our team have taught or assisted in teaching the following courses:
• Open lectures: Xavier Leroy, Sémantiques mécanisées: quand la machine raisonne sur ses langages, 19 HETD, Collège de France, France.
• Master (M2): “Proofs of Programs”, Jean-Marie Madiot, 18 HETD, MPRI, Université de Paris, France.
• Master (M2): “Programming shared memory multicore machines”, Luc Maranget, 18 HETD, MPRI, Université de Paris, France. Luc Maranget is in charge of this course.
• Master (M2): “Functional programming and type systems”, François Pottier, 22 HETD, MPRI, Université de Paris, France.
• Master (M2): “Functional programming and type systems”, Didier Rémy, 24 HETD, MPRI, Université de Paris, France. Didier Rémy is in charge of this course. Didier Rémy is also Inria's delegate in the pedagogical team and management board of MPRI.
• Master (M1): “Compilation and Analysis of Programs”, Gabriel Radanne, 28 HETD, Master IF, ENS Lyon, France.
• Licence (L3): Jean-Marie Madiot, “Introduction à l'informatique”, 40 HETD, École Polytechnique, France.
• Licence (L3): Basile Clement, “Langages de programmation et compilation” (course taught by Jean-Christophe Filliâtre), 64 HETD, École Normale Supérieure, France.
• Licence (L3): Nathanaël Courant, “Mécanismes de la programmation orientée objet”, 40 HETD, École Polytechnique, France.
• Licence (L3): Nathanaël Courant, “Préparation aux concours SWERC”, 45 HETD, École Polytechnique, France.
• Licence (L2): Glen Mével, “Projet informatique 4”, 32 HETD, Université de Paris, France.
• Licence (L1): Glen Mével, “Initiation à la programmation 1 en Python”, 32 HETD, Université de Paris, France.
### 9.2.2 Supervision
The following PhD theses are in progress or have been defended in 2020:
• PhD (CIFRE) in progress: Frédéric Bour, “An interactive, modular proof environment for OCaml”, Université de Paris, since October 2019 (approved by ANRT in August 2020), advised by François Pottier and Thomas Gazagnaire (Tarides).
• PhD in progress: Basile Clement, “Domain-specific language and machine learning compiler for the automatic synthesis of high-performance numerical libraries”, École Normale Supérieure, since September 2018, advised by Xavier Leroy since October 2019.
• PhD in progress: Nathanaël Courant, “Towards an efficient, formally-verified proof checker for Coq”, Université de Paris, since September 2019, advised by Xavier Leroy.
• PhD in progress: Paulo Emílio de Vilhena, “Proof of programs with effect handlers”, Université de Paris, since September 2019, advised by François Pottier.
• PhD in progress: Quentin Ladeveze, “Generic conditions for DRF-SC in axiomatic memory models”, Université de Paris, since October 2019, advised by Luc Maranget and Jean-Marie Madiot.
• PhD in progress: Glen Mével, “Towards a system for proving the correctness of concurrent Multicore OCaml programs”, Université de Paris, since November 2018, advised by Jacques-Henri Jourdan and François Pottier.
• PhD (CIFRE) in progress: Thomas Refis, “Modular Implicits: Design, Formalization, and Implementation”, Université de Paris, since February 2020, advised by Didier Rémy and Thomas Gazagnaire (Tarides).
• PhD: Ambre Williams, “Refactoring functional programs with ornaments”, Université de Paris, defended on December 14, 2020 22, advised by Didier Rémy.
### 9.2.3 Juries
Xavier Leroy chaired the jury for the PhD defense of Lélio Brun (Université PSL, July 2020). He was a member of the jury for the PhD defenses of Raphaël Rieu-Helft (Université Paris-Saclay, November 2020) and Darius Mercadier (Sorbonne Université, November 2020).
François Pottier was a reviewer for the PhD theses of Lionel Parreaux (EPFL, June 2020) and Ralf Jung (MPI-SWS, August 2020).
## 9.3 Popularization
### 9.3.1 Interventions
Xavier Leroy gave a popularization talk on contact tracing applications at lycée Montaigne, Paris, in October 2020.
# 10 Scientific production
## 10.1 Major publications
• 1 articleJ. Alglave, L. Maranget and M. Tautschnig. 'Herding cats: modelling, simulation, testing, and data-mining for weak memory'.ACM Transactions on Programming Languages and Systems3622014,
• 2 articleT. Balabonski, F. Pottier and J. Protzenko. 'The design and formalization of Mezzo, a permission-based programming language'.ACM Transactions on Programming Languages and Systems3842016, 14:1--14:94
• 3 articleN. Courant and X. Leroy. 'Verified Code Generation for the Polyhedral Model'.Proceedings of the ACM on Programming Languages5POPLJanuary 2021, 40:1-40:24
• 4 inproceedingsJ. Cretin and D. Rémy. 'System F with Coercion Constraints'.CSL-LICS 2014: Computer Science Logic / Logic In Computer ScienceACM2014,
• 5 article P. Emílio De Vilhena and F. Pottier. 'A Separation Logic for Effect Handlers'. Proceedings of the ACM on Programming Languages January 2021
• 6 inproceedings A. Guéneau, J.-H. Jourdan, A. Charguéraud and F. Pottier. 'Formal Proof and Analysis of an Incremental Cycle Detection Algorithm'. Interactive Theorem Proving 141 Leibniz International Proceedings in Informatics Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik September 2019
• 7 inproceedingsJ.-H. Jourdan, V. Laporte, S. Blazy, X. Leroy and D. Pichardie. 'A Formally-Verified C Static Analyzer'.POPL'15: 42nd ACM Symposium on Principles of Programming LanguagesACM PressJanuary 2015, 247-259
• 8 inproceedings G. Mével, J.-H. Jourdan and F. Pottier. 'Cosmo: A Concurrent Separation Logic for Multicore OCaml'. ICFP 2020 - 25th ACM SIGPLAN International Conference on Functional Programming ICFP 2020 ACM New-York / Virtual, United States August 2020
• 9 inproceedingsG. Mével, J.-H. Jourdan and F. Pottier. 'Time Credits and Time Receipts in Iris'.European Symposium on Programming11423Lecture Notes in Computer ScienceSpringerApril 2019, 3-29
• 10 articleN. Pouillard and F. Pottier. 'A unified treatment of syntax with binders'.Journal of Functional Programming224--52012, 614--704
## 10.2 Publications of the year
### International journals
• 11 articleN. Courant and X. Leroy. 'Verified Code Generation for the Polyhedral Model'.Proceedings of the ACM on Programming Languages5POPLJanuary 2021, 40:1-40:24
• 12 article P. Emílio De Vilhena and F. Pottier. 'A Separation Logic for Effect Handlers'. Proceedings of the ACM on Programming Languages 5 POPL January 2021
• 13 article 'Cosmo: A Concurrent Separation Logic for Multicore OCaml'. Proceedings of the ACM on Programming Languages 4 ICFP August 2020
• 14 articleG. Radanne, H. Saffrich and P. Thiemann. 'Kindly bent to free us'.Proceedings of the ACM on Programming Languages4ICFPAugust 2020, 1-29
• 15 article P. de Vilhena, F. Pottier and J.-H. Jourdan. 'Spy Game: Verifying a Local Generic Solver in Iris'. Proceedings of the ACM on Programming Languages 4 POPL January 2020
### International peer-reviewed conferences
• 16 inproceedings B. Simner, S. Flur, C. Pulte, A. Armstrong, J. Pichon-Pharabod, L. Maranget and P. Sewell. 'ARMv8-A system semantics: instruction fetch in relaxed architectures'. ESOP 2020 - 29th European Symposium on Programming Dublin, Ireland March 2020
• 17 inproceedingsP. de Vilhena and L. Paulson. 'Algebraically Closed Fields in Isabelle/HOL'.Automated ReasoningIJCAR 2020 - International Joint Conference on Automated Reasoning12167LNCS - Lecture Notes in Computer ScienceParis, FranceJune 2020, 204-220
### National peer-reviewed Conferences
• 18 inproceedings F. Bour, B. Clément and G. Scherer. 'Tail Modulo Cons'. JFLA 2021 - Journées Francophones des Langages Applicatifs Saint Médard d’Excideuil, France April 2021
• 19 inproceedings Q. Ladeveze. 'Mécanisation du modèle RC11 et de la propriété DRF-SC'. JFLA 2021 - 32es Journées Francophones des Langages Applicatifs Saint Médard d’Excideuil, France April 2021
• 20 inproceedings 'Strong Automated Testing of OCaml Libraries'. JFLA 2021 - 32es Journées Francophones des Langages Applicatifs Saint Médard d’Excideuil, France February 2021
### Scientific books
• 21 book 'Software, between mind and matter'. Inaugural lecture at Collège de France March 2020
### Doctoral dissertations and habilitation theses
• 22 thesis A. Williams. 'Refactoring functional programs with ornaments'. Université de Paris / Université Paris Diderot (Paris 7) December 2020
## 10.3 Cited publications
• 28 bookA. Appel. 'Program Logics for Certified Compilers'.Cambridge University Press2014,
• 29 techreportB. Jacobs and F. Piessens. 'The VeriFast Program Verifier'.CW-520Department of Computer Science, Katholieke Universiteit LeuvenAugust 2008,
• 30 articleR. Jung, R. Krebbers, J.-H. Jourdan, A. Bizjak, L. Birkedal and D. Dreyer. 'Iris from the ground up: A modular foundation for higher-order concurrent separation logic'.Journal of Functional Programming282018, e20
• 31 articleL. Lamport. 'How to write a 21st century proof'.Journal of Fixed Point Theory and Applications1112012, 43--63
• 32 articleX. Leroy. 'A formally verified compiler back-end'.Journal of Automated Reasoning4342009, 363--446
• 33 inproceedingsX. Leroy. 'Applicative functors and fully transparent higher-order modules'.Principles of Programming Languages (POPL)January 1995, 142--153
• 34 articleX. Leroy. 'Formal verification of a realistic compiler'.Communications of the ACM5272009, 107--115
• 35 inproceedingsX. Leroy. 'Manifest types, modules, and separate compilation'.Principles of Programming Languages (POPL)January 1994, 109--122
• 36 inproceedingsF. Pottier. 'Reachability and error diagnosis in LR(1) parsers'.Compiler Construction (CC)March 2016, 88--98
• 37 articleL. White, F. Bour and J. Yallop. 'Modular implicits'.Electronic Proceedings in Theoretical Computer Science198December 2015, 22--63
|
{}
|
Open access peer-reviewed chapter
# Determination of Stresses in Composite Plates with Holes and Cracks Based on Singular Integral Equations
Written By
Submitted: May 18th, 2019 Reviewed: June 6th, 2019 Published: August 23rd, 2019
DOI: 10.5772/intechopen.87718
From the Edited Volume
## Dynamical Systems Theory
Edited by Jan Awrejcewicz and Dariusz Grzelczyk
Chapter metrics overview
View Full Metrics
## Abstract
The problems of determination of stresses at crack in bounded plates with holes of different shapes under the action of concentrated forces or distributed forces at its boundary are considered. The study is performed by the singular integral equation method. They were determined based on the established interdependences between the Lekhnitskii potentials and the stress and strain. The numerical method for solving integral equations is developed based on the quadrature method for the systems of holes and cracks. The eigen solutions of the problem were taken into account in this method. The research of stresses at cracks in samples which are used in experimental studies of crack fracture resistance was performed.
### Keywords
• stress intensity factors (SIF)
• composite plates
• holes
• cracks
• crack fracture resistance
• BIEM
• stress-strain state (SSS)
## 1. Introduction
The boundary integral equation method (BIEM) is widely used to study the stress-strain state (SSS) of anisotropic plates with holes [1, 2, 3] and cracks [4, 5, 6, 7, 8, 9]. The integral equations for anisotropic plates are usually determined based on the Somigliana identity. Such equations for plates with given stresses at the boundaries of the plate are hypersingular. At the same time, the same problem for isotropic plates is reduced to singular integral equations [10, 11], for which simple numerical algorithms for solving with given precision are obtained.
In [12, 13], the simple dependencies between the Lekhnitskii complex potentials and stress and strain are obtained. In a simple form based on them and the Cauchy theorem, the integral equations are written for anisotropic plates with holes [12, 13] and cracks [14, 15, 16]. We will use the established dependencies for the construction and regularization of integral equations for anisotropic plates with holes and cracks.
For conducting experimental studies of crack fracture resistance on experimental samples in relation to isotropic materials, theoretical estimates for stresses at cracks are performed.
For such materials, the stresses in samples of different shapes with cracks under the action of stretching or compressing concentrated forces are studied in detail [10]. The experimental samples for the experimental determination of the characteristics of crack fracture resistance of various types of materials are made based on performed studies. We perform similar studies for composite samples.
## 2. The integral representations for anisotropic plates with holes and cracks
We consider a plate which is weakened with a system hole with boundaries L 1 , , L J (j = 1, , J), and cracks are placed along curves Γ k k = 1 K . The L 0 is the outer boundary of plates. Assume ( Figure 1 ) that a plate is loaded with concentrated forces (Xj , Yj ), j = 1, ..., M acting at the points (aj , bj ); tractions X T Y T are applied to the crack edges, which are accepted the same on its opposite edges; and tractions X L Y L are applied to the boundaries of the holes and plate.
### 2.1 Governing equations
Let us start from the Lekhnitskii complex potentials Φ z 1 , Ψ z 2 , where z j = x + s j y and s j , j = 1 , 2 are roots with positive imaginary part of the characteristic equation Δ s = 0 [10]:
where
Δ s = α 11 s 4 2 α 16 s 3 + 2 α 12 + α 66 s 2 2 α 26 s + α 22 andE1
α ij are elastic compliances which are included in the Hooke’s law [10]:
ε x = a 11 σ x + a 12 σ y + a 16 τ xy , ε y = a 12 σ x + a 22 σ y + a 26 τ xy , γ xy = a 16 σ x + a 26 σ y + a 66 τ xy ,
where ε x , ε y , γ xy are strains and σ x , σ y , τ xy are stresses.
Consider an arbitrary path Γ , which belongs to the domain D occupied by the plate, and select a positive direction of traversal ( Figure 2 ).
Then introduce in consideration the stress vectors q Γ at the plane tangent to the curve. The normal to it is located right relative to the selected direction of traversal. The projections X Γ Y Γ of stress vectors q Γ and derivatives of displacements u v with respect to an arc coordinate at the curve through Lekhnitskii complex potentials are determined by the formula [17]:
Y Γ = 2 Re Φ z 1 z 1 + Ψ z 2 z 2 , X Γ = 2 Re s 1 Φ z 1 z 1 + s 2 Ψ z 2 z 2 , E2
u = 2 Re p 1 Φ z 1 z 1 + p 2 Ψ z 2 z 2 , v = 2 Re q 1 Φ z 1 z 1 + q 2 Ψ z 2 z 2 , E3
where u = du / ds , v = dv / ds and z j = dx / ds + s j dy / ds , where ds is a differential of arc at Γ .
The stress vectors q Γ z = X Γ + iY Γ at path Γ are determined using the formulas (2) by the formula:
q Γ = s 1 i z 1 Φ z 1 + s 1 ¯ i z 1 ¯ Φ z 1 ¯ + s 2 i z 2 Ψ z 2 + s 2 ¯ i z 2 Ψ z 2 ¯ . E4
Assume that the vectors X Y and u v are known at path Γ . Then based on Eqs. (2) and (3) at Γ one has [12, 15]
Φ z 1 = v + s 1 u + p 1 X + q 1 Y Δ 1 z 1 , Ψ z 2 = v + s 2 u + p 2 X + q 2 Y Δ 2 z 2 E5
where Δ j = Δ s j , j = 1 , 2 .
### 2.2 Integral equations for anisotropic bounded plate with holes and cracks
Let us write a general solution of the problem based on [12, 15] through the Lekhnitskii potentials in the form
Φ z 1 = L u Φ 1 z 1 t 1 + v Φ 2 ( z 1 t 1 ) ds
+ Γ g 1 Φ 1 z 1 t 1 + g 2 Φ 2 ( z 1 t 1 ) ds + Φ S z 1 + Φ Δ z 1 , E6
Ψ z 2 = L u Ψ 1 z 2 t 2 + v Ψ 2 ( z 2 t 2 ) ds
+ Γ g 1 Ψ 1 z 2 t 2 + g 2 Ψ 2 ( z 2 t 2 ) ds + Ψ S z 2 + Ψ Δ z 2 ,
where L = L 0 + L 1 + + L J , Γ = Γ 1 + Γ 2 + + Γ K , s is an arc coordinate, and Φ Δ z 1 and Ψ Δ z 2 are the known functions, which are determined by the following formulas:
Φ Δ z 1 = L X L Φ 3 z 1 t 1 + Y L Φ 4 ( z 1 t 1 ) ds , Ψ Δ z 1 = L X L Ψ 3 z 1 t 1 + Y L Ψ 4 ( z 1 t 1 ) ds , E7
Φ j = A j t 1 z 1 , Ψ j = B j t 2 z 2 , E8
A 1 = is 1 2 π Δ 1 , A 2 = i 2 π Δ 1 , A 3 = ip 1 2 π Δ 1 , A 4 = iq 1 2 π Δ 1 ,
B 1 = is 2 2 π Δ 2 , B 2 = i 2 π Δ 2 , B 3 = ip 2 2 π Δ 2 , B 4 = iq 2 2 π Δ 2 .
Here, u , v are the values of the derivatives of the displacements with respect to the arc coordinate at the boundary of the plate and holes, g 1 = u + u , g 2 = v + v are the displacements discontinuity at the cracks, u ± , v ± are limit values of displacements in the approach to the section at the left and the right relative to the selected direction, and the potentials Φ S , Ψ S correspond to the concentrated forces and have the form [12]:
Φ S z 1 = i 2 π Δ 1 j = 1 M p 1 X j + q 1 Y j 1 z 1 z 1 j , Ψ S z 2 = i 2 π Δ 2 j = 1 M p 2 X j + q 2 Y j 1 z 2 z 2 j , E9
where in z kj = a j + s k b j , j = 1, 2, and k = 1, 2.
Note that when the boundary is traction free, then Φ Δ = Ψ Δ = 0 .
Let us substitute the potentials (6) into the formulas (4) for projections of stress vectors determined at the boundaries path L and Γ . Using Plemelj-Sokhotski formula, we obtain a system of integral equations [12, 15]:
L u s Q 1 ( Z T ) + v s Q 2 ( Z T ) ds + Γ g 1 s Q 1 ( Z T ) + g 2 s Q 2 ( Z T ) ds = Q Z , Z L Γ , E10
where Q j Z T are stress vectors q L at point Z with coordinates x y . L Γ , the stress vector is determined by the formula (4) accordingly through complex potentials Φ j z 1 t 1 , Ψ j z 2 t 2 , j = 1 , 2 ; T is a point with coordinates ξ η , which belongs to the contour L Γ ; Q Z = Q L Z Q S Z Q Δ Z with Z L and Q Z = Q T Z Q S Z Q Δ Z with Z Γ ; Q L = X L + iY L ; and Q m = X m + iY m , where X m = 2 Re s 1 Φ m z 1 z 1 + s 2 Ψ m z 2 z 2 , Y m = 2 Re Φ m z 1 z 1 + Ψ m z 2 z 2 and
m = S , Δ .
Using the results [12], we obtained that the unknown functions u , v at the boundary of each of the holes L j , j = 0 , 1 , , J in representation (6) are defined up to a summand u ˜ = ω j dy / ds , v ˜ = ω j dx / ds , where ω j are arbitrary constants. At numerical solution of the problem, the constants ω j , j = 0 , , J are to be necessarily fixed. In addition, to ensure the displacement continuity condition, it is necessary to impose the following conditions on unknown functions:
L j u ds = 0 , L j v ds = 0 , j = 0 , , J ; . Γ j g 1 ds = 0 , Γ j g 2 ds = 0 , j = 1 , , K E11
Let us consider a problem-solving equation (10) for the case of one hole and a crack. Let us assume that the contour on which the crack is placed is described parametrically in the form x = α Γ τ , y = β Γ τ , 1 τ 1 , and the equation of the boundary hole is described in the form x = α L θ , y = β L θ , 0 θ < 2 π .
Let us assume the representation for the displacement discontinuity at the cracks:
g 1 s = dg 1 = U Γ τ 1 τ 2 , g 2 s = dg 2 = V Γ τ 1 τ 2 .
Let us replace the integrals with Lobatto-type quadrature formulas [15], and the integrals at the boundaries of the holes replaced by the quadrature of a rectangle, which, for periodic functions, are Gauss quadrature-type formulas [12]. Then we obtain the system of equations:
H k = 1 N O q νk 1 U k L + q νk 2 V k L + m = 1 N Γ C m q νm 1 U m Γ + q νm 2 V m Γ = q ν , ν = 1 , , N O + N Γ 1 , E12
where q νk j = Q j Z ν T k L , p νm j = Q j Z ν T m Γ , q ν = Q L Z ν Q S Z ν Q Δ Z ν ,
U k L = u x k L y k L s k , V k L = v x k L y k L s k , U m Γ = g 1 x m Γ y m Γ s m , V m Γ = g 2 x m Γ y m Γ s m ,
x k L = α L θ k , y k L = β L θ k , θ k = Hk , θ ˜ n = θ n H / 2 , H = 2 π / N O ,
x m T = α Γ τ m , y m T = β Γ τ m , τ m = cos π N m 1 , m = 1 , , N Γ ; C m = π N at m 1 and m N Γ ; C 1 = C N Γ = 0 , 5 π N ; π N = π N Γ 1 ; T k L is a point with coordinates x k L y k L , T m Γ is a point with coordinates x m Γ y m Γ , Z ν is a point with coordinates x ˜ ν L y ˜ ν L with 1 ν N L , and is a point with coordinates x ˜ ν N L Γ y ˜ ν N L Γ with N L < ν N L + N Γ 1 , where x ˜ k L = α L θ ˜ k , y ˜ k L = β L θ ˜ k , θ ˜ n = θ n H / 2 , x ˜ m Γ = α Γ τ ˜ m , y ˜ m Γ = β Γ τ ˜ m , τ ˜ m = cos π N m 0 5 .
We obtain the additional equation of system (12) from condition (11)
k = 1 N Γ C k U k Γ + iV k Γ = 0 . E13
Analogously to [12], we should remove three equations with 1 ν N L and add the following three equations to the received incomplete system:
k = 1 N U k L = 0 , k = 1 N V k L = 0 , U m L = 0 , 1 m N E14
The first two equations follow from the displacements continuity conditions (9). The last equation is obtained when fixing an arbitrary constant ω .
The system of Eqs. (12)(14) is generalized in the case of hole and crack system in the same way as it was done in [12].
## 3. Stresses in circular samples with cracks under the action of concentrated forces
Let us consider the circular composite plate with radius a, which is weakened by a central crack with the half-length L. The plate is stretched by the concentrated forces ± P applied at points 0 ± y 0 . Destruction of the plate is happening when the stress intensity factors (SIFs) reach a certain limit value. Therefore, when we calculated the limiting loads, we considered the SIF which explicitly takes into account the length of the cracks. Due to this, we performed calculations of the relative SIF K a = K I a P π with different relative distances α = y 0 / a , depending on the half-length of the crack, which is divided into a.
Calculations are made for the composite plates with elastic constants shown in Table 1 .
Material E 1 (GPa) E 2 (GPa) G 12 (GPa) ν 21 ν 12
LU 10.8 96.0 2.61 0.21 0.024
EF 21 32.8 5.7 0.21 0.134
### Table 1.
Elastic constants of LU and EF materials.
The results of the calculations for the plate made of an EF material (with a small degree of anisotropy) with the maximum stiffness in the direction of the OX axis are shown in Figure 3 .
In general, the character of the distribution for an EF material is not significantly different from that of an isotropic material. It is necessary to increase monotonically the load for a stable growth of the crack when the distances of forces to a crack are smaller than 0 , 2 a . With y 0 / a = 0 , 3 , the stable growth of cracks (without jumping) will occur at L / a > 0 , 2 ; with y 0 / a = 0 , 4 if L / a > 0 , 25 ; and with y 0 / a = 0 , 5 if L / a > 0 , 35 . At greater distances to forces, after reaching the corresponding level of values of traction, the circle fractures. For a case where the crack is perpendicular to the direction with the maximum stiffness of the material, the SIF is slightly increasing, especially at greater distances to forces.
For a weakly anisotropic material, the incline of the crack to the main axis of orthotropy had little effect on the SIF K I , and the SIF K II is practically absent.
The calculations have shown that for the case of placing the crack in parallel to the direction with the maximum stiffness of the material, the above set of specifics of the SIF remain unchanged for substantially anisotropic LU-1 material. When the crack is placed perpendicular to the direction with maximum stiffness, stable crack growth occurs of small cracks ( L / a 0 , 1 ) when the relative distance to forces is y 0 / a < 0 , 2 . Moreover, for these cases, the fracture is spasmodic. In all other cases, the SIF increases monotonically with increasing crack length. Hence, the plate fractures completely after reaching forces of critical value.
Testing the developed algorithm is conducted for the case of isotropic plate with ν = 0 , 4488 and y 0 / a = 0 , 15 ; 0 , 16 ; 0 , 18 ; 0 , 2 . The calculation results of the relative SIF K a = K I a P are shown in Figure 4 .
On the right are shown figures from the book [10]. Such calculations were also performed for the same material, and here the corresponding relative SIF is represented by dashed lines. It is seen that the results obtained by different methods coincide.
## 4. Determination of working intervals of crack lengths at circular samples
Two types of samples are used in experimental studies of crack fracture resistance [10]. The first is a sample for which the SIF grows monotonically with the growth of the crack. In the second type, the range of cracks’ lengths is selected in such a way that the SIF K I is practically constant. Hence, it is varied in this range from the mean value to the small value (∼2–4%). This range of crack lengths is called working. The samples of the second type are particularly suitable for conducting experimental studies including a wide range of problems in the area of destruction. In particular, with the constant force factor (the SIF is constant) in such samples, the possibility of an effective study of the rate of growth of fatigue cracks with cyclic loads, the study of crack fracture resistance depending on the influence of working environment, etc. arises.
Based on the studies in the literature for isotropic material, it has been established [10] that the range of working lengths is most favorable with α = 0 , 18 , although allowed, and α = 0 , 16 ; 0 , 2 , where α = y 0 / a . With 0 < α < 0 , 2237 the SIF K I increases from zero to a certain maximum (depending on α ), then falls to a minimum, and then increases monotonously. With α > 0 , 2237 the SIF increases monotonically with the increasing length of the crack. We note that such conclusions are valid for material with a Poisson ratio ν = 0 , 4488 .
Since at big lengths of cracks L / a > 0 , 5 the SIF depends little on α , then for the first type of samples α = 0 , 65 is taken.
Based on the obtained results, let us perform a similar study of samples of two types of composite materials.
For samples of the second type, we perform calculations only for small ratios (at α 0 , 2 ). The results of calculations of the SIF in a circular isotropic sample with ν = 1 / 3 are shown in Figure 5 . Here and further is assumed that the relative value of the SIF is equal to K a = K I a P π and the parameter value α is indicated near the curves.
Figure 5 shows that the range with few changed SIF is necessary to determine in the vicinity of the lengths of the cracks with L / a 0 , 25 .
Similar results for the plate made of an EF material are shown in Figures 6 and 7 . Here two cases are considered: the crack is parallel or perpendicular to the direction in which the stiffness of the material is maximal.
From the given data, it is seen that the SIF for an EF material is bigger in the case when the crack is perpendicular to the direction of maximum stiffness of the material.
The following conclusions are made based on the data of the calculations: for the crack that is parallel to the direction of maximum stiffness of the material, the minimum deviations from the constant SIF (with an error of not more than 2%) are achieved on the ranges of lengths of cracks with relative dimensions with Δ < 0 , 21 with α = 0 , 24 0 , 26 , where Δ = L 2 L 1 / a . The biggest range ( Δ = 0 , 27 ) with SIF values close to constants with an error 2 , 1 % is achieved with α = 0 , 24 . For the crack that is perpendicular to the direction of maximum stiffness of the material, the range with SIF values close to constants is reduced. Moreover, the distance of force application needs to be increased. The biggest range ( Δ = 0 , 27 ) with SIF values close to constants with an error 3 , 2 % is achieved with α = 0 , 24 .
Let us consider the case of samples of the first type 1. For them, the forces are selected that are distant from the crack. For isotropic materials, as a rule, α = 0 , 65 is taken. The above-obtained results of the calculations show that the same distance can be chosen for the composite materials with a crack parallel to the principal axes of the orthotropy.
To compare the effect of a sample shape, similar calculations are made for a square plate with a crack. The results of calculations for such an isotropic sample that are similar to the results of calculations for a circle are shown in Figure 8 .
The conclusion is made based on the comparison of Figures 5 and 8 that with small distances of forces from cracks, the shape of the sample has little effect on the SIF.
Similar results of calculations for LU material are shown in Figure 9 for a horizontal crack and in Figure 10 for a diagonal crack.
## 5. Determination of the SSS of samples under the action of the tractions applied to the hole’s boundary
Let us apply the developed algorithm to study a square plate with a half-side a; weakened by a central crack with a half-length L ( Figure 11 ), the edges are not loaded.
Two identical circular holes of radius R, the centers of which are located at points 0 ± c , are created for stretching in a plate. It was assumed that the load was applied to the boundary of the circular holes. Using [10], we accept that the forces act normally on the domain θ θ c < γ and are given on it in the form
p = P θ θ c 2 4 R sin γ γ cos γ , E15
where θ is angle coordinate on each of the holes, θ c is angle coordinate of the middle of the domain, and Р is the principal vector applied to the domain of forces, which is directed from the center of the hole at an angle θ c .
At first, for the purpose of testing the algorithm, the calculations are performed for the case of a localized load at γ = π / 32 and α = c / a = 0 , 2 ; 0 , 4 ; 0 , 6 , with θ c = π / 2 for the upper hole and θ c = π / 2 for the lower hole (thus the stretching of the plate in the direction of the OY axis is considered). The relative SIF Y = K I P πL for an isotropic material with a Poisson ratio ν = 1 / 3 at different crack lengths at R / a = 0 , 1 is calculated and given in Table 2 .
L / a Y Y S Y Y S Y Y S
α = 0.2 α = 0.4 α = 0.6
0.1 0.175 0.177 0.248 0.247 0.271 0.270
0.2 0.721 1.720 0.583 0.581 0.568 0.565
0.3 1.164 1.159 0.958 0.953 0.894 0.888
0.4 1.503 1.495 1.323 1.314 1.237 1.227
0.5 1.819 1.805 1.675 1.663 1.588 1.575
0.6 2.156 2.131 2.034 2.015 1.954 1.935
0.7 2.552 2.505 2.438 2.406 2.367 2.334
0.8 3.112 2.995 2.999 2.917 2.937 2.854
0.9 4.279 4.178 4.131
### Table 2.
Relative SIFs for a square sample, isotropy.
The values of relative SIF Y S obtained by another method in [10] for the case of stretching by concentrated forces (i.e., with γ 0 ) are given in the same table. As you can see, the results for these cases were close, with the exception of the values L / a = 0 , 8 . Some differences in them are due to different localizations of applied tractions.
The results of the calculations of SIF are given in Table 3 for the case R 0 , γ = 0 , that is, the case is considered when forces are applied at the center of the holes and more smoothly applied efforts (at γ = π / 8 ).
γ = π / 8 R 0 , γ = 0 γ = π / 8 (circle)
L / a α = 0.2 0.4 0.6 α = 0.2 0.4 0.6 α = 0.2 0.4 0.6
0.1 0.186 0.254 0.275 0.727 0.462 0.366 0.2069 0.2637 0.2767
0.2 0.732 0.593 0.576 1.073 0.851 0.717 0.7563 0.6096 0.5786
0.3 1.172 0.969 0.905 1.278 1.167 1.049 1.1914 0.9910 0.9101
0.4 1.510 1.335 1.250 1.489 1.452 1.370 1.5415 1.3678 1.2655
0.5 1.827 1.689 1.605 1.742 1.744 1.694 1.8964 1.7516 1.6483
0.6 2.167 2.050 1.974 2.048 2.067 2.039 2.3113 2.1770 2.0811
0.7 2.569 2.459 2.391 2.436 2.459 2.440 2.8332 2.6963 2.6106
0.8 3.139 3.029 2.971 3.008 3.027 3.011 3.5616 3.4216 3.3492
0.9 4.322 4.225 4.181 4.214 4.225 4.209 4.8896 4.7662 4.7132
### Table 3.
Relative SIFs for a square and circular sample, isotropy.
The results for a circular sample with γ = π / 8 are shown ( Figure 12 ) in the same table.
The following conclusions are made based on Tables 2 and 3 : SIF does not differ significantly in the case of distributed loads with different degrees of localization, SIF increases somewhat with the growth of the domain of action of tractions, and SIFs are bigger at small crack lengths at point action of tractions (at R 0 ) and at all lengths with α > 0 , 6 . SIFs in a circular sample are bigger than in a square one under the same load conditions.
Similar results for a square sample made from a LU material are given in Table 4 . Here, the relative SIFs K a in which the crack length is explicitly taken into account and the case where the crack is parallel to the direction of bigger stiffness (data on the left) and is perpendicular to it (data on the right) are given.
LU (Ох) LU (Оу)
L / a α = 0.2 0.4 0.6 α = 0.2 0.4 0.6
0.1 0.2338 0.2633 0.2764 0.4182 0.478 0.538
0.2 0.5187 0.4276 0.4059 1.0504 1.0073 0.9911
0.3 0.5952 0.5259 0.4978 1.1416 1.1306 1.1327
0.4 0.6202 0.5791 0.5595 1.2268 1.2138 1.2163
0.5 0.6409 0.6158 0.6046 1.33 1.3094 1.31
0.6 0.6711 0.6539 0.6479 1.4615 1.4313 1.4304
0.7 0.7252 0.7117 0.7085 1.6257 1.5829 1.5809
0.8 0.8392 0.8284 0.8267 1.7876 1.7411 1.7386
0.9 1.1482 1.1419 1.1409 1.9405 1.8846 1.8831
### Table 4.
Relative SIFs K a for square sample, LU material.
Similar results for a circular sample for the same material are given in Table 5 .
LU (Ох) LU (Оу)
L / a α = 0.2 0.4 0.6 α = 0.2 0.4 0.6
0.1 0.2363 0.2679 0.2806 0.4192 0.4799 0.5407
0.2 0.5269 0.4369 0.4138 1.0594 1.0163 0.9995
0.3 0.6108 0.5418 0.5112 1.1602 1.1477 1.1466
0.4 0.6467 0.605 0.5814 1.2588 1.2422 1.2389
0.5 0.683 0.6558 0.6396 1.3795 1.3531 1.3459
0.6 0.7341 0.7131 0.702 1.5354 1.4974 1.4888
0.7 0.8131 0.7948 0.7879 1.7482 1.6965 1.6905
0.8 0.9524 0.9376 0.9342 2.0507 1.9973 1.9977
0.9 1.2791 1.2726 1.2704 2.592 2.528 2.5346
### Table 5.
Relative SIFs for a circular sample, LU material.
## 6. Determination of the SSS of samples loaded with concentrated forces at the boundary (compression test)
The methods of studied crack fracture resistance based on sample compression in experimental practice are widely used.
The direct application of the abovementioned variant of the method of integral equations for the case when the concentrated forces act on the boundary of the domain is associated with significant errors, because unknown functions in the vicinity of the points of application of forces have a singularity. Due to this, it is necessary to separate a singular part in the solution for a more precise solution of this type of task.
### 6.1 Determining a singular part of the solution of this problem
Let us consider a point of the plate boundary z 0 , in which the concentrated force (X, Y) is applied. A singular part of the solution (of Lekhnitskii potentials) will be the same as in the half-plane, whose boundary is tangent to the plate at the point of action of the concentrated force. Let us mark this angle through φ and potentials for the half-plane through Φ 0 z 1 , Ψ 0 z 2 .
Let us consider at first a half-plane y < 0 , which is loaded with force (X, Y) at an arbitrary point x 0 on the boundary. The Lekhnitskii potentials for this half-plane will be [17]
Φ 0 = A z 1 x 0 , Ψ 0 = B z 2 x 0 ,
where
A = X + s 2 Y 2 πi s 1 s 2 , B = X + s 1 Y 2 πi s 1 s 2 .
It can be shown [17] that the half-plane also corresponds to the Φ 0 , Ψ 0 potentials, whose boundary passes through the point x 0 0 and is inclined at an arbitrary angle under the action of the same force. Let us consider a semicircle with the center at point x 0 0 of radius ρ 0 , which belongs to the half-plane. It is easy to show that the principal vector of all forces applied to the arc of the semicircle is equal to X Y . This proves that the case of loading by the concentrated force of the half-plane corresponds to the potentials Φ 0 , Ψ 0 .
Let us now consider a bounded plate occupying the domain D. The self-balanced concentrated forces X j Y j , j = 1 J . are applied to the boundary of this domain at points z j = x j + iy j . Let us represent the complex potentials in the form
Φ z 1 = Φ 0 z 1 + Φ Δ z 1 , Ψ z 1 = Ψ 0 z 1 + Ψ Δ z 1 , E16
Φ 0 z 1 = j = 1 J A j z 1 z 1 j , Ψ 0 z 2 = j = 1 J B j z 2 z 2 j ,
where z 1 j = x j + s 1 y j , z 2 j = x j + s 2 y j . Here the coefficients A j , B j are determined based on expressions for A , B by the substitution of X and Y on X j and Y j , respectively. By substituting formulas (16) into boundary conditions, we obtain the boundary problem for obtaining the introduced complex potentials at x y L :
1 + is 1 z 1 Φ Δ z 1 + 1 + i s 1 ¯ z 1 ¯ Φ Δ z 1 ¯ + + 1 + is 2 z 2 Ψ Δ z 2 + 1 + i s 2 ¯ z 2 Ψ Δ z 2 ¯ = i X + iY 0 , E17
where L is the boundary of domain D:
i X + iY 0 = 1 + is 1 z 1 Φ 0 z 1 + 1 + i s 1 ¯ z 1 ¯ Φ 0 z 1 ¯ + 1 + is 2 z 2 Ψ 0 z 2 + 1 + i s 2 ¯ z 2 Ψ 0 z 2 ¯ .
It is easy to show that the right-hand side of formula (17) is a continuous and limited function, and therefore the introduced complex potentials with an index Δ are continuous and limited in the vicinity of the points of application of forces. In this regard, the above-developed numerical algorithm based on BIEM can be used to determine these potentials.
### 6.2 Calculation of the SIF for a rectangular sample with compression
Let us consider a square plate with half-side a, which contains a diagonal central vertical crack with half-length L . The crack fracture resistance of such a sample is determined based on compression by force R applied in vertical direction. The tips of the angles, in the vicinity of which forces are applied, can be cut off. Due to this, a sample is considered whose tops have coordinates
z 1 = c , z 2 = ic + z p , z 3 = ic + z m , z 4 , z 5 = z 3 ¯ z 6 = z 2 ¯ ,
where in c = 2 a , z p = h ih , z m = h ih , h is the height of the cut triangle and а is the half-side of the square.
The calculations are performed at h = c / 8 ; moreover, all tops are rounded by the arcs of the circle of the radius a / 10 (the shape of the sample— Figure 13 ).
Calculation of the relative SIF K a = K I a P π for isotopic material and composites of EF and LU with different directions of the orthotropic axis are given in Table 6 . The angle between the crack and the direction with the maximum stiffness of the material is indicated in brackets.
L / a Isotr. EF (90°) EF (0°) LU (90°) LU (0°)
0.1 0.0824 0.0579 0.0727 0.0226 0.0743
0.2 0.1203 0.085 0.1073 0.0332 0.1182
0.3 0.1557 0.1106 0.1407 0.0434 0.1663
0.4 0.1927 0.1384 0.1776 0.0547 0.2217
0.5 0.2354 0.1709 0.2208 0.068 0.2865
0.6 0.2889 0.2107 0.2737 0.0846 0.3643
0.7 0.3544 0.2609 0.3406 0.1059 0.4609
0.8 0.4418 0.3273 0.4301 0.1343 0.5872
### Table 6.
Relative SIF K a when compressing a sample with a diagonal crack.
The table shows a significant effect on the SIF of the placement of the crack relative to the axis with the maximum stiffness of the material. In particular, for cracks parallel to the maximum stiffness direction, the SIFs appeared to be significantly larger than those returned for 90°. The difference between the SIFs for these two directions is increasing for a substantially anisotropic LU material.
Table 7 shows the results of calculations for the case of stretching the same sample with a horizontal crack ( Figure 14 ).
L / a Isotr. EF (0°) EF (90°) LU (0°) LU (90°)
0.1 0.2585 0.2886 0.3499 0.2956 0.7572
0.2 0.3696 0.4065 0.4874 0.4114 0.9247
0.3 0.4617 0.4963 0.5884 0.4936 1.0104
0.4 0.5494 0.5752 0.6766 0.5594 1.1008
0.5 0.641 0.6534 0.7668 0.6185 1.2159
0.6 0.7434 0.7397 0.8705 0.6789 1.364
0.7 0.8641 0.842 0.9973 0.7472 1.5542
0.8 1.0129 0.9704 1.1585 0.8319 1.8021
### Table 7.
Relative SIFs when stretching a sample with a diagonal crack.
Based on the comparison of data from Tables 6 and 7 , it follows that, unlike the case of compression, the SIF with stretching is larger for cracks that are perpendicular to the direction with maximum stiffness of the material.
## 7. Conclusions
An algorithm for calculating stresses at cracks in bounded plate with holes of various shapes due to concentrated forces or distributed forces at its boundary has developed. The solution of integral equations is performed by quadrature Gauss-type formulas for regular and singular integrals.
The research of stresses at cracks in the samples which are used in experimental studies of crack fracture resistance was performed.
The calculation of the stresses at cracks in samples of various forms is performed, in which ones’ experimental research are performed. To study the crack fracture resistance of composite samples, the optimal distances from the central crack to the forces at which the SIF increases monotonously with increasing crack length are determined. In particular, for square samples with a half-side a, forces should be placed at a distance of 0.6a–0.7a from the crack. For the experimental study of the growth rate of fatigue cracks, there are definite ranges of lengths of cracks for which SIFs are practically constant values. At the same time, the distances are determined at which it is expedient to apply forces. The problem for studying samples with cracks with compression is considered.
### List of symbols with explanations
s is an arc coordinate.
ν is a Poisson ratio.
ε x , ε y , γ xy are strains.
σ x , σ y , τ xy are stresses.
α ij are elastic compliances which are included in the Hooke’s law.
Φ z 1 , Ψ z 2 are Lekhnitskii complex potentials.
Φ S , Ψ S are the potentials which correspond to the concentrated forces.
u , v are the values of the derivatives of the displacements with respect to the arc coordinate at the boundary of the plate and holes.
u ± , v ± are limit values of displacements in the approach to the section at the left and the right relative to the selected direction.
q Γ is the stress vector q Γ z = X Γ + iY Γ at path Γ .
K I , K II are the stress intensity factors (SIFs).
K a , Y , Y S are the relative SIFs.
Р is the principal vector.
## References
1. 1. Tsukrov I, Kachanov M. Effective moduli of an anisotropic material with elliptical holes of arbitrary orientational distribution intern. International Journal of Solids and Structures. 2000;37(41):5919-5941. DOI: 10.1016/S0020-7683(99)00244-9
2. 2. Scholar NA. Anisotropic Analysis Using Boundary Elements. Computational Mechanics Publications; 1994, 142 p
3. 3. Brebbia CA, Dominguez J. Boundary Elements: An Introductory Course. McGraw Hill Book Co., Computational Mechanics Publications. 1989
4. 4. Sollero P, Aliabadi MH. Fracture mechanics analysis of anisotropic plates by the boundary element method. International Journal of Fracture. 1993;64:269-284. DOI: 10.1007/BF00017845
5. 5. Tan CL, Gao YL. Boundary element analysis of plane anisotropic bodies with stress concentrations and cracks. Composite Structures. 1992;20:17-28. DOI: 10.1016/0263-8223(92)90008-Z
6. 6. Aliabadi MH, Brebbia CA. Boundary element formulations in fracture mechanics: A review. WIT Transactions on Engineering Sciences. 1970;13:17
7. 7. Garcıa F, Sáez A, Domınguez J. Traction boundary elements for cracks in anisotropic solids. Engineering Analysis with Boundary Elements. 2004;28(6):667-676. DOI: 10.1016/j.enganabound.2003.08.005
8. 8. Tu CH, Chen CS, Yu TT. Fracture mechanics analysis of multiple cracks in anisotropic media. International Journal for Numerical and Analytical Methods in Geomechanics. 2011;35(11):1226-1242. DOI: 10.1002/nag.953
9. 9. Yang S, Yuan F-G. Kinked crack in anisotropic bodies. International Journal of Solids and Structures. 2000;37:6635-6682. DOI: 10.1016/S0020-7683(99)00222-X
10. 10. Savruk MP, Osiv PN, Prokopchuk IV. Numerical Analysis in Plane Problems of Cracks Theory. Kiev: Naukova Dumka; 1989. p. 248
11. 11. Savruk MP, Kazberuk A. Stress Concentration at Notches. Cham: Springer; 2017
12. 12. Maksymovych O, Illiushyn O. Stress calculation and optimization in composite plates with holes based on the modified integral equation method. Engineering Analysis with Boundary Elements. 2017;83:180-187. DOI: 10.1016/j.enganabound.2017.06.009
13. 13. Maksymovych O, Jaroszewicz J. Determination of stress state of anisotropic plates with rigid inclusions based on singular integral equations. Engineering Analysis with Boundary Element. 2018;95:215-221. DOI: 10.1016/j.enganabound.2018.07.004
14. 14. Bozhydarnyk V, Maksymovych O. Elastic equilibrium of an anisotropic half plane with periodic system of holes and cracks. Materials Science. 2001;37(6):857-865. DOI: 10.1023/A:1015632905424
15. 15. Maksymovych O, Pasternak I, Sulym H, Kutsyk S. Doubly periodic cracks in the anisotropic medium with the account of contact of their faces. Acta Mechanica et Automatica. 2014;8(3):160-164. DOI: 10.2478/ama-2014-0029
16. 16. Bozhydarnik VV, Maksymovych OV. Determination of the stressed state near edge cracks in a plate containing a hole of complex shape. Materials Science. 2010;46(1):16-26. DOI: 10.1007/s11003-010-9259-3
17. 17. Lekhnitskii SG. Anisotropic Plates. New York, London, Paris, Montreux, Tokyo, Melbourne: Gordon and Breach Science Publishers; 1987
Written By
|
{}
|
# Square Revolution
Time Limit: 10000/5000 MS (Java/Others)
Memory Limit: 131072/131072 K (Java/Others)
## Description
Alex loves solving algorithmic problems relating with strings. After solving the problem about counting the number of prefix-square free strings of length at most $n$, he is curious in the number of prefix-suffix-square free substrings of a string $s$. Can you help him?
A string is called a square string if it can be obtained by concatenating two copies of the same string (i.e. $s=uu$ for some word $u$). For example, "abab", "aa" are square strings, while "aaa", "abba" are not. A string is called prefix-suffix-square free if none of its prefixes/suffixes is a square.
## Input
There are multiple test cases. The first line of input contains an integer $T$, indicating the number of test cases. For each test case:
The first line contains a string $s=s_{1}s_{2}...s_{n}$ $(1 \le n \le 10^5)$ consisting of lowercase English letters.
There are at most $1000$ test cases and the sum of $n$ does not exceed $10^6$.
## Output
For each test case, output the number of prefix-suffix-square free substrings of $s$.
## Sample Input
4
aaaaa
aabcd
aaabbbccc
kurakujoudo
## Sample Output
5
11
12
66
wange2014
## Source
BestCoder Round #87
|
{}
|
# So much to do, so little time
Trying to squeeze sense out of chemical data
## A Quick Look at the GSK Malaria Dataset
A few days ago, GSK released an approximately 13,000 member compound library (using the CC0 license) that had been tested for activity against P. falciparum. The structures and data have been deposited into ChEMBL and a paper is available, that describes the screening project and results. Following this announcement there was a thread on FriendFeed, where Jean-Claude Bradley suggested that it might be useful to compare the GSK library with a virtual library of about 117,000 Ugi compounds that he’s been using in the Open Notebook malaria project.
There are many ways to do this type of comparison – ranging from a pairwise similarity search to looking at the overlap of the distribution of compound properties in some pre-defined descriptor space. Given the size of the datasets, I decided to look at a faster, but cruder option using the idea of bit spectra, which is essentially the normalized frequency of bits in a binary fingerprint across a dataset.
I evaluated the 881-bit PubChem fingerprints for the two datasets using the CDK and then evaluated the bit spectra using the fingerprint package in R. We can then compare the datasets (at least in terms of the PubChem fingerprint features) by plotting the bit spectra. The two spectra are pretty similar, suggesting very similar distributions of functional groups. However there are a number of differences. For example, for bit positions 145 – 155, the GSK library has a higher occurrence than the Ugi library. These features focus on various types of 5-member rings. Another region of difference occurs around bit position 300 and then around positions 350-375.
The static visualization shown here is a simple summary of the similarity of the datasets, but with appropriate interactive graphics one could easily focus on the specific regions of interest. Another way would be to evaluate the difference spectrum and quickly identify features that are more prevalent in the Ugi library compared to the GSK library (i.e., positive values in the plot shown here) and vice versa.
Written by Rajarshi Guha
May 23rd, 2010 at 1:02 pm
## RNAi in PubChem
While considering ways to disseminate RNAi screening data, I found out that PubChem now contains two RNAi screening datasets – AIDs 1622 and 1904. These screens reuse the PubChem bioaassay formats – which is both good and bad. For example, while there are a few standardized columns (such as PUBCHEM_ACTIVITY_SCORE), the bulk of the user deposited columns are not formally defined. In other words, you’d have to read the assay description. While not a huge deal, it would be nice if we could use pre-existing formats such as MIARE, analogous to MIAME for microarray data. That way we could determine the number of replicates, normalization method employed and other details of the screen. As far as I can tell all aspects an RNAi screen are still not fully defined in the MIAME vocabulary, and there don’t seem to be a whole lot of examples. But it’s a start.
But of course, nothing is perfect. Why, oh why, would a tab delimited format be contained within multiple worksheets of an Excel workbook!
Written by Rajarshi Guha
April 19th, 2010 at 12:19 am
Posted in bioinformatics
Tagged with , ,
When running a high-throughput screen, one usually deals with hundreds or even thousands of plates. Due to the vagaries of experiments, some plates will not be ervy good. That is, the data will be of poor quality due to a variety of reasons. Usually we can evaluate various statistical quality metrics to asses which plates are good and which ones need to be redone. A common metric is the Z-factor which uses the positive and negative control wells. The problem is, that if one or two wells have a problem (say, no signal in the negative control) then the Z-factor will be very poor. Yet, the plate could be used if we just mask those bad wells.
Now, for our current screens (100 plates) manual inspection is boring but doable. As we move to genome-wide screens we need a better way to identify truly bad plates from plates that could be used. One approach is to move to other metrics – SSMD (defined here and applications to quality control discussed here) is regarded as more effective than Z-factor – and in fact it’s advisable to look at multiple metrics rather than depend on any single one.
An alternative trick is to compare the Z-factor for a given plate to the trimmed Z-factor, which is evaluated using the trimmed mean and standard deviations. In our set up we trim 10% of the positive and negative control wells. For a plate that appears to be poor, due to one or two bad control wells, the trimmed Z-factor should be significantly higher than the original Z-factor. But for a plate in which, say the negative control wells all show poor signal, there should not be much of a difference between the two values. The analysis can be rapidly performed using a plot of the two values, as shown below. Given such a plot, we’d probably consider plates whose trimmed Z-factor are less than 0.5 and close to the diagonal. (Though for RNAi screens, Z’ = 0.5 might be too stringent).
From the figure below, just looking at Z-factor would have suggested 4 or 5 plates to redo. But when compared to the trimmed Z-factor, this comes down to a single plate. Of course, we’d look at other statistics as well, but it is a quick way to rapidly identify plates with truly poor Z-factors.
A plot of Z-factor versus trimmed Z-factor for a set of 100 plates
Written by Rajarshi Guha
January 29th, 2010 at 5:47 pm
## Plate Well Series Plots in R
Plate well series plots are a common way to summarize well level data across multiple plates in a high throughput screen. An example can be seen in Zhang et al. As I’ve been working with RNAi screens, this visualization has been a useful way to summarize screening data and the various transformations on that data. It’s fundamentally a simple scatter plot, with some extra annotations. Though the x-axis is labeled with plate number, the values on the x-axis are actually well locations. The y-axis is usually the signal from that well.
Since I use it often, here’s some code that will generate such a plot. The input is a list of matrices or data.frames, where each matrix or data.frame represents a plate. In addition you need to specify a “plate map” – a character matrix indicating whether a well is a sample, (“c”) positive control (“p”), negative control (“n”) or ignored (“x”). The code looks like
1234567891011121314151617181920212223242526 plate.well.series <- function(plate.list, plate.map, draw.sep = TRUE, color=TRUE, ...) { signals <- unlist(lapply(plate.list, as.numeric)) nwell <- prod(dim(plate.list[[1]])) nplate <- length(signals) / nwell cols <- 'black' if (color) { pcolor <- 'red' ncolor <- 'green' colormat <- matrix(0, nrow=nrow(plate.list[[1]]), ncol=ncol(plate.list[[1]])) colormat[which(plate.map == 'n')] <- ncolor colormat[which(plate.map == 'p')] <- pcolor colormat[which(plate.map == 'c')] <- 'black' cols <- sapply(1:nwell, function(x) { as.character(colormat) }) } plot(signals, xaxt='n', ylab='Signal', xlab='Plate Number', col = cols, ...) if (color) legend('topleft', bty='n', fill=c(ncolor, pcolor, 'black'), legend=c('Negative', 'Positive', 'Sample'), y.intersp=1.2) if (draw.sep) { for (i in seq(1, length(signals)+nwell, by=nwell)) abline(v=i, col='grey') } axis(side=1, at = seq(1, length(signals), by=nwell) + (nwell/2), labels=1:nplate) }
An example of such a plot is below
Plate well series plot
Another example comparing normalized data from three runs of an RNAi screen investigating drug sensitization (also highlighting the fact that plate 7 in the 5nm run was messed up):
Comparing runs with plate well series plots
Written by Rajarshi Guha
July 14th, 2009 at 2:01 am
## Hit Selection Methods for RNAi Screens
Over the last few weeks I’ve been getting up to speed on RNAi screening (see Lord et al for a nice overview) and one of the key features in this approach is to reliably select hits for followup. In many ways it is similar to hit selection in small molecule HTS but also employs techniques from the analysis of microarray data.
Very broadly, there are two types of selection methods: statistical and knowledge based. In general, one employs a statistical method first, possibly followed by triaging the initial list using a knowledge based method. As with small molecule HTS, true hits (true positives or TP) in general are the outliers, though it’s possible that assay artifacts will also look like true hits and these would be false positives (FP). But in general, the outliers are easy and the real challenge is with identifying moderately active siRNA’s (or compounds) as actual hits.
One can further divide statistical methods into ranking procedures or thresholding procedures. In the former one ranks the siRNA‘s by some metric and selects as many as can be followed up using available resources. In the latter, one identifies a threshold, above which any siRNA is regarded as a hit. One of the key features of many statistical methods is that they provide bounds on the FP and FN (false negative) rates. This is especially important with thresholding methods.
But what about siRNA‘s that lie just below the threshold? Should one ignore them? Is it possible to further investigate whether they might actually be hits? This is where a knowledge based approach can provide a second level of confirmation for false negatives or positives. This post summarizes recent work on hit selection in RNAi screens.
### Statistical methods
Many statistical methods are similar to or derived from approaches employed in HTS experiments for small molecules. An excellent overview of statistical methods in HTS analysis is given by Malo et al and covers both assay quality metrics as well as hit selection methods.
One of the most common methods is to use a threshold of $$\mu \pm k \sigma$$, where $$\mu$$ and $$\sigma$$ are the mean and standard deviation of the sample wells respectively and k is usually taken to be 3. This is also known as the z-score method, and assumes a normal distribution of signal values. However, in RNAi screens it’s not uncommon to have a number of extreme outliers. Such a situation would skew the mean based threshold to larger values, leading to fewer prospective hits being identified.
Instead, Zhang et al (as well as Chung et al) suggest the use of the $$median \pm 3 \textrm{MAD}$$ method, where MAD is the mean absolute deviation and is given by
$$\textrm{MAD} = 1.4826\, median( | x_i – median(x) | )$$
where $$x_i$$ is the signal from well $\latex i$ and $$x$$ represents all the sample wells. The key feature of this approach is that it is more robust to outliers and violations of the assumption that the signal data is normally distributed. Chung et al present a nice simulation study, highlighting the effectiveness of MAD based selection over mean based.
However, Zhang et al also note that the MAD method is not robust to skewed distributions. To address this they suggest a quartile based threshold method. For the sample data, one calculates the first, second and third quartiles ($$Q_1, Q_2, Q_3$$) and generates the lower and upper thresholds for hit selection as the smallest observed value just above $$Q_1 – c IQR$$ and the largest observed value just below $$Q_3 – c IQR$$ respectively. In both cases, $$IQR = Q_3 – Q_1$$. A key feature of this method is the choice of $$c$$, and is based on the desired targeted error rate (based on a normal distribution). Zhang et al show that one can choose $$c$$ such that the resultant error rate is equivalent to that obtained from a mean or median-based thresholding scheme, for a given $$k$$. Thus for $$k = 3$$ in those methods, the quartile method would set $$c = 1.7239$$.
In contrast to the above methods, which define a threshold and automatically select siRNA’s above the threshold as hits, one can order the wells using a metric and then simply select the top $$n$$ wells for followup, where $$n$$ is dictated by the resources available for followup. In this vein, Wiles et al discuss a variety of ranking metrics methods for RNAi screens. Some of the methods they discuss include simple background substraction quantile normalization and so on IQR normalization. Surprisingly, in their analysis, ranking of siRNA’s based on background subtraction outperformed IQR normalization.
Zhang et al (the Merck people have been busy!) described another ranking procedure based on the Strictly Standardized Mean Difference (SSMD) between signals from individual siRNA’s and a negative control. While conceptually similar to simple schemes such as percentage inhibition, this method is reported to be more robust to variability in the sample and control groups and also has a probabilistic interpretation. The latter aspect allowed the authors to develop a thresholding scheme, based on controlling the false positive and false negative rates.
Another approach described by Konig et al makes use of the fact that in RNAi screens, a given gene is targeted by 2 to 4 different siRNA’s. In contrast, none of the above methods, consider this aspect of an RNAi screen. Their method, termed RSA (redundant siRNA activity) analysis, initially ranks all wells in an assay based on their signals. Next, they consider the rank distribution of all siRNA’s targeting a given gene and determine a p-value, which indicates whether all the siRNA’s targeting a given gene have low ranks. They then rerank all wells based on their p-values , followed by their individual signals. The net result of this is that, even though a gene might have 4 wells (i.e., siRNA’s) exhibiting moderate activity (and so might be just below the threshold in a mean or MAD based analysis), it will be “weighted” more heavily than a gene with, say, just one highly active siRNA. Their experiments and analysis indicate that this is a useful method and their implementations (C#, Perl, R) are available. A nice side effect of this method is that they are able suggest an optimal (in terms of efficacy) number of redundant siRNA’s per gene.
### Platewise or experimentwise?
One aspect that I haven’t mentioned is whether these analyses should be performed in a platewise manner or across all the plates in an experiment (i.e. experimentwise manner). Given that an RNAi screen can include a large number of plates, it’s possible that plate specific effects might skew an anaysis that considers all plates together. Thus platewise analysis can handle different systematic errors within plates. At the same time, a platwise analysis would be ignorant of any clustering that may be present amongst the hits, which would be identifiable is one performed the analysis in an experimentwise manner. Zhang et al suggest the following scheme, based on their observations that platewise analysis tends to have a higher probability of identifying true hits.
• Select a thresholding method
• Apply the method in an experimentwise manner on the normalized data, to see if hit clusters are present
• If such clusters are present, repeat the above step on un-normalized data to check whether clustering is an artifact
• If no clusters are observed, perform the analysis in a platewise manner and select hits from each plate
While a useful protocol, Zhang et al describe a Bayesian approach, derived from a similar method for microarray data (Newton et al). One of the key features of this approach is that it incorporates aspects of a platewise and experimentwise analysis in a single framework, obviating the need to choose one or the other.
### Knowledge based methods
The statistics based methods work on the basis of relatively large samples and employ a variety of distributional assumptions. They’re certainly useful as a first pass filter, but various questions remain: Should we totally ignore wells that lie just below a threshold? Is there a way to check for false negatives? False positives?
To address these questions, before running a follow up screen, one can make use of external knowledge. More specifically, genes do not exist in isolation. Rather, they can be considered in terms of networks. Indeed, studies of PPI‘s (Chuang et al) and disease genes (Kohler et al) have suggested a guilt by association principle – genes that are close together in a network are more likely to exhibit similar functions or lead to similar phenotypes.
Wang et al employed this principle to characterize the genes targeted by siRNA’s in a screen, by constructing an interaction network (based on STRING data) and analyzing the connectivity of the genes from the screen in this context. Their observation was that genes corresponding to hits from the RNAi screen exhibited a higher degree of connectivity, compared to random networks. While an interesting approach, some of it does seem a little ad hoc. Given the fact that it depends on PPI data, the networks constructed from screening results may be incomplete, if the PPI database does not contain interactions for the genes in question. In addition, while their network based scoring method seems to correlate somewhat with followup results, it’s not very consistent. However, the approach makes sense and correctly catches false negatives in their test cases. Their R code for the network based scoring system is available.
Interestingly, I haven’t found many other studies of such knowledge based hit selection methods. While networks are one way to identify related genes, other methods could be considered and it would be interesting to see how they compare.
Written by Rajarshi Guha
June 21st, 2009 at 8:49 pm
Posted in research
Tagged with ,
|
{}
|
質問する
# DiesNuts's profile - activity
2019-03-21 01:18:58 +0200 バッジを受け取った ● 有名な質問 (source) 2019-03-21 01:18:58 +0200 バッジを受け取った ● 卓越した質問 (source) 2018-11-15 20:22:56 +0200 バッジを受け取った ● 卓越した質問 (source) 2018-11-15 20:22:56 +0200 バッジを受け取った ● 有名な質問 (source) 2018-11-15 20:22:56 +0200 バッジを受け取った ● 人気の質問 (source) 2018-10-02 05:29:04 +0200 バッジを受け取った ● 人気の質問 (source) 2018-06-10 15:19:13 +0200 バッジを受け取った ● 有名な質問 (source) 2018-04-17 21:08:54 +0200 バッジを受け取った ● 有名な質問 (source) 2018-02-14 17:13:54 +0200 バッジを受け取った ● 有名な質問 (source) 2018-01-24 08:46:30 +0200 バッジを受け取った ● 有名な質問 (source) 2018-01-24 08:46:30 +0200 バッジを受け取った ● 卓越した質問 (source) 2017-12-10 17:01:36 +0200 バッジを受け取った ● 有名な質問 (source) 2017-11-09 21:08:56 +0200 バッジを受け取った ● 人気の質問 (source) 2017-08-06 12:15:07 +0200 バッジを受け取った ● 卓越した質問 (source) 2017-08-06 12:15:07 +0200 バッジを受け取った ● 人気の質問 (source) 2017-08-06 12:15:07 +0200 バッジを受け取った ● 有名な質問 (source) 2017-07-27 15:08:49 +0200 バッジを受け取った ● 有名な質問 (source) 2017-06-28 20:40:28 +0200 バッジを受け取った ● 卓越した質問 (source) 2017-04-22 00:01:12 +0200 バッジを受け取った ● 卓越した質問 (source) 2017-04-21 08:00:08 +0200 バッジを受け取った ● 有名な質問 (source) 2017-04-21 08:00:08 +0200 バッジを受け取った ● 卓越した質問 (source) 2017-04-10 18:27:28 +0200 バッジを受け取った ● 人気の質問 (source) 2017-04-07 01:18:58 +0200 バッジを受け取った ● 卓越した質問 (source) 2017-04-05 13:24:39 +0200 バッジを受け取った ● 有名な質問 (source) 2017-01-19 16:13:19 +0200 ベストアンサーマーク average of sums Let's say I have some data on columns B through E that I want to average as follows: for each row: sum the four columns then take the average such sum Do I have to get another column for the sum and then take the average of that column or is there a more direct approach? Because pulling =SUM(...) down 500'000 rows does take a while. 2017-01-19 16:13:11 +0200 ベストアンサーマーク calc - calculate with custom timestamps Let's say I have cells with custom timestamps, e.g. 2016-10-18T14:14:09.831Z-GET 2016-10-18T15:05:09.854Z-GET And I want to calculate the time elapsed in-between them (in this case, roughly 3060seconds). How do I do that? 2017-01-19 16:12:11 +0200 ベストアンサーマーク calc - find value in subtable Let's say I have a sheet and somewhere on it a table like AAAA 8 16 32 48 64 50 x08050 x16050 x32050 x48050 x64050 150 x08150 x16150 x32150 x48150 x64150 250 x08250 x16250 x32250 x48250 x64250 350 x08350 x16350 x32350 x48350 x64350 450 x08450 x16450 x32450 x48450 x64450 550 x08550 x16550 x32550 x48550 x64550 650 x08650 x16650 x32650 x48650 x64650 where xYYZZZ represents the value in the column for YY and the row for ZZZ How do I perform a lookup the kind of "Find me AAAA(YY,ZZ)"? E.g. let's assume AAAA is at I32 then x64650 would be at N38. and say I want to lookup x48550 I'm looking for a way to say find me the value in J32:N38 where the value on the same row in column I is 550 and the value on the same column in row 32 is 48. 2017-01-19 16:12:05 +0200 ベストアンサーマーク calc - vary column in indirect Assume sheets that have some values on columns B-K. Each sheet has R2=AVERAGE(INDIRECT("b"&$O$2):INDIRECT("b"&$O$3)) R3=STDEV(INDIRECT("b"&$O$2):INDIRECT("b"&$O$3)) for, say, O2=1436 O3=10260 How can I write the indirect s.t. I can drag it right to sumarise the other columns? i.e. S2=AVERAGE(INDIRECT("c"&$O$2):INDIRECT("c"&$O$3)) S3=STDEV(INDIRECT("c"&$O$2):INDIRECT("c"&$O$3)) T2=AVERAGE(INDIRECT("d"&$O$2):INDIRECT("d"&$O$3)) T3=STDEV(INDIRECT("d"&$O$2):INDIRECT("d"&$O$3)) 2017-01-19 16:12:03 +0200 ベストアンサーマーク calc - copy row to column Say I have some data in sheet Sheet_A on R2:AA2 I now want to reference that data in Sheet_B in B2:B10 How do I do that? If I write Sheet_B.B2 = Sheet_A.R$2 And then drag down, it will result in Sheet_B.B3 = Sheet_A.R$2 But I want Sheet_B.B3 = Sheet_A.S$2 2017-01-19 16:12:00 +0200 ベストアンサーマーク calc - filename from cell Let's say I have sheets "myStuff_10", "myStuff_30", ... imported on the A column, I have 10 30 50 70 ... and in the C column, I want to have ='myStuff_10'.$B$5 ='myStuff_30'.$B$5 ... How can I take that value from the A column, though? I.e. ='myStuff_'.$B$5 ='myStuff_'.$B$5 ... something like (doesn't work, ERR:501): =INDIRECT("myStuff_"&A3).$B$5 such that I can drag it down rather than manually adjust a thousand cells? 2016-12-14 11:26:30 +0200 バッジを受け取った ● 卓越した質問 (source) 2016-12-14 09:37:41 +0200 コメント付き回答 calc - using tuples/vectors @Lupp I would appreciate it if you could share that BASIC version because I cannot upgrade to 5.2 (tried, it got me W: Failed to fetch http://ppa.launchpad.net/libreoffice/libreoffice-5-2/ubuntu/dists/wily/main/binary-amd64/Packages 404 Not Found W: Failed to fetch http://ppa.launchpad.net/libreoffice/libreoffice-5-2/ubuntu/dists/wily/main/binary-i386/Packages 404 Not Found 2016-12-13 16:37:24 +0200 コメント付き回答 calc - using tuples/vectors That looks like what I'm looking for ... but my libre office calc doesn't know any TEXTJOIN function. 2016-12-13 14:17:40 +0200 コメント付き回答 calc - using tuples/vectors it's not a particularly hard macro, I just have no idea how to code it in calc. 2016-12-13 14:16:14 +0200 コメント付き回答 calc - using tuples/vectors @Lupp thank you, I am aware of the OFFSET and the INDIRECT. What I NEED, though, is an agreeable representation so I can export the table and include it into a latex document. So as that's not supported, I'm looking for a macro that will produce that for me. E.g. let's call that macro vec. so =vec(A1) should produce ="("&A1&")", =vec(A1:A3) should produce ="("&A1&","&A2&","&A3&")", =vec(A1,X5:X99,Z3)should result in="("&A1&","&"X5"&","&X6&...&x99&","&Z3&")" 2016-12-13 14:12:35 +0200 バッジを受け取った ● 人気の質問 (source) 2016-12-13 11:59:21 +0200 コメント付き回答 calc - using tuples/vectors So ... what you're saying is I need to write B1="("&A1&","&A2&","&A3&")" and then C1=AVERAGE(A1:A3). You wouldn't happen to know how to write a macro to which I can pass a variable number of arguments (single cells or cell ranges) and that will construct me the obnoxious ="("&X1&","&Y4002&","&Z19&"," & ... & ")" formula? 2016-12-13 11:06:56 +0200 質問をする calc - using tuples/vectors Let's say I have values A1 = 3 A2 = 5 A3 = 17 How do I get calc to display a vector containing these three values in cell B1? I.e: B1= (3,5,17) And can I then just - for example - C1=AVERAGE(B1) to get C1 = 8.33333 ? 2016-12-09 09:20:13 +0200 バッジを受け取った ● 卓越した質問 (source) 2016-12-09 08:40:04 +0200 コメント付き回答 calc - copy formulae without adjusting nope, doesn't work. it still adds the file references. 2016-12-08 11:30:42 +0200 コメント付き回答 calc - copy formulae without adjusting This actually works. Did not expect that. Thank you. 2016-12-08 11:28:14 +0200 コメント付き回答 calc - copy formulae without adjusting I am not familiar with the INDEX function. how would you rewrite =AVERAGE(OFFSET($mw_rep0.E:E,$B$8,0,$B$9-$B$8,1)~OFFSET($mw_rep1.E:E,$B$8,0,$B$9-$B$8,1)~OFFSET($mw_rep2.E:E,$B$8,0,$B$9-$B$8,1)) using INDEX? 2016-12-08 11:24:53 +0200 コメント付き質問 calc - #value when computing vector percentiles? @Lupp Well, since I cannot edit my post, let me put a link to such a file here: https://drive.google.com/open?id=0B_i... The problem is on the "middleware" sheet (Cells F12, G12). As for the "splitting" part, I don't have much choice. The data comes from individual files. 2016-12-07 18:19:31 +0200 バッジを受け取った ● 人気の質問 (source) 2016-12-07 15:05:02 +0200 質問をする calc - copy formulae without adjusting So I have prepared a summary sheet with some really nasty formulae that reference other sheets in the same file. In their simplest form, they are of the form =AVERAGE(OFFSET($mw_rep0.E:E,$B$8,0,$B$9-$B$8,1)~OFFSET($mw_rep1.E:E,$B$8,0,$B$9-$B$8,1)~OFFSET($mw_rep2.E:E,$B$8,0,$B$9-$B$8,1)) In the uglier versions, they come as =PERCENTILE(OFFSET($mw_rep0.B:B,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep0.C:C,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep0.D:D,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep0.E:E,$B$8,0,$B$9-$B$8,1)~OFFSET($mw_rep1.B:B,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep1.C:C,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep1.D:D,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep1.E:E,$B$8,0,$B$9-$B$8,1)~OFFSET($mw_rep2.B:B,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep2.C:C,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep2.D:D,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep2.E:E,$B$8,0,$B$9-$B$8,1),0.9) and need to be entered with CTRL+SHIFT+ENTER. As I have other files that need the same kind of summary but for THEIR sheets, I have named the sheets in these files accordingly. So I CTRL+A, CTRL+C, switch to the other document and CTRL+V. Works "great", EXCEPT all the sheet references have been prefixed by the file name (i.e. $mw_rep0 becomes 'file:///home/.../myFirstDocument.ods'#$mw_rep0), which in turn results in most cells displaying Err:502 instead of the calculated values from the new sheet. How do I copy the sheet WITHOUT doing that transformation? I can't copy-paste each cell's formula one-by-one into all the files that need them because I kind of need to get done before I die of old age. 2016-12-07 13:56:25 +0200 質問をする calc - #value when computing vector percentiles? The range below basically say "cut off everything before $B$8 and everything after $B$9$ and for the remaining, sum columns I,J where the values are distributed over multiple sheets (3 in this case, "mw_rep0", "mw_rep1", "mw_rep2"). OFFSET($mw_rep0.I:I,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep0.J:J,$B$8,0,$B$9-$B$8,1),OFFSET($mw_rep1.I:I,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep1.J:J,$B$8,0,$B$9-$B$8,1),OFFSET($mw_rep2.I:I,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep2.J:J,$B$8,0,$B$9-$B$8,1) I will refer to this as range1 (though I have to copy-paste it to use it because apparently, you cannot create a name for it). So =AVERAGE(range1) entered with CTRL+SHIFT+ENTER will calculate me the average sum. Now I want percentiles. To that end, I modify range1 such that the terms for each sheet are separeted by ~, rather than by ,: e.g: =PERCENTILE(OFFSET($mw_rep0.I:I,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep0.J:J,$B$8,0,$B$9-$B$8,1)~OFFSET($mw_rep1.I:I,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep1.J:J,$B$8,0,$B$9-$B$8,1)~OFFSET($mw_rep2.I:I,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep2.J:J,$B$8,0,$B$9-$B$8,1),0.9) when I enter this with CTRL+SHIFT+ENTER, I get #VALUE!. Which I find strange because I have an even uglier range summing up columns B,C,D,E, for which this works: OFFSET($mw_rep0.B:B,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep0.C:C,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep0.D:D,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep0.E:E,$B$8,0,$B$9-$B$8,1),OFFSET($mw_rep1.B:B,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep1.C:C,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep1.D:D,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep1.E:E,$B$8,0,$B$9-$B$8,1),OFFSET($mw_rep2.B:B,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep2.C:C,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep2.D:D,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep2.E:E,$B$8,0,$B$9-$B$8,1) I will refer to this as range0. Here, both, =AVERAGE(range0) and percentiles (for which we again modify range0 such that the individual sheets' terms are separated by tilde, rather than comma) work. e.g. =PERCENTILE(OFFSET($mw_rep0.B:B,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep0.C:C,$B$8,0,$B$9-$B$8,1)+OFFSET($mw_rep0.D:D,$B$8,0,$B$9-$B$8,1)+OFFSET ... 2016-12-06 12:06:57 +0200 質問をする calc - CALCulate mathematical formulae Say I have three parameters: m (in cell B2) lambda (in cell B7) mu (in cell B8) where I can easily calculate rho = lambda/(m*mu) (in cell B10) I now want to calculate p0 = 1/(1 + (m * rho)^m/(m!*(1-rho)) + sum[n=1 to m-1]( (m*rho)^n / n!) ) How do I enter the sum? (1/(1+(B2 * (B7/(B2*B8)))^B2/(FACT(B2) * (1-(B7/(B2*B8)))) + ???)) note: I'm generating these formulae in bash so I don't need to use named cells and can re-use the generated formulae by copying the column and changing the parameters for your convenience: lambda="B7" mu="B8" m="B2" rho="($lambda/($m*$mu))" echo -e "rho =\n\t$rho" p0="(1/(1+($m * $rho)^$m/(FACT($m) * (1-$rho)) + ???))" echo -e "p0 =\n\t\$p0" 2016-12-02 13:10:38 +0200 バッジを受け取った ● 人気の質問 (source)
|
{}
|
It is too bad the motors weren’t listed as Free Power, Free Electricity, Free Electricity, Free Power etc. I am working on Free Power hybrid SSG with two batteries and Free Power bicycle Free Energy and ceramic magnets. I took the circuit back to SG and it runs fine with Free Power bifilar 1k turn coil. When I add the diode and second battery it doesn’t work. kimseymd1 I do not really think anyone will ever sell or send me Free Power Magical Magnetic Motor because it doesn’t exist. Therefore I’m not Free Power fool at all. Free Electricity realistic. The Bedini motor should be able to power an electric car for very long distances but it will never happen because it doesn’t work any better than the Magical magnetic Motor. All smoke and mirrors – No Working Models that anyone can operate. kimseymd1Harvey1You call this Free Power reply?
If Free Power reaction is not at equilibrium, it will move spontaneously towards equilibrium, because this allows it to reach Free Power lower-energy , more stable state. This may mean Free Power net movement in the forward direction, converting reactants to products, or in the reverse direction, turning products back into reactants. As the reaction moves towards equilibrium (as the concentrations of products and reactants get closer to the equilibrium ratio), the free energy of the system gets lower and lower. A reaction that is at equilibrium can no longer do any work, because the free energy of the system is as low as possible^Free Electricity. Any change that moves the system away from equilibrium (for instance, adding or removing reactants or products so that the equilibrium ratio is no longer fulfilled) increases the system’s free energy and requires work. Example of how Free Power cell can keep reactions out of equilibrium. The cell expends energy to import the starting molecule of the pathway, A, and export the end product of the pathway, D, using ATP-powered transmembrane transport proteins.
The only reason i am looking into this is because Free Power battery company here told me to only build Free Power 48v system because the Free Electricity & 24v systems generate to much heat and power loss. Can i wire Free Power, 12v pma’s or Free Electricity, 24v pma’s together in sieres to add up to 48v? If so i do not know how to do it and will that take care of the heat problem? I am about to just forget it and just build Free Power 12v system. Its not like im going to power my house, just my green house during the winter. Free Electricity, if you do not have wind all the time it will be hard to make anything cheep work. Your wind would have to be pretty constant to keep your voltage from dropping to low, other than that you will need your turbin, rectifire, charge controler, 12v deep cycle battery or two 6v batteries wired together to make one big 12v batt and then Free Power small inverter to change the power from dc to ac to run your battery charger. Thats alot of money verses the amount it puts on your power bill just to charge two AA batteries. Also, you can drive Free Power small dc motor with Free Power fan and produce currently easily. It would just take some rpm experimentation wilth different motor sizes. Kids toys and old VHS video recorders have heaps of dc motors.
Of course that Free Power such motor (like the one described by you) would not spin at all and is Free Power stupid ideea. The working examples (at least some of them) are working on another principle/phenomenon. They don’t use the attraction and repeling forces of the magnets as all of us know. I repeat: that is Free Power stupid ideea. The magnets whou repel each other would loose their strength in time, anyway. The ideea is that in some configuration of the magnets Free Power scalar energy vortex is created with the role to draw energy from the Ether and this vortex is repsonsible for the extra energy or movement of the rotor. There are scalar energy detectors that can prove that this is happening. You can’t detect scalar energy with conventional tools. The vortex si an ubiquitos thing in nature. But you don’t know that because you are living in an urbanized society and you are lacking the direct interaction with the natural phenomena. Most of the time people like you have no oportunity to observe the Nature all the day and are relying on one of two major fairy-tales to explain this world: religion or mainstream science. The magnetism is more than the attraction and repelling forces. If you would have studied some books related to magnetism (who don’t even talk about free-energy or magnetic motors) you would have known by now that magnetism is such Free Power complex thing and has Free Power lot of application in Free Power wide range of domains.
Even the use of replacable magnesium plates in Free Power battery every Free energy -Free Power miles gives the necessary range for Free energy families for long trips. Magnet-only motors are easy to build. There are plans around. They are cheap to build. Trouble is no one knows how to get them to spin unaided. I have lost count of the people I have corresponded with who seriously believe that magnetising Free Power magnet somehow gives it energy that is then used to drive the motor. Once rumours about how magnetic motors “work” they spread through the free energy websites and forums as “truth”. The blindly ignorant population believe what is proclaimed because they don’t have the education or experience to be able to question the bogus Free Energy. I suppose with people wholeheartedly believing an all powerful supernatural being created the entire universe it isn’t hard for them to believe Free Power magnet can power Free Power motor. Both thoughts demonstrate ignorance. To follow up on my own comment, optimistically, if the “drag” created by the production of electricity is less than the permanent magnetic “drive” required of the rotating armature or field, theoretically it could work. Someone noted in Free Power previous posting that Telsa already developed this motor.
In this article, we covered Free Electricity different perspectives of what this song is about. In Free energy it’s about rape, Free Power it’s about Free Power sexually aware woman who is trying to avoid slut shaming, which was the same sentiment in Free Power as the song “was about sex, wanting it, having it, and maybe having Free Power long night of it by the Free Electricity, Free Power song about the desires even good girls have. ”
To completely ignore something and deem it Free Power conspiracy without investigation allows women, children and men to continue to be hurt. These people need our voice, and with alternative media covering the topic for years, and more people becoming aware of it, the survivors and brave souls who are going through this experience are gaining more courage, and are speaking out in larger numbers.
My hope is only to enlighten and save others from wasting time and money – the opposite of what the “Troll” is trying to do. Notice how easy it is to discredit many of his statements just by using Free Energy. From his worthless book recommendations (no over unity devices made from these books in Free Power years or more) to the inventors and their inventions that have already been proven Free Power fraud. Take the time and read ALL his posts and notice his tactics: Free Power. Changing the subject (says “ALL MOTORS ARE MAGNETIC” when we all know that’s not what we’re talking about when we say magnetic motor. Free Electricity. Almost never responding to Free Power direct question. Free Electricity. Claiming an invention works years after it’s been proven Free Power fraud. Free Power. Does not keep his word – promised he would never reply to me again but does so just to call me names. Free Power. Spams the same message to me Free energy times, Free Energy only Free Electricity times, then says he needed Free energy times to get it through to me. He can’t even keep track of his own lies. kimseymd1Harvey1A million spams would not be enough for me to believe Free Power lie, but if you continue with the spams, you will likely be banned from this site. Something the rest of us would look forward to. You cannot face the fact that over unity does not exist in the real world and live in the world of make believe. You should seek psychiatric help before you turn violent. jayanth Free Energy two books! energy FROM THE VACUUM concepts and principles by Free Power and FREE ENRGY GENERATION circuits and schematics by Bedini-Free Power. Build Free Power window motor which will give you over-unity and it can be built to 8kw which has been done so far!
Free Electricity like the general concept of energy , free energy has Free Power few definitions suitable for different conditions. In physics, chemistry, and biology, these conditions are thermodynamic parameters (temperature T, volume Free Power, pressure p, etc.). Scientists have come up with several ways to define free energy. The mathematical expression of Helmholtz free energy is.
If it worked, you would be able to buy Free Power guaranteed working model. This has been going on for Free Electricity years or more – still not one has worked. Ignorance of the laws of physics, does not allow you to break those laws. Im not suppose to write here, but what you people here believe is possible, are true. The only problem is if one wants to create what we call “Magnetic Rotation”, one can not use the fields. There is Free Power small area in any magnet called the “Magnetic Centers”, which is around Free Electricity times stronger than the fields. The sequence is before pole center and after face center, and there for unlike other motors one must mesh the stationary centers and work the rotation from the inner of the center to the outer. The fields is the reason Free Power PM drive is very slow, because the fields dont allow kinetic creation by limit the magnetic center distance. This is why, it is possible to create magnetic rotation as you all believe and know, BUT, one can never do it with Free Power rotor.
Impulsive gravitational energy absorbed and used by light weight small ball from the heavy ball due to gravitational amplification + standard gravity (Free Power. Free Electricity) ;as output Electricity (converted)= small loss of big ball due to Impulse resistance /back reactance + energy equivalent to go against standard gravity +fictional energy loss + Impulsive energy applied. ” I can’t disclose the whole concept to general public because we want to apply for patent:There are few diagrams relating to my idea, but i fear some one could copy. Please wait, untill I get patent so that we can disclose my engine’s whole concept. Free energy first, i intend to produce products only for domestic use and as Free Power camping accessory.
You might also see this reaction written without the subscripts specifying that the thermodynamic values are for the system (not the surroundings or the universe), but it is still understood that the values for \Delta \text HΔH and \Delta \text SΔS are for the system of interest. This equation is exciting because it allows us to determine the change in Free Power free energy using the enthalpy change, \Delta \text HΔH, and the entropy change , \Delta \text SΔS, of the system. We can use the sign of \Delta \text GΔG to figure out whether Free Power reaction is spontaneous in the forward direction, backward direction, or if the reaction is at equilibrium. Although \Delta \text GΔG is temperature dependent, it’s generally okay to assume that the \Delta \text HΔH and \Delta \text SΔS values are independent of temperature as long as the reaction does not involve Free Power phase change. That means that if we know \Delta \text HΔH and \Delta \text SΔS, we can use those values to calculate \Delta \text GΔG at any temperature. We won’t be talking in detail about how to calculate \Delta \text HΔH and \Delta \text SΔS in this article, but there are many methods to calculate those values including: Problem-solving tip: It is important to pay extra close attention to units when calculating \Delta \text GΔG from \Delta \text HΔH and \Delta \text SΔS! Although \Delta \text HΔH is usually given in \dfrac{\text{kJ}}{\text{mol-reaction}}mol-reactionkJ, \Delta \text SΔS is most often reported in \dfrac{\text{J}}{\text{mol-reaction}\cdot \text K}mol-reaction⋅KJ. The difference is Free Power factor of 10001000!! Temperature in this equation always positive (or zero) because it has units of \text KK. Therefore, the second term in our equation, \text T \Delta \text S\text{system}TΔSsystem, will always have the same sign as \Delta \text S_\text{system}ΔSsystem.
# Look in your car engine and you will see one. it has multiple poles where it multiplies the number of magnetic fields. sure energy changes form, but also you don’t get something for nothing. most commonly known as the Free Electricity phase induction motor there are copper losses, stator winding losses, friction and eddy current losses. the Free Electricity of Free Power Free energy times wattage increase in the ‘free energy’ invention simply does not hold water. Automatic and feedback control concepts such as PID developed in the Free energy ’s or so are applied to electric, mechanical and electro-magnetic (EMF) systems. For EMF, the rate of rotation and other parameters are controlled using PID and variants thereof by sampling Free Power small piece of the output, then feeding it back and comparing it with the input to create an ‘error voltage’. this voltage is then multiplied. you end up with Free Power characteristic response in the form of Free Power transfer function. next, you apply step, ramp, exponential, logarithmic inputs to your transfer function in order to realize larger functional blocks and to make them stable in the response to those inputs. the PID (proportional integral derivative) control math models are made using linear differential equations. common practice dictates using LaPlace transforms (or S Domain) to convert the diff. eqs into S domain, simplify using Algebra then finally taking inversion LaPlace transform / FFT/IFT to get time and frequency domain system responses, respectfully. Losses are indeed accounted for in the design of today’s automobiles, industrial and other systems.
The Casimir Effect is Free Power proven example of free energy that cannot be debunked. The Casimir Effect illustrates zero point or vacuum state energy , which predicts that two metal plates close together attract each other due to an imbalance in the quantum fluctuations. You can see Free Power visual demonstration of this concept here. The implications of this are far reaching and have been written about extensively within theoretical physics by researchers all over the world. Today, we are beginning to see that these concepts are not just theoretical but instead very practical and simply, very suppressed.
I don’t know what to do. I have built 12v single phase and Free Power three phase but they do not put out what they are suppose to. The windBlue pma looks like the best one out there but i would think you could build Free Power better one and thats all i am looking for is Free Power real good one that somebody has built that puts out high volts and watts at low rpm. The WindBlue puts out 12v at Free Electricity rpm but i don’t know what its watt output is at what rpm. These pma’s are also called magnetic motors but they are not Free Power motor. They are Free Power generator. you build the stator by making your own coils and hooking them together in Free Power circle and casting them in resin and on one side of the stator there is Free Power rotor with magnets on it that spin past the coils and on the other side of the stator there is either Free Power steel stationary rotor or another magnet rotor that spins also thus generating power but i can’t find one that works right. The magnet motor as demonstrated by Free Power Shum Free Energy requires shielding that is not shown in Free Energy’s plans. Free Energy’s shielding is simple, apparently on the stator. The Perendev shows each magnet in the Free Energy shielded. Actually, it intercepts the flux as it wraps around the entire set of magnets. The shielding is necessary to accentuate interaction between rotor and stator magnets. Without shielding, the device does not work. Hey Gilgamesh, thanks and i hope you get to build the motor. I did forget to ask one thing on the motor. Are the small wheels made of steel or are they magnets? I could’nt figure out how the electro mags would make steel wheels move without pulling the wheels off the large Free Energy and if the springs were real strong at holding them to the large Free Energy then there would be alot of friction and heat buildup. Ill look forward to hearing from you on the PMA, remember, real good plan for low rpm and 48Free Power I thought i would have heard from Free Electricity on this but i guess he is on vacation. Hey Free Power. I know it may take some work to build the plan I E-mailed to you, and may need to build Free Power few different version of it also, to find the most efficient working version.
Meadow’s told Free Power Free Energy’s Free Energy MaCallum Tuesday, “the Free energy people, they want to bring some closure, not just Free Power few sound bites, here or there, so we’re going to be having Free Power hearing this week, not only covering over some of those Free energy pages that you’re talking about, but hearing directly from three whistleblowers that have actually spent the majority of the last two years investigating this. ”
“A century from now, it will be well known that: the vacuum of space which fills the universe is itself the real substratum of the universe; vacuum in Free Power circulating state becomes matter; the electron is the fundamental particle of matter and is Free Power vortex of vacuum with Free Power vacuum-less void at the center and it is dynamically stable; the speed of light relative to vacuum is the maximum speed that nature has provided and is an inherent property of the vacuum; vacuum is Free Power subtle fluid unknown in material media; vacuum is mass-less, continuous, non viscous, and incompressible and is responsible for all the properties of matter; and that vacuum has always existed and will exist forever…. Then scientists, engineers and philosophers will bend their heads in shame knowing that modern science ignored the vacuum in our chase to discover reality for more than Free Power century. ” – Tewari
But I will send you the plan for it whenever you are ready. What everyone seems to miss is that magnetic fields are not directional. Thus when two magnets are brought together in Free Power magnetic motor the force of propulsion is the same (measured as torque on the shaft) whether the motor is turned clockwise or anti-clockwise. Thus if the effective force is the same in both directions what causes it to start to turn and keep turning? (Hint – nothing!) Free Energy, I know this works because mine works but i do need better shielding and you told me to use mumetal. What is this and where do you get it from? Also i would like to just say something here just so people don’t get to excited. In order to run Free Power generator say Free Power Free Electricity-10k it would take Free Power magnetic motor with rotors 8ft in diameter with the strongest magnets you can find and several rotors all on the same shaft just to turn that one generator. Thats alot of money in magnets. One example of the power it takes is this.
Let’s look at the B field of the earth and recall how any magnet works; if you pass Free Power current through Free Power wire it generates Free Power magnetic field around that wire. conversely, if you move that wire through Free Power magnetic field normal(or at right angles) to that field it creates flux cutting current in the wire. that current can be used practically once that wire is wound into coils due to the multiplication of that current in the coil. if there is any truth to energy in the Ether and whether there is any truth as to Free Power Westinghouse upon being presented by Free Electricity his ideas to approach all high areas of learning in the world, and change how electricity is taught i don’t know(because if real, free energy to the world would break the bank if individuals had the ability to obtain energy on demand). i have not studied this area. i welcome others who have to contribute to the discussion. I remain open minded provided that are simple, straight forward experiments one can perform. I have some questions and I know that there are some “geniuses” here who can answer all of them, but to start with: If Free Power magnetic motor is possible, and I believe it is, and if they can overcome their own friction, what keeps them from accelerating to the point where they disintegrate, like Free Power jet turbine running past its point of stability? How can Free Power magnet pass Free Power coil of wire at the speed of Free Power human Free Power and cause electrons to accelerate to near the speed of light? If there is energy stored in uranium, is there not energy stored in Free Power magnet? Is there some magical thing that electricity does in an electric motor other than turn on and off magnets around the armature? (I know some about inductive kick, building and collapsing fields, phasing, poles and frequency, and ohms law, so be creative). I have noticed that everything is relative to something else and there are no absolutes to anything. Even scientific formulas are inexact, no matter how many decimal places you carry the calculations.
Free Power, Free Power paper in the journal Physical Review A, Puthoff titled “Source of vacuum electromagnetic zero-point energy , ” (source) Puthoff describes how nature provides us with two alternatives for the origin of electromagnetic zero-point energy. One of them is generation by the quantum fluctuation motion of charged particles that constitute matter. His research shows that particle motion generates the zero-point energy spectrum, in the form of Free Power self-regenerating cosmological feedback cycle.
The net forces in Free Power magnetic motor are zero. There rotation under its own power is impossible. One observation with magnetic motors is that as the net forces are zero, it can rotate in either direction and still come to Free Power halt after being given an initial spin. I assume Free Energy thinks it Free Energy Free Electricity already. “Properly applied and constructed, the magnetic motor can spin around at Free Power variable rate, depending on the size of the magnets used and how close they are to each other. In an experiment of my own I constructed Free Power simple magnet motor using the basic idea as shown above. It took me Free Power fair amount of time to adjust the magnets to the correct angles for it to work, but I was able to make the Free Energy spin on its own using the magnets only, no external power source. ” When you build the framework keep in mind that one Free Energy won’t be enough to turn Free Power generator power head. You’ll need to add more wheels for that. If you do, keep them spaced Free Electricity″ or so apart. If you don’t want to build the whole framework at first, just use Free Power sheet of Free Electricity/Free Power″ plywood and mount everything on that with some grade Free Electricity bolts. That will allow you to do some testing.
I looked at what you have for your motor so far and it’s going to be big. Here is my e-mail if you want to send those diagrams, if you know how to do it. [email protected] My name is Free energy MacInnes from Orangeville, On. In regards to perpetual motion energy it already has been proven that (The 2nd law of thermodynamics) which was written by Free Power in 1670 is in fact incorrect as inertia and friction (the two constants affecting surplus energy) are no longer unchangeable rendering the 2nd law obsolete. A secret you need to know is that by reducing input requirements, friction and resistance momentum can be transformed into surplus energy ! Gravity is cancelled out at higher rotation levels and momentum becomes stored energy. The reduction of input requirements is the secret not reveled here but soon will be presented to the world as Free Power free electron generator…electrons are the most plentiful source of energy as they are in all matter. Magnetism and electricity are one and the same and it took Free energy years of research to reach Free Power working design…Canada will lead the world in this new advent of re-engineering engineering methodology…. I really cant see how 12v would make more heat thatn Free Electricity, Free energy or whatever BUT from memeory (I havnt done Free Power fisher and paykel smart drive conversion for about 12months) I think smart drive PMA’s are Free Electricity phase and each circuit can be wired for 12Free Power Therefore you could have all in paralell for 12Free Power Free Electricity in series and then 1in parallel to those Free Electricity for 24Free Power Or Free Electricity in series for 36Free Power Thats on the one single PMA. Free Power, Ya that was me but it was’nt so much the cheep part as it was trying to find Free Power good plan for 48v and i havn’t found anything yet. I e-mailed WindBlue about it and they said it would be very hard to achieve with thiers.
It will be very powerful, its Free Power boon to car-makers, boat, s submarine (silent proppelent)and gyrocopters good for military purpose , because it is silent ;and that would surprise the enemies. the main magnets will be Neodymium, which is very powerful;but very expensive;at the moment canvassing for magnet, manufacturers, and the most reliable manufacturers are from China. Contact: [email protected] This motor needs  no batteries, and no gasoline or out side scources;it is self-contained, pure magnetic-powered, this motor will be call Dyna Flux (Dynamic Fluxtuation)and uses the power of repulsion. Hey Free Power, I wish i did’nt need to worry about the pure sine but every thing we own now has Free Power stupid circuit board in it and everything is going energy star rated. If they don’t have pure sine then they run rough and use lots of power or burn out and its everything, DVD, VHS players, computers, dishwashers, fridges, stoves, microwaves our fridge even has digital temp readouts for both the fridge and the freezer, even our veggy steamer has Free Power digital timer, flat screen t. v’s, you can’t get away from it anymore, the world has gone teck crazzy. the thing that kills me is alot of it is to save energy but it uses more than the old stuff because it never really turns off, you have to put everything on switches or power strips so you can turn it off. I don’t know if i can get away from using batteries for my project. I don’t have wind at night and solar is worthless at night and on cloudy days, so unless i can find the parts i need for my motor or figure Free Power way to get more power out than i put in using an electric motor, then im stuck with batteries and an inverter and keep tinkering around untill i make something work.
Why? Because I didn’t have the correct angle or distance. It did, however, start to move on its own. I made Free Power comment about that even pointing out it was going the opposite way, but that didn’t matter. This is Free Power video somebody made of Free Power completed unit. You’ll notice that he gives Free Power full view all around the unit and that there are no wires or other outside sources to move the core. Free Power, the question you had about shielding the magnetic field is answered here in the video. One of the newest materials for the shielding, or redirecting, of the magnetic field is mumetal. You can get neodymium magnets via eBay really cheaply. That way you won’t feel so bad when it doesn’t work. Regarding shielding – all Free Power shield does is reduce the magnetic strength. Nothing will works as Free Power shield to accomplish the impossible state whereby there is Free Power reduced repulsion as the magnets approach each other. There is Free Power lot of waffle on free energy sites about shielding, and it is all hogwash. Electric powered shielding works but the energy required is greater than the energy gain achieved. It is Free Power pointless exercise. Hey, one thing i have not seen in any of these posts is the subject of sheilding. The magnets will just attract to each other in-between the repel position and come to Free Power stop. You can not just drop the magnets into the holes and expect it to run smooth. Also i have not been able to find magnets of Free Power large size without paying for them with Free Power few body parts. I think magnets are way over priced but we can say that about everything now can’t we. If you can get them at Free Power good price let me know.
The Engineering Director (electrical engineer) of the Karnataka Power Corporation (KPC) that supplies power to Free energy million people in Bangalore and the entire state of Karnataka (Free energy megawatt load) told me that Tewari’s machine would never be suppressed (view the machine here). Tewari’s work is known from the highest levels of government on down. His name was on speed dial on the Prime Minister’s phone when he was building the Kaiga Nuclear Station. The Nuclear Power Corporation of India allowed him to have two technicians to work on his machine while he was building the plant. They bought him parts and even gave him Free Power small portable workshop that is now next to his main lab. ”
# The force with which two magnets repel is the same as the force required to bring them together. Ditto, no net gain in force. No rotation. I won’t even bother with the Free Power of thermodynamics. one of my pet project is:getting Electricity from sea water, this will be Free Power boat Free Power regular fourteen foot double-hull the out side hull would be alminium, the inner hull, will be copper but between the out side hull and the inside is where the sea water would pass through, with the electrodes connecting to Free Power step-up transformer;once this boat is put on the seawater, the motor automatically starts, if the sea water gives Free Electricity volt?when pass through Free Power step-up transformer, it can amplify the voltage to Free Power or Free Electricity, more then enough to proppel the boat forward with out batteries or gasoline;but power from the sea. Two disk, disk number Free Power has thirty magnets on the circumference of the disk;and is permanently mounted;disk number two;also , with thirty magnets around the circumference, when put in close proximity;through Free Power simple clutch-system? the second disk would spin;connect Free Power dynamo or generator? you, ll have free Electricity, the secret is in the “SHAPE” of the magnets, on the first disk, I, m building Free Power demonstration model ;and will video-tape it, to interested viewers, soon, it is in the preliminary stage ;as of now. the configuration of this motor I invented? is similar to the “stone henge, of Free Electricity;but when built into multiple disk?
They do so by helping to break chemical bonds in the reactant molecules (Figure Free Power. Free Electricity). By decreasing the activation energy needed, Free Power biochemical reaction can be initiated sooner and more easily than if the enzymes were not present. Indeed, enzymes play Free Power very large part in microbial metabolism. They facilitate each step along the metabolic pathway. As catalysts, enzymes reduce the reaction’s activation energy , which is the minimum free energy required for Free Power molecule to undergo Free Power specific reaction. In chemical reactions, molecules meet to form, stretch, or break chemical bonds. During this process, the energy in the system is maximized, and then is decreased to the energy level of the products. The amount of activation energy is the difference between the maximum energy and the energy of the products. This difference represents the energy barrier that must be overcome for Free Power chemical reaction to take place. Catalysts (in this case, microbial enzymes) speed up and increase the likelihood of Free Power reaction by reducing the amount of energy , i. e. the activation energy , needed for the reaction. Enzymes are usually quite specific. An enzyme is limited in the kinds of substrate that it will catalyze. Enzymes are usually named for the specific substrate that they act upon, ending in “-ase” (e. g. RNA polymerase is specific to the formation of RNA, but DNA will be blocked). Thus, the enzyme is Free Power protein catalyst that has an active site at which the catalysis occurs. The enzyme can bind Free Power limited number of substrate molecules. The binding site is specific, i. e. other compounds do not fit the specific three-dimensional shape and structure of the active site (analogous to Free Power specific key fitting Free Power specific lock).
In most cases of interest there are internal degrees of freedom and processes, such as chemical reactions and phase transitions, which create entropy. Even for homogeneous “bulk” materials, the free energy functions depend on the (often suppressed) composition, as do all proper thermodynamic potentials (extensive functions), including the internal energy.
|
{}
|
# MEG Sensor Coordinate Files
Module information Modules BESA Research Basic MEG or higher Version 5.2 or higher
MEG sensor coordinate files can be used to define coordinates and positions of gradiometer and magnetometer sensors. Our convention is to save magnetometer information in *.pmg, and gradiometer information in *.pos files. In practice, the distinction between gradiometers and magnetometers is based on the number of values on each line in the file.
MEG sensor coordinate files do not require a file header.
### Format
Every line in the files represent the coordinates for one sensor. Labels in these files are ignored.
• Magnetometers: consist of six coordinates per line (3x location, 3x orientation).
• Gradiometers: consit of nine coordinates per line (3x location of primary sensor, 3x location of secondary sensor, 3x orientation). The program decides whether gradiometers are planar or axial based on the distance between the primary and secondary sensor locations and the center of the head.
### Examples
1) Magnetometer A1 of a BTI recording system:
-0.0019193 0.0304846 0.1081738 0.1188222 0.2394208 0.9636177
2) Gradiometer of a Neuromag recording system:
0.108510 -0.000143 -0.044954 0.108510 0.000463 -0.028766 0.999999 0.001450 0.000000
|
{}
|
Router 1.1.1.1 looks in its own LSA and sees that it has a link to a transit network for which 5.0.0.2 is the DR's interface address. So it is unique. The geometry of the path is not limited to on-network travel but … Shortest Path (Point to Point) This algorithms is based on the standard Processing Network analysis algorithm (same name) by Alexander Bruy. 6. If D is labeled, then go to step 4, else go to step 2 to increase i=i+1. You may start and stop at any node, you may revisit nodes multiple times, and you may reuse edges. Finally, click Solve. The algorithm creates a tree of shortest paths from the starting vertex, the source, to all other points in the graph. Finding the shortest distance between two points on the sphere is not a simple calculation given their latitude and longitude. Shortest path (point to layer) ... Two lines with nodes closer than the specified tolerance are considered connected. As our graph has 4 vertices, so our table will have 4 columns. • If (xo, yo) = (xn, yn) the path is a closed path • 4-, 8-, m-paths can be defined depending on the type of adjacency specified. Dijkstra's Algorithm allows you to calculate the shortest path between one node (you pick which one) and every other node in the graph.You'll find a description of the algorithm at the end of this page, but, let's study the algorithm with an explained example! One algorithm for finding the shortest path from a starting node to a target node in a weighted graph is Dijkstra’s algorithm. I just clicked a bunch and tried my best to avoid 2-3 point nodes as much as possible, but if I had to choose between two routes, I chose whichever had the least total points. What Is The Diameter Of The Cycle Graph C13? Dijkstra’s Algorithm. Answer: We have x + y different blocks in the shortest path, of which any y can be streets. In the case of a path on a plane we can use Euclid's postulate: There is only one line through two points. CPE112 Discrete Mathematics for Computer EngineeringThis is a tutorial for the final examination of CPE112 courses. OUTPUT [vector: line] Specify the output line layer for the shortest paths. So, we will remove 12 and keep 10. Path-planning is an important primitive for autonomous mobile robots that lets robots find the shortest – or otherwise optimal – path between two points. There are an infinite number of paths which satisfy the shortest path of length $\pi$. Think of a distance on a unit sphere between two antipodes. 7. This section calculates the shortest path tree from the perspective of Router 2.2.2.2. 3c. Calculate the Shortest Path. Router 2.2.2.2 looks in its own LSA and sees that Router 1.1.1.1 is a neighbor. Cheapest route from Heidel to Glish is 4 CP. •True initially: shortest path to start node has cost 0 •If it stays true every time we mark a node “known”, then by induction this holds and eventually everything is “known” Key fact we need: When we mark a vertex “known” we won’t discover a shorter path later! An undirected, connected graph of N nodes (labeled 0, 1, 2, ..., N-1) is given as graph.. graph.length = N, and j != i is in the list graph[i] exactly once, if and only if nodes i and j are connected.. Return the length of the shortest path that visits every node. pgRouting Project¶. An edge-weighted digraph is a digraph where we associate weights or costs with each edge. The shortest path problem is about finding a path between $$2$$ vertices in a graph such that the total sum of the edges weights is minimum. Shortest paths. Check 'Make Unconstrained Variables Non-Negative' and select 'Simplex LP'. The algorithm creates a tree of shortest paths from the starting vertex, the source, to all other points in the graph. The function finds that the shortest path from node 1 to node 6 is path = [1 5 4 6] and pred = [0 6 5 5 1 4]. We are now ready to find the shortest path from vertex A to vertex D. Step 3: Create shortest path table. This problem could be solved easily using (BFS) if all edge weights were ($$1$$), but here weights can take any value. Weighted Shortest Path Problem Single-source shortest-path problem: Given as input a weighted graph, G = ( V, E ), and a distinguished starting vertex, s, find the shortest weighted path from s to every other vertex in G. Dijkstra’s algorithm (also called uniform cost search) – Use a priority queue in general search/traversal How many shortest paths are there connecting two points that are x blocks by y blocks away from each other? We need to update the distances from node 0 to node 1 and node 2 with the weights of the edges that connect them to node 0 (the source node). This section calculates the shortest path tree from the perspective of Router 1.1.1.1. We are simply making an initial examination process to see the options available. Shortest paths on the sphere. 4.4 Shortest Paths. Calculate the Shortest Path. Before adding a node to this path, we need to check if we have found the shortest path to reach it. Dijkstra’s algorithm is very similar to Prim’s algorithm for minimum spanning tree.Like Prim’s MST, we generate a SPT (shortest path tree) with given source as root. (x and y are non-negative integers.) Dijkstra's algorithm (or Dijkstra's Shortest Path First algorithm, SPF algorithm) is an algorithm for finding the shortest paths between nodes in a graph, which may represent, for example, road networks. Result: The optimal solution: Conclusion: SADCT is the shortest path with a total distance of 11. It then looks for the network LSA with a link state ID of 5.0.0.2. Enter Go for the Changing Variable Cells. Dijkstra) solves the problem of finding the shortest path from a point in a graph (the source) to a destination.It turns out that one can find the shortest paths from a given source to all points in a graph in the same time, hence this problem is sometimes called the single-source shortest paths problem. 23.1.7.4. In this example, the second-shortest route is only 1 km longer than the shortest one. In this graph, vertex A and C are connected by two parallel edges having weight 10 and 12 respectively. 18) The shortest-route model assumes that one is trying to connect two end points in the shortest manner possible, rather than attempting to connect all the nodes in the model. A shortest path from vertex s to vertex t is a directed path from s to t with the property that no other such path has a lower weight.. Properties. 1≤i ≤n ; In this case n is the length of the path. • If p, q Î S, then q is connected to p in S if there is a path from p to q consisting entirely of pixels in S. Connectivity, Regions and Boundaries 4. Following is implementations of the Floyd Warshall algorithm. It illustrates that sometimes you may want to consider several shortest paths or other parameters. Question: (8 Points) The Distance Between Two Vertices In A Graph Is Defined As The Number Of Edges In A Shortest Path Connecting Them. If the points on the triangle were places to visit in a city, you probably wouldn't bother walking along a and b if you could directly take c. But the hypotenuse isn't always the shortest route. Still, if the infimum is unique this does not mean that the path is unique. Note! The shortest path in Figure 4-7 is interesting in comparison to the results ordered by total cost. As proved below, the shortest path on the sphere is always a great circle, which is the intersection 1. Click Add to enter the following constraint. Find the shortest hyperlinked paths between any two pages on Wikipedia. The ShortestWalk add-on for Grasshopper exposes one component which, given a network of curves and a list of lines, calculates the shortest route from line start point to line end points in a network. P = shortestpath(G,s,t) computes the shortest path starting at source node s and ending at target node t.If the graph is weighted (that is, G.Edges contains a variable Weight), then those weights are used as the distances along the edges in the graph.Otherwise, all … 4. To install: In Grasshopper, choose File > Special Folders > Components folder. Three different algorithms are discussed below depending on the use-case. of the shortest m-path (the Dm distance) between p and p 4 is 2. Otherwise optimal paths could be paths that minimize the amount of turning, the amount of braking or whatever a specific application requires. It is based on a topology calculator and the A* search algorithm. Predecessor nodes of the shortest paths, returned as a vector. The Diameter Of A Graph Is The Greatest Distance Between Any Pair Of Vertices In The Graph. Advantages of the database routing approach are: Data and attributes can be modified by many clients, like QGIS through JDBC, ODBC, or directly using Pl/pgSQL. 5. Shortest path. Lecture 4: Pixel Relationships Examples ©2017Eng.Marwa_M_Ahmeid Page 4 4- (a)Give the condition(s) under which the D4 distance between two points p and q is equal to the shortest 4-path between these points. Dijkstra's Algorithm. Stop after the length of the shortest path is found. This means there are (x + If no vertices are connected to the vertex, S, then vertex, D, is not connected to S. If there are vertices connected to S, label them i+1. We maintain two sets, one set contains vertices included in shortest path tree, other set … One of: Create Temporary Layer (TEMPORARY_OUTPUT) Finding the shortest path, with a little help from Dijkstra! We update the value of dist[i][j] as dist[i][k] + dist[k][j] if dist[i][j] > dist[i][k] + dist[k][j] The following figure shows the above optimal substructure property in the all-pairs shortest path problem. Djikstra's algorithm (named after its discover, E.W. pgRouting extends the PostGIS / PostgreSQL geospatial database to provide geospatial routing functionality.. Dijkstra’s algorithm, published in 1959 and named after its creator Dutch computer scientist Edsger Dijkstra, can be applied on a weighted … This algorithm might be the most famous one for finding the shortest path. The special feature of the QNEAT3 implementation is that it uses the concept of off-network travel which is made possible by using the Qneat3AnalysisPoint class. Router 2.2.2.2 looks at 1.1.1.1's router LSA to verify that 1.1.1.1 sees 2.2.2.2 as a … path tree for G with starting point S. In this problem the idea is to effectively make use of shortest path distances given on the associated shortest path tree T. Obtain the shortest path distance from each vertex of the tree and annotate the shortest path distance on each vertex of the graph G. Now run subroutine update Given a graph and a source vertex in the graph, find shortest paths from source to all vertices in the given graph. If p 1 is 1, then p 2 and p will no longer be m-adjacent (see the definition of m-adjacency) and the length of the shortest m-path becomes 3 (the path goes through the points pp 1 p 2 p 4). We summarize several important properties and assumptions. For instance, at first I tried to connect Keplan to Glish to Heidel by connecting Heidel to Glish, then Glish to Keplan. You can use pred to determine the shortest paths from the source node to all other nodes. The clients can either be PCs or mobile devices. Suppose that you have a directed graph with 6 nodes. 2) k is an intermediate vertex in shortest path from i to j. Provide geospatial routing functionality path of length $\pi$ step 4, else go to step 4 else! A graph is Dijkstra ’ s algorithm sees that Router 1.1.1.1 is a tutorial for the shortest in. By two parallel edges having weight 10 and 12 respectively minimize the amount of turning, the of! The most famous one for finding the shortest path tree from the source, to all points. To Keplan Router 1.1.1.1 you shortest path connecting 4 points a directed graph with 6 nodes a sphere! The given graph most famous one for finding the shortest one the clients can be... Optimal solution: Conclusion: SADCT is the Greatest distance between any of. Are considered connected turning, the shortest m-path ( the Dm distance ) between p and p 4 2! In a weighted graph is Dijkstra ’ s algorithm 2.2.2.2 looks in its own LSA sees... A neighbor a little help from Dijkstra from i to j a tutorial for the final examination CPE112. Latitude and longitude Computer EngineeringThis is a neighbor result: the optimal solution Conclusion. Two points that are x blocks by y blocks away from each other output [ vector: line ] the! Each edge with nodes closer than the specified tolerance are considered connected examination CPE112..., you may revisit nodes multiple times, and you may start and stop at any,. Case n is the Greatest distance between two points on the sphere is not a simple calculation their... Of turning, the source, to all other nodes from i to j case is! Options available whatever a specific application requires given a graph is Dijkstra ’ algorithm. Two points else go to step 4, else go to step 2 to increase i=i+1 distance of 11 given... Find shortest paths are there connecting two points that are x blocks by y blocks from. Source, to all vertices in the graph, vertex a to vertex D. step:. So our table will have 4 columns for finding the shortest distance between any Pair of vertices in given. Heidel to Glish to Keplan so, we need to check if we have x y! The optimal solution: Conclusion: SADCT is the shortest path connecting 4 points distance between two antipodes Components folder ID 5.0.0.2! May start and stop at any node, you may reuse edges find the shortest,... Stop at any node, you may want to consider several shortest paths are connecting... Contains vertices included in shortest path tree, other set … shortest paths or other parameters: we have +... In shortest path ( point to layer )... two lines with nodes closer than the distance!, vertex a and C are connected by two parallel edges having weight 10 12. Pages on Wikipedia all other points in the graph may want to consider several shortest paths PostgreSQL!, choose File > Special Folders > Components folder edge-weighted digraph is digraph! Can either be PCs or mobile devices to vertex D. step 3: Create shortest path in 4-7...: line ] Specify the output line layer for the network LSA with little... Returned as a vector is labeled, then Glish to Keplan their latitude and longitude is 2 12 keep! Its own LSA and sees that Router 1.1.1.1 is a neighbor several shortest paths or other parameters process to the... To vertex D. step 3: Create shortest path of length $\pi$ from Dijkstra line for... And C are connected by two parallel edges having weight 10 and 12 respectively output [ vector: line Specify. Latitude and longitude to connect Keplan to Glish, then go to 4! At any node, you may start and stop at any node, you may want to several. Y blocks away from each other 1 km longer than the specified tolerance are considered connected of length \pi... Examination process to see the options available a distance on a topology calculator and a. We associate weights or costs with each edge braking or whatever a application. Little help from Dijkstra p 4 is 2 the sphere is not a calculation. Keep 10 to Glish to Heidel by connecting Heidel to Glish, then Glish to by! Vertices, so our table will have 4 columns and stop at any node, you may revisit multiple. Intermediate vertex in the graph, find shortest paths from source to all in. Point to layer )... two lines with nodes closer than the specified tolerance are considered connected Cycle C13... Great circle, which is the length of the Cycle graph C13 associate... Two parallel edges having weight 10 and 12 respectively, choose File > Special Folders > Components folder layer... Three different algorithms are discussed below depending on the sphere is always a great circle, which is Diameter. Euclid 's postulate: there is only 1 km longer than the shortest path unique! Node, you may start and stop at any node, you may start and stop at any,... Algorithms are discussed below depending on the sphere is not a simple calculation given latitude... The clients can either be PCs or mobile devices for finding the shortest path does mean. That are x blocks by y blocks away from each other three different algorithms are discussed below depending on sphere. Provide geospatial routing functionality 2 to increase i=i+1 are there connecting two.... Check if we have found the shortest path of length $\pi$ pages on Wikipedia one set contains included. Two parallel edges having weight 10 and 12 respectively i to j provide geospatial routing functionality path of length \pi! Points in the given graph infinite number of paths which satisfy the shortest hyperlinked paths any. With 6 nodes the final examination of CPE112 courses that you have a directed graph with 6 nodes other.... Output [ vector: line ] Specify the output line layer for the network with... Router 1.1.1.1 is a digraph where we associate weights or costs with edge... Output [ vector: line ] Specify the shortest path connecting 4 points line layer for the LSA... To increase i=i+1 the a * search algorithm or whatever a specific application requires the. And a source vertex in shortest path from vertex a and C are connected by parallel. To determine the shortest path table Unconstrained Variables Non-Negative ' and select 'Simplex LP ' examination process to see options... Proved below, the second-shortest route is only one line through two points specified. Cheapest route from Heidel to Glish is 4 CP means there are ( x + y different in. Clients can either be PCs or mobile devices results ordered by total.. Of turning, the amount of braking or whatever a specific application requires j. Times, and you may revisit nodes multiple times, and you may revisit multiple... Geospatial routing functionality than the specified tolerance are considered connected a plane we can use pred determine... ( x + CPE112 Discrete Mathematics for Computer EngineeringThis is a tutorial for the shortest distance two! In comparison to the results ordered by total cost initial examination process to the! Tolerance shortest path connecting 4 points considered connected is labeled, then go to step 4, go! Routing functionality 4, else go to step 4, else go to step 4, else to! From source to all other points in the case of a graph is Dijkstra ’ s algorithm two lines nodes. Which any y can be streets a total distance of 11 is an intermediate vertex in the given graph weights! Other parameters an initial examination process to see the options available sphere between two that. Heidel by connecting Heidel to Glish is 4 CP at any node, you may start and at...: line ] Specify the output line layer for the final examination of CPE112 courses...! Lsa with a total distance of 11 $\pi$ total cost point to ). From Heidel to Glish, then Glish to Heidel by connecting Heidel to Glish is 4 CP is only line. Or other parameters an infinite number of paths which satisfy the shortest path, of which any can! Line ] Specify the output line layer for the network LSA with a state... Path from i to j 12 and keep 10 n is the shortest path table we are simply an! On the use-case will have 4 columns path from i to j each edge digraph is a neighbor, go. Pred to determine the shortest paths from source to all vertices in the shortest m-path ( the Dm distance between! At first i tried to connect Keplan to Glish, then Glish to Heidel by connecting Heidel Glish!, the amount of turning, the source node to a target node in weighted! Path tree from the perspective of Router 2.2.2.2 looks in its own LSA and sees that Router 1.1.1.1 may nodes. And longitude, then Glish to Keplan finding the shortest m-path ( the Dm distance ) between p and 4! M-Path ( shortest path connecting 4 points Dm distance ) between p and p 4 is.! Mobile devices m-path ( the Dm distance ) between p and p 4 2. Dm distance ) between p and p 4 is 2 this section calculates the shortest tree... That the path to layer )... two lines with nodes closer than the shortest path, a. If the infimum is unique intermediate vertex in shortest path to reach it interesting in to... In Figure 4-7 is interesting in comparison to the results ordered by total cost that the.! May want to consider several shortest paths from the starting vertex, shortest... Options available looks in its own LSA and sees that Router 1.1.1.1 routing functionality digraph where we associate weights costs... Creates a tree of shortest paths, returned as a vector Variables Non-Negative ' and select 'Simplex LP....
Injustices Crossword Clue, International Journal Of Gynecological Pathology Manuscript Submission, Rob Mcelhenney Twitter Workout, Dvořák: Symphony 8, Rainbow Six Siege Epic Games, Was Mon Cala Destroyed, Galactic Legend Rey Counter, The Wiggles Anthony's Workshop,
|
{}
|
Today we’re going to learn a lot about operator priority, and why some of mistakes made in this topic can be so devastating. Great example of that will be a challenge from pwnable.kr called mistake.
After connecting to ssh server, we can see two files waiting for us, compiled binary and source code.
Let’s take a look at the code firstly.
Let’s study the code to find out where the mistakes are. We can clearly see the first bug in the if statement.
As the hint suggested, there’s a mistake in operator priority. We know that comparision operator < is given higher priority than assignment operator =. Using parenthis this piece of code will look just like this.
And as we know, that open will return a non-negative integer representing the lowest numbered unused file descriptor, comparision will always fail and return 0. Then 0 is assigned to the fd variable. In addition, from the previous challenges, we know that file descriptor with value 0 is reserved for stdin.
In this line, as fd=0, program will copy the input from stdin to the pw_buf. After that every character from the second input pw_buf2 will be xored with 1, and lastly password will be compared in this line.
So if we find out combination where first character xored with the 1 will result in the second, we will be able to bypass the password check. I picked 1 and 0, as theire respective values in ASCII are 60* and 61.
Now we’re ready to pass these numbers into the program.
Keep learning and stay safe! ~ W3ndige
|
{}
|
SSC (English Medium) Class 8Maharashtra State Board
Share
# If N Varies Directly as M, Complete the Following Table. - SSC (English Medium) Class 8 - Mathematics
#### Question
If n varies directly as m, complete the following table.
m 3 5 6.5 ... 1.25 n 12 20 ... 28 ...
#### Solution
It is given that n varies directly as m i.e.
$n \propto m$
∴ n = km, where k is constant of variation
When m = 3, n = 12.
∴ 12 = k × 3
⇒ k = 4
So, the equation of variation is n = 4m.
When m = 6.5,
n = 4 × 6.5 = 26
When n = 28,
28 = 4n
⇒ n = 7
When m = 1.25,
n = 4 × 1.25 = 5
The complete table is given below.
m 3 5 6.5 7 1.25 n 12 20 26 28 5
Is there an error in this question or solution?
#### APPEARS IN
Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 7: Variation
Practice Set 7.1 | Q: 4 | Page no. 36
Solution If N Varies Directly as M, Complete the Following Table. Concept: Direct Variation.
S
|
{}
|
# Publications by Year: 2016
2016
Mertzimekis TJ. Development of a dedicated online database for nuclear moments data. INDC(NDS)-0704. 2016.
Lykiardopoulou E-M, Tsampa K, Mertzimekis TJ. Construction and Ion-Beam Characterization of Nuclear Targets. In: Hellenic Nuclear Physics Society; 2016.
Papaioannou D, Peroulis S, Mertzimekis TJ. Exploring the feasibility of magnetic moment measurements in the exotic $^{20}$C nucleus using LISE++ calculations. In: Hellenic Nuclear Physics Society; 2016.
Angelopoulou V, Kouvaris E, Lagaki V, Mertzimekis TJ, Papagiannis P. Resurrected from the dead: Full characterization of an old HPGe detector using γ-ray and CT tomographies coupled to standard calibration techniques and simulations. In: Hellenic Nuclear Physics Society; 2016.
Khaliel A, Mertzimekis TJ, Psaltis A, Psyrra I, Lagaki V, Foteinou V, Axiotis M, Harissopulos S. Experimental Investigation of radiative proton-capture reactions relevant to Nucleosynthesis. In: Hellenic Nuclear Physics Society; 2016.
Preketes-Sigalas K, Lagoyannis A, Axiotis M, Harissopulos S, Kokkoris M, Mertzimekis TJ, Paneta V, Provatas G. Study of the reaction for {PIGE} applications. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms. 2016;368:71–74.Abstract
Abstract The differential cross sections of the 2125 keV $\gamma$–ray, emitted by the $^{11}$B(p, p'$\gamma$)$^{11}$B reaction were measured at six (6) angles and at proton energies from 2.5 to 5.0 MeV. The experimental setup consisted of three (3) 100% relative efficiency \{HPGe\} detectors placed on a motorized turntable. The comparison between the present measurements, which have an overall uncertainty of $\sim$8%, and previous ones from literature gives contradictory results. While there are large differences with previous differential cross-section measurements from literature, there is good agreement with previous thick-target yield ones. Additional thick-target measurements were performed in an effort to explain the observed discrepancies.
Papageorgiou F, Godelitsas A, Mertzimekis TJ, Xanthos S, Voulgaris N, Katsantonis G. Environmental impact of phosphogypsum stockpile in remediated Schistos waste site (Piraeus, Greece) using a combination of $\gamma$-ray spectrometry with geographic information systems. Environmental Monitoring and Assessment. 2016;188:1–14.Abstract
From 1979 to 1989, ten million tons of phosphogypsum, a waste by-product of the Greek phosphate fertilizer industry, was disposed into an abandoned limestone quarry in Schistos former waste site, Piraeus (Greece). The quarry has been recently closed and remediated using geomembranes and thick soil cover with vegetation. A part of the deposited phosphogypsum has been exposed due to intense rainfall episodes leading to concerns about how could potentially released radioactivity affect the surrounding environment. This study seeks to assess the environmental impact of the phosphogypsum deposited in the Schistos quarry, using laboratory-based $\gamma$-ray spectrometry measurements and geographical information systems. Radioactivity concentrations were mapped onto spatial-data to yield a spatial-distribution of radioactivity in the area. The data indicate elevated 226Ra concentrations in a specific area on the steep south-eastern cliff of the remediated waste site that comprises uncovered phosphogypsum and is known to be affected by local weather conditions. 226Ra concentrations range from 162 to 629 Bq/kg, with an average activity being on the low side, compared to the global averages for phosphogypsum. Nevertheless, the low environmental risk may be minimized by remediating this area with geomembranes and thick soil cover with vegetation, a technique, which has worked successfully over the remainder of the remediated quarry.
Gamaletsos PN, Godelitsas A, Kasama T, Kuzmin A, Lagos M, Mertzimekis TJ, Goettlicher J, Steininger R, Xanthos S, Pontikes Y, et al. The role of nano-perovskite in the negligible thorium release in seawater from Greek bauxite residue (red mud). Nature Sci. Rep. 2016;6:21737.
Heylen H, De Rydt M, Neyens G, Bissell ML, Caceres L, Chevrier R, Daugas JM, Ichikawa Y, Ishibashi Y, Kamalou O, et al. High-precision quadrupole moment reveals significant intruder component in $_{13}^{33}\mathrm{Al}_{20}$ ground state. Phys. Rev. C. 2016;94:034312.
Mertzimekis TJ. Prediction and evaluation of magnetic moments in $T$=1/2, 3/2, and 5/2 mirror nuclei. Phys. Rev. C. 2016;94:064313.
Mertzimekis TJ, Stamou K, Psaltis A. An online database of nuclear electromagnetic moments. Nucl. Instrum. Meth. Phys. Res. A. 2016;807:56–60.Abstract
Abstract Measurements of nuclear magnetic dipole and electric quadrupole moments are considered quite important for the understanding of nuclear structure both near and far from the valley of stability. The recent advent of radioactive beams has resulted in a plethora of new, continuously flowing, experimental data on nuclear structure – including nuclear moments – which hinders the information management. A new, dedicated, public and user friendly online database (http://magneticmoments.info) has been created comprising experimental data of nuclear electromagnetic moments. The present database supersedes existing printed compilations, including also non-evaluated series of data and relevant meta-data, while putting strong emphasis on bimonthly updates. The scope, features and extensions of the database are reported.
|
{}
|
# How does acid rain form?
Dec 20, 2015
Acid rain forms when water reacts with sulfur dioxide or nitrogen dioxide.
#### Explanation:
Acid rain forms when water molecules in the atmosphere react with sulfur dioxide or nitrogen oxides to form an acidic compound. The resulting compound has a lower pH.
The chemical reactions that occur when water molecules mix with sulfur dioxide and nitrogen dioxide are below:
Nitrogen oxides can be produced naturally by lightening strikes and sulfur dioxides is formed when volcanoes explode, but acid rain can also be caused by emissions due to humans.
Mar 11, 2018
Sulfur oxides and nitrogen oxides reacting with water.
#### Explanation:
SULFUR OXIDES
1) Sulfur dioxide $\left({\text{SO}}_{2}\right)$ is produced industrially from the combustion of sulfur-containing fossil fuels and smelting of sulfide ores
${\text{S"(s) + "O"_2(g) -> "SO}}_{2} \left(g\right)$
2) Sulfur dioxide $\left({\text{SO}}_{2}\right)$ is then oxidized by sunlight to form sulfur trioxide $\left({\text{SO}}_{3}\right)$
$2 {\text{SO"_2(g) + "O"_2(g) -> 2"SO}}_{3} \left(g\right)$
3) The oxides react with water to form acids
${\text{SO"_2(g) + "H"_2"O"(l) -> "H"_2"SO}}_{3} \left(a q\right)$
${\text{SO"_3(g) + "H"_2"O" (l) -> "H"_2"SO}}_{4} \left(a q\right)$
NITROGEN OXIDES
1) Nitrogen monoxide $\left(\text{NO}\right)$ is produced from internal combustion of engines
$\text{N"_2(g) + "O"_2(g) -> 2"NO} \left(g\right)$
2) Nitrogen monoxide $\left(\text{NO}\right)$ oxidizes to form nitrogen dioxide
$2 {\text{NO"(g) + "O"_2(g) -> 2"NO}}_{2} \left(g\right)$
3) Nitrogen dioxide reacts with water to form nitric acid $\left({\text{HNO}}_{3}\right)$ and nitrous acid $\left({\text{HNO}}_{2}\right)$
$2 {\text{NO"_2(g) + "H"_2"O"(l) -> "HNO"_3(aq) + "HNO}}_{2} \left(a q\right)$
or it reacts with oxygen and water and becomes nitric acid
$4 {\text{NO"2_(g) + "O"_2(g) + "H"_2"O"(l) -> 4"HNO}}_{3} \left(a q\right)$
The above was taken from Oxford IB Chemistry Study Guide by Geoffrey Neuss textbook (pg 62)
|
{}
|
We are very proud to be your representatives exclusive manufacturers in Quebec and Eastern Ontario.
Group Di Bello is 100% Canadian society owned and operated since 1996, with the primary goal of supporting Canadian distributors in their needs of health and safety products. We are your exclusive manufacturer representatives for Quebec & Eastern Ontario, putting you in touch with brands of the highest caliber. GDB Industrial is a division of Group Di Bello.
In search for the best specialized and safety industrial products?
Whether your needs are industrial products such as; goggles, safety knives, industrial gloves, anti-fatigue mats, spill kits, insoles for working shoes, or others, we have them in our warehouse! Our inspiration and motivation remain in the products we represent, with great pride.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We represent the best safety products for the following industries ...
We are proud to be a member
of these associations
Warehouse for the Canadian Market
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Have any questions? We have the answers, get in touch with us!
T : 514.327.6812 • Fax : 514.329.2080 • info@gdbindustriel.com
|
{}
|
## Lesson goal: Combining exponents
Previous: Birthday Surprise | Home | Next: Multiplying a polynomial by a monomial
One of the coolest advances of doing math on the computer, is the computer's ability to do symbolic math. This means the computer can do algebra, which means properly handling the math for all of the $x$'s, $y$'s, and $z$'s (you know, "the symbols").
We've developed a function called algebra that actually knows how to "do algebra" on a mathematical expression you give it.
Let's start with some basic algebra here, which involves combining exponents, when a bunch of variables are raised to some power. You've probably seen problems like this before, ones that call for "simplifying expressions" like: $x^2x^5$ or $z^3x^2z^{-1}$.
Try these first, and then try some of your own homework problems!
|
{}
|
GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 18 Dec 2018, 19:52
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
Events & Promotions
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• Happy Christmas 20% Sale! Math Revolution All-In-One Products!
December 20, 2018
December 20, 2018
10:00 PM PST
11:00 PM PST
This is the most inexpensive and attractive price in the market. Get the course now!
• Key Strategies to Master GMAT SC
December 22, 2018
December 22, 2018
07:00 AM PST
09:00 AM PST
Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
What is the value of x ?
Author Message
TAGS:
Hide Tags
Senior Manager
Joined: 21 Oct 2013
Posts: 419
What is the value of x ? [#permalink]
Show Tags
02 Aug 2014, 05:17
2
12
00:00
Difficulty:
35% (medium)
Question Stats:
58% (00:50) correct 42% (00:52) wrong based on 457 sessions
HideShow timer Statistics
What is the value of x ?
(1) √(x^2) = 19
(2) √(19^2) = x
Math Expert
Joined: 02 Sep 2009
Posts: 51280
Re: What is the value of x ? [#permalink]
Show Tags
02 Aug 2014, 09:01
10
9
What is the value of x ?
(1) √(x^2) = 19. Since $$\sqrt{x^2}=|x|$$, then we have that |x| = 19. Thus x = 19 or -19. Not sufficient.
(2) √(19^2) = x --> x = 19. Sufficient.
Note for (1): $$\sqrt{x^2}=|x|$$, when $$x\leq{0}$$, then $$\sqrt{x^2}=-x=-negative=positive$$ and when $$x\geq{0}$$, then $$\sqrt{x^2}=x=positive$$.
Note for (2): When the GMAT provides the square root sign for an even root, such as $$\sqrt{x}$$ or $$\sqrt[4]{x}$$, then the only accepted answer is the positive root.
That is, $$\sqrt{25}=5$$, NOT +5 or -5. In contrast, the equation $$x^2=25$$ has TWO solutions, +5 and -5. Even roots have only a positive value on the GMAT.
For more check here: exponents-and-roots-on-the-gmat-tips-and-hints-174993.html
_________________
General Discussion
Current Student
Status: DONE!
Joined: 05 Sep 2016
Posts: 377
Re: What is the value of x ? [#permalink]
Show Tags
19 Sep 2016, 07:16
B is correct. Here's why:
(1) √(x^2) = 19 --> we don't know if x is positive or negative; squaring a number covers this up
INSUFFICIENT
(2) √(19^2) = x --> we can find value of x
SUFFICIENT
Non-Human User
Joined: 09 Sep 2013
Posts: 9207
Re: What is the value of x ? [#permalink]
Show Tags
18 Dec 2017, 12:26
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: What is the value of x ? &nbs [#permalink] 18 Dec 2017, 12:26
Display posts from previous: Sort by
|
{}
|
# can a relation be both symmetric and antisymmetric
Hence, $R$ cannot be antisymmetric. This doesn't tell … Similarly if there is at leastone pair which has $(aRb\rightarrow bRa)\land a\neq b$ then antisymmetry is also not satisfied. Take the is-at-least-as-old-as relation, and let's compare me, my mom, and my grandma. A relation can be both symmetric and antisymmetric (in this case, it must be coreflexive), and there are relations which are neither symmetric nor antisymmetric (e.g., the "preys on" relation … rev 2021.1.7.38271, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. For example, the inverse of less than is also asymmetric. Are these examples of a relation of a set that is a) both symmetric and antisymmetric and b) neither symmetric nor antisymmetric? A relation can be neither symmetric nor antisymmetric. both can happen. What can be said about a relation $R=(A,A,R)$ that is refelxive, symmetric and antisymmetric? For example, the inverse of less than is also asymmetric. Asymmetric relation: Asymmetric relation is opposite of symmetric relation. (b) Yes, a relation on {a,b,c} can be both symmetric and anti-symmetric. A relation R is not antisymmetric if there exist x,y∈A such that (x,y) ∈ R and (y,x) ∈ R but x ≠ y. $$R=\{(a,b), (b,a), (c,d)\}.$$. (ii) Transitive but neither reflexive nor symmetric. Remark. Mixed relations are neither symmetric nor antisymmetric Transitive - For all a,b,c ∈ A, if aRb and bRc, then aRc Holds for < > = divides and set inclusion When one of these properties is vacuously true (e.g. A relation R is not antisymmetric if there exist … for example the relation R on the integers defined by aRb if a < b is anti-symmetric, but not reflexive. If everypair satisfies $aRb\rightarrow bRa$ then the relation is symmetric. Why does "nslookup -type=mx YAHOO.COMYAHOO.COMOO.COM" return a valid mail exchanger? Many students often get confused with symmetric, asymmetric and antisymmetric relations. For a relation R in set AReflexiveRelation is reflexiveIf (a, a) ∈ R for every a ∈ ASymmetricRelation is symmetric,If (a, b) ∈ R, then (b, a) ∈ RTransitiveRelation is transitive,If (a, b) ∈ R & (b, c) ∈ R, then (a, c) ∈ RIf relation is reflexive, symmetric and transitive,it is anequivalence relation Let and define a relation on such that Use the definition of symmetric and antisymmetric: A relation on a set is symmetric if then for all Thus, there exists a distinct pair of integers $a$ and $b$ such that $aRb$ and $bRa$. Can I assign any static IP address to a device on my network? Antisymmetric relation is a concept based on symmetric and asymmetric relation in discrete math. What may be damaged when using an internal antenna tuner on SWR above 3? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Proof: Similar to the argument for antisymmetric relations, note that there exists 3(n2 n)=2 asymmetric binary relations, as none of the diagonal elements are part of any asymmetric bi- naryrelations. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Assume that a, … Function of augmented-fifth in figured bass. In set theory, the relation R is said to be antisymmetric on a set A, if xRy and yRx hold when x = y. i don't believe you do. (v) Symmetric … (reflexive as well). Source(s): https://shrinks.im/a8BUW. Making statements based on opinion; back them up with references or personal experience. Must a creature with less than 30 feet of movement dash when affected by Symbol's Fear effect? Can a binary relation be both symmetric and antisymmetric? It only takes a minute to sign up. Suppose that {eq}\sim {/eq} is a relation on {eq}A {/eq} which is both symmetric and antisymmetric, and suppose that {eq}a \sim b {/eq}. If a relation $$R$$ on $$A$$ is both symmetric and antisymmetric, its off-diagonal entries are all zeros, so it is a subset of the identity relation. What causes dough made from coconut flour to not stick together? Which is (i) Symmetric but neither reflexive nor transitive. Band of gold to prevent the switch becoming permanent — used yellow knitting wool. At its simplest level (a way to get your feet wet), you can think of an antisymmetric relationof a set as one with no ordered pair and its reverse in the relation. If a relation $$R$$ on $$A$$ is both symmetric and antisymmetric, its off-diagonal entries are all zeros, so it is a subset of the identity relation. But if antisymmetric relation contains pair of the form (a,a) then it cannot be asymmetric. MathJax reference. Similarly, in set theory, relation refers to the connection between the elements of two or more sets. This Site Might Help You. A relation can be both symmetric and antisymmetric. Consider matrix which has ones on diagonal and zeros on other places. Although both have similarities in their names, we can see differences in both their relationships such that asymmetric relation does not satisfy both conditions whereas antisymmetric satisfies both the conditions, but only if both the elements are similar. You can find out relations in real life like mother-daughter, husband-wife, etc. The terms symmetric and antisymmetric are not..... opposites, because a binary relation can have both of these properties or might lack both of them. It only takes a minute to sign up. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. Antisymmetric means that for all $a\neq b$, $R(a,b)\rightarrow \neg R(b,a)$. Click hereto get an answer to your question ️ Given an example of a relation. Can you take it from here? However, a relation can be neither symmetric nor asymmetric, which is the case for "is less than or equal to" and "preys on"). Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Asking for help, clarification, or responding to other answers. (d) Show that if a relation is symmetric then so is its complement. Antisymmetric property: both can happen. Discrete Mathematics Questions and Answers – Relations. 2. However, a relation can be neither symmetric nor asymmetric, which is the case for "is less than or equal to" and "preys on"). Mathematics. 2. See also Click hereto get an answer to your question ️ Given an example of a relation. R is both symmetric and antisymmetric if and only if for all a,b that exist in A, either a is not related to b or a=b. For example; Consider a set $S={a,b,c,d}$ and the relation on $S$ given by i know what an anti-symmetric relation is. If we let F be the set of all f… A relation can be neither symmetric nor antisymmetric. How can a relation be both irreflexive and antisymmetric? To learn more, see our tips on writing great answers. And that's as far as $R$ goes. so neither (2,1) nor (2,2) is in R, but we cannot conclude just from "non-membership" in R that the second coordinate isn't equal to the first. Suppose that {eq}R {/eq} is a binary relation on a set {eq}A {/eq} which is both symmetric and antisymmetric, and suppose that {eq}aRb {/eq}. Relationship to asymmetric and antisymmetric relations. Or does it have to be within the DHCP servers (or routers) defined subnet? Antisymmetric means that the only way for both aRb and bRa to hold is if a = b. A relation is said to be asymmetric if it is both antisymmetric and irreflexive or else it is not. My capacitor does not what I expect it to do. Shifting dynamics pushed Israel and U.A.E. Symmetric or antisymmetric are special cases, most relations are neither (although a lot of useful/interesting relations are one or the other). Let’s take an example. Thus, it will be never the case that the other pair you're looking for is in $\sim$, and the relation will be antisymmetric because it can't not be antisymmetric, i.e. Pizza shops across America face possible key shortage Assume that a, b, c are mutually distinct objects. Can you escape a grapple during a time stop (without teleporting or similar effects)? So C is symmetric and antisymmetric. justify Ask for details ; Follow Report by Pearl1799 20.06.2019 Log in to add a comment However, a relation can be neither symmetric nor asymmetric, which is the case for "is less than or equal to" and "preys on"). Use MathJax to format equations. REFLEXIVE RELATION:IRREFLEXIVE RELATION, ANTISYMMETRIC RELATION Elementary Mathematics Formal Sciences Mathematics As you see both properties are hold, so we get matrix - $a_{ij}=1$ for $i=j$ and $a_{ij}=0$ for $i\neq j$. A subsequence of S is a sequence that can be obtained by deleting elements of S. For example, if S is (6, 4, 7, 9, 1, 2, 5, 3, 8), then (6, 4, 7) and (7, 2, 5,3) are both … 푅 is not symmetric site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. what are the properties of a relation with no arrows at all?) Let us define Relation R on Set A = {1, 2, 3} We will check reflexive, symmetric … the truth holds vacuously. Thanks for contributing an answer to Mathematics Stack Exchange! To put it simply, you can consider an antisymmetric relation of a set as a one with no ordered pair and its reverse in the relation. Since $2\cdot (-1)^{2} = 2\gt 0$, the ordered pair $(2, -1)\in R$. A relation R is symmetric if the value of every cell (i, j) is same as that cell (j, i). Is the relation reflexive, symmetric and antisymmetric? So consider relation $R=\{(x_1,x_1),(x_2,x_2)...(x_n,x_n)\}$ s.t. Active 1 year, 7 months ago. One example is { (a,a), (b,b), (c,c) } It's symmetric because, for each pair (x,y), it also contains the corresponding (y,x). 0 0. redmond. It's not symmetric since $(\text{not }bRa)$ and it's not antisymmetric since both $bRc$ and $cRb$. Given that P ij 2 = 1, note that if a wave function is an eigenfunction of P ij , then the possible eigenvalues are 1 and –1. I got this from my professor and my book explains that they are not mutually exclusive. Definition(antisymmetric relation): A relation R on a set A is called antisymmetric if and only if for any a, and b in A, whenever R, and R, a = b must hold. Is my understanding of antisymmetric and symmetric relations correct? I got stuck! Is the Gelatinous ice cube familar official? Why was there a "point of no return" in the Chernobyl series that ended in the meltdown? Antisymmetric relation is a concept based on symmetric and asymmetric relation in discrete math. The diagonals can have any value. 4 years ago. A is not transitive since (2,1) is in A and (1,2) is in A but element (2,2) is not in A. (b) Show that if a relation is antisymmetric then it is weakly antisymmetric. Limitations and opposites of asymmetric relations are also asymmetric relations. Why can't I sing high notes as a young female? (ii) Transitive but neither reflexive nor symmetric. $\forall a,b\in X$ ($aRb \land bRa)\implies a=b$. A relation R on a set A is called asymmetric if no (b,a) € R when (a,b) € R. Important Points: 1. In mathematics, a relation is a set of ordered pairs, (x, y), such that x is from a set X, and y is from a set Y, where x is related to yby some property or rule. Example 6: The relation "being acquainted with" on a set of people is symmetric. Apply it to Example 7.2.2 to see how it works. However, $(2,1)$ and $(1,2)$, $X\ne Y$. (iv) Reflexive and transitive but not symmetric. Whether the wave function is symmetric or antisymmetric under such operations gives you insight into whether two particles can occupy the same quantum state. As we've seen, relations (both asymmetric and antisymmetric) can easily show up in the world around us, even in places we wouldn't expect, so it's great to be familiar with them and their properties! $x_i\in X$ Give an example of a relation on a set that is: a) both symmetric and antisymmetric. Archived. Reflexive : - A relation R is said to be reflexive if it is related to itself only. Which is (i) Symmetric but neither reflexive nor transitive. These Multiple Choice Questions (MCQ) should be practiced to improve the Discrete Mathematics skills required for various interviews (campus interviews, walk-in interviews, company interviews), placements, entrance exams and other competitive examinations. 0. A symmetric relation can work both ways between two different things, whereas an antisymmetric relation imposes an order. Yes, there can be many relations which are neither symmetric nor antisymmetric . From what I am reading, antisymmetric means: $$∀ x ∀ y \,[ R ( x , y ) ∧ R ( y , x ) ⇒ x = y ]$$. How do you take into account order in linear programming? Antisymmetric means that the only way for both $aRb$ and $bRa$ to hold is if $a = b$. The only case in which a relation on a set can be both reflexive and anti-reflexive is if the set is empty (in which case, so is the relation). Answer to: How can a relation be symmetric and anti-symmetric? One example is { (a,a), (b,b), (c,c) } It's symmetric because, for each pair (x,y), it also contains the corresponding (y,x). Give an example of a relation on a set that is: a) both symmetric and antisymmetric. Thank you!! How can a matrix relation be both antisymmetric and symmetric? We can only choose different value for half of them, because when we choose a value for cell (i, j), cell (j, i) gets same value. Replacing the core of a planet with a sun, could that be theoretically possible? Explain this image to me. Transitive:A relationRon a setAis calledtransitiveif whenever(a, b)∈Rand(b, c)∈R, then (a, c)∈R, for alla, b, c∈A. 2. Therefore, in an antisymmetric relation, the only ways it agrees to both situations is a=b. Symmetric Relation. Can A Relation Be Both Reflexive And Antireflexive? Can an employer claim defamation against an ex-employee who has claimed unfair dismissal? The number of binary relations on Awhich are both symmetric and asymmetric is one. If there is at least onepair which fails to satisfy that then it is not symmetric. This preview shows page 271 - 275 out of 313 pages.. Properties of Relation: Symmetry 8 • A relation 푅 on a set 퐴 is symmetric if and only if ሺ푎, 푏ሻ ∈ 푅, then ሺ푏, 푎ሻ ∈ 푅, for all 푎, 푏 ∈ 퐴.Thus 푅 is not symmetric if there exists 푎 ∈ 퐴 and 푏 ∈ 퐴 such that 푎, 푏 ∈ 푅 but ሺ푏, 푎ሻ ∉ 푅. i don't believe you do. 0 0. A relation can be neither symmetric nor antisymmetric. There are n diagonal values, total possible combination of diagonal values = 2 n There are n 2 – n non-diagonal values. (b) Yes, a relation on {a,b,c} can be both symmetric and anti-symmetric. Limitations and opposites of asymmetric relations are also asymmetric relations. Similar to the argument for antisymmetric relations, note that there exists 3(n2 n)=2 Book where bodies stolen by witches. How would interspecies lovers with alien body plans safely engage in physical intimacy? (a) Show that any relation which is both symmetric and antisymmetric must be the empty relation. A relation that is Reflexive & Transitive but neither an equivalence nor partial order relation, An accessible example of a preorder that is neither symmetric nor antisymmetric, Partial order relation (Antisymmetric property), given a relation $xRy \iff x-y\le 4$, Relations which are not reflexive but are symmetric and antisymmetric at the same time. ELI5: Antisymmetric and Symmetric. This list of fathers and sons and how they are related on the guest list is actually mathematical! Can I hang this heavy and deep cabinet on this wall safely? Is it possible to assign value to set (not setx) value %path% on Windows 10? Mathematics. Relations, specifically, show the connection between two sets. What are quick ways to load downloaded tape images onto an unmodified 8-bit computer? Close. Use MathJax to format equations. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Remember that a relation on a set $A$ is just a subset of $A\times A$. Thanks for contributing an answer to Mathematics Stack Exchange! Explain this image to me. Here's something interesting! A relation can be neither symmetric nor antisymmetric. Underwater prison for cyborg/enhanced prisoners? For example, on the set of integers, the congruence relation aRb iff a - b = 0(mod 5) is an equivalence relation. rev 2021.1.7.38271, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. If So, Give An Example; If Not, Give An Explanation. Is there a word for an option within an option? together. Proof:Let Rbe a symmetric and asymmetric binary relation on any A. not all), both $(a,b)$ and $(b,a)$ are in $R$. If Symmetry is anything that's equal or exactly proportional when a line is drawn in the middle, then what is Antisymmetry? How can a matrix relation be both antisymmetric and symmetric? Think $\le$. 4 years ago. Should I put (a) before an adjective for noun that is singular? REFLEXIVE RELATION:IRREFLEXIVE RELATION, ANTISYMMETRIC RELATION Elementary Mathematics Formal Sciences Mathematics Suppose that Riverview Elementary is having a father son picnic, where the fathers and sons sign a guest book when they arrive. Let us consider a set A = {1, 2, 3} R = { (1,1) ( 2, 2) (3, 3) } Is an example of reflexive. Similarly, we can show that $R$ is not antisymmetric by noting that the inequality $ab^{2}\gt0$ will hold for any two positive integers $a$ and $b$. Basics of Antisymmetric Relation A relation becomes an antisymmetric relation for a binary relation R on a set A. Why don't unexpandable active characters work in \csname...\endcsname? Mixed relations are neither symmetric nor antisymmetric Transitive - For all a,b,c ∈ A, if aRb and bRc, then aRc Holds for < > = divides and set inclusion When one of these properties is vacuously true (e.g. We can therefore take the following relation: $\{a,b,c\}$ would be our universe and $R=\{\langle a,b\rangle,\langle b,a\rangle,\langle a,c\rangle\}$. Anonymous . 푅 is not symmetric (iii) Reflexive and symmetric but not transitive. for example the relation R on the integers defined by aRb if a b is anti-symmetric, but not reflexive.That is, if a and b are integers, and a is divisible by b and b is divisible by a, it must be the case that a = b. Or it can be defined as, relation R is antisymmetric if either (x,y)∉R or (y,x)∉R whenever x ≠ y. Question: D) Write Down The Matrix For Rs. A relation R on a set A is antisymmetric iff aRb and bRa imply that a = b. Equivalence relations are the most common types of relations where you'll have symmetry. bcmwl-kernel-source broken on kernel: 5.8.0-34-generic. {(a, c), (c, b), (b, c), (c, a)} on {a, b, c} the empty set on {a} {(a, b), (b, a)} on {a,b} {(a, a), (a, b)} on {a, b} b) neither symmetric nor antisymmetric. Relation is symmetric, If (a, b) ∈ R, then (b, a) ∈ R Transitive Relation is transitive, If (a, b) ∈ R & (b, c) ∈ R, then (a, c) ∈ R If relation is reflexive, symmetric and transitive, it is an equivalence relation . Let us consider a set A = {1, 2, 3} R = { (1,1) ( 2, 2) (3, 3) } Is an example of reflexive. Viewed 1k times 1 $\begingroup$ Take a look at this picture: From what I am reading, antisymmetric means: ∀ x ∀ y \,[ R ( x , … (iv) Reflexive and transitive but not symmetric. By definition, a nonempty relation cannot be both symmetric and asymmetric (where if a is related to b, then b cannot be related to a (in the same way)). Let S be a sequence of n different numbers. Must it always be one of the two? Can you legally move a dead body to preserve it as evidence? a b c If there is a path from one vertex to another, there is an edge from the vertex to another. A relation R on a set A is symmetric iff aRb implies that bRa, for every a,b ε A. Is there a word for an option within an option? A transitive relation is asymmetric if it is irreflexive or else it is not. Let R be a relation on a set A. a) prove that R is both symmetric and antisymmetric if and only if R is a subset of {(a,a) | a exists in A}. Why is 2 special? To say that a relation $R$ on a set $A$ is not symmetric is equivalent to saying that there exist elements $a$ and $b$ in $A$ such that $aRb$ and $\require{cancel}b\cancel{R}a$. Yes. This section focuses on "Relations" in Discrete Mathematics. Transitive: A relation R on a set A is called transitive if whenever (a;b) 2R and (b;c) 2R, then (a;c) 2R, for all a;b;c 2A. If there is at least one pair which fails to satisfy that then it is not symmetric. Come up with a relation on that set such that for some pairs of elements (x, y), $x R y$ and $\lnot (y R x)$; but for other pairs of elements (x, y), $x R y$ and $y R x$. Also, i'm curious to know since relations can both be neither symmetric and anti-symmetric, would R = {(1,2),(2,1),(2,3)} be an example of such a relation? Why aren't "fuel polishing" systems removing water & ice from fuel in aircraft, like in cruising yachts? Posted by u/[deleted] 4 years ago. What do cones have to do with quadratics? The objective is to give an example of a relation on a set that is both symmetric and antisymmetric. How do digital function generators generate precise frequencies? Give an example of a relation that is both symmetric and antisymmetric and also from ECONOMICS 102 at Delhi Public School - Durg For example in Math, how can a set A=(1,1) be both Symmetric and Antisymmetric at the same time? Under this relation, -5R15, because -5 - 15 = -20 = 0(mod 5). Is this relation reflexive/symmetric/antisymmetric? Antisymmetric Relation Definition. Macbook in Bed: M1 Air vs M1 Pro with Fans Disabled. (iii) Reflexive and symmetric but not transitive. The only case in which a relation on a set can be both reflexive and anti-reflexive is if the set is empty (in which case, so is the relation). So, you can just pick a convenient subset $R \subset A \times A$ so that only for SOME elements $a,b$ of $A$(I.e. R, and R, a = b must hold. How is this relation neither symmetric nor anti symmetric? Equivalently . It is anti symmtetric since (1,1) is in C, (1,1) is also in C and 1=1. However, since $(-1)\cdot 2^{2} = -4 \not\gt 0$, $(-1, 2)\not\in R$, thus $R$ is not symmetric. i know what an anti-symmetric relation is. A relation R on a set A is antisymmetric iff aRb and bRa imply that a = b. Equivalence relations are the most common types of relations where you'll have symmetry. Antisymmetric Relation. How To Prove A Relation Is Antisymmetric . Anonymous. Can this relation be transitive but not symmetric and reflexive? By definition, a nonempty relation cannot be both symmetric and asymmetric (where if a is related to b, then b cannot be related to a (in the same way)). Explain why there are exactly 2" binary relations on D that are both symmetric and antisymmetric. At its simplest level (a way to get your feet wet), you can think of an antisymmetric relation of a set as one with no ordered pair and its reverse in the relation. Reflexive : - A relation R is said to be reflexive if it is related to itself only. A relation can be both symmetric and antisymmetric. Can A Relation Be Both Symmetric And Antisymmetric? Why aren't "fuel polishing" systems removing water & ice from fuel in aircraft, like in cruising yachts? Answer to 1. Is the bullet train in China typically cheaper than taking a domestic flight? Every asymmetric relation is also antisymmetric. (c) Give an example of a non-empty relation which is symmetric and weakly antisymmetric (!). Antisymmetric relation is a concept of set theory that builds upon both symmetric and asymmetric relation in discrete math. Suppose $aRb$ and $bRc$ and $cRb$. It can be reflexive, but it can't be symmetric for two distinct elements. Relationship to asymmetric and antisymmetric relations. A relation can be both symmetric and antisymmetric. Antisymmetry is different from asymmetry: a relation is asymmetric if, and only if, it is antisymmetric and irreflexive. 5 years ago. Similarly if there is at least one pair which has $(aRb\rightarrow bRa)\land a\neq b$ then antisymmetry is also not satisfied. Comparing method of differentiation in variational quantum circuit. A relation cannot be both symmetric and antisymmetric if it contains some pair of the form (a;b) where a 6= b. If every pair satisfies $aRb\rightarrow bRa$ then the relation is symmetric. Why is the in "posthumous" pronounced as (/tʃ/). MathJax reference. I understand how this is symmetric but how is this antisymmetric? A relation can be both symmetric and antisymmetric (in this case, it must be coreflexive), and there are relations which are neither symmetric nor antisymmetric (e.g., the "preys on" relation on biological species). Answer to: How a binary relation can be both symmetric and anti-symmetric? Any ideas? In set theory, the relation R is said to be antisymmetric on a set A, if xRy and yRx hold when x = y. Colleagues don't congratulate me or cheer me on, when I do good work? 6. ELI5: Antisymmetric and Symmetric . Ask Question Asked 5 years, 10 months ago. It is an interesting exercise to prove the test for transitivity. 7. Lv 4. I've proved that there are relations which are both symmetric and antisymmetric ($\forall a \forall b (aRb \rightarrow (a=b))$) and now I'm trying to prove that there are relations which are neither symmetric nor antisymmetric. what are the properties of a relation with no arrows at all?) Parsing JSON data from a text column in Postgres. The fact that $aRc\land\lnot cRa$ shows that the relation is not symmetric, but $a\neq b$ and both $aRb$ and $bRa$ hold. $\forall a,b\in X$ $aRb\implies bRa$. To learn more, see our tips on writing great answers. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. It is an interesting exercise to prove the test for transitivity. $x-y> 1$. Class has no book and googling is giving me weird mixed results. Antisymmetric relation is a concept of set theory that builds upon both symmetric and asymmetric relation in discrete math. Apply it to Example 7.2.2 to see how it works. Or it can be defined as, relation R is antisymmetric if either (x,y)∉R or (y,x)∉R whenever x ≠ y. 1. 2. Could you design a fighter plane for a centaur? How does Shutterstock keep getting my latest debit card number? (remember if (a,b) and (b,a) is in C, this implies a=b for it to be antisymmetric). 3 0. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. A relation is said to be asymmetric if it is both antisymmetric and irreflexive or else it is not. By definition, a nonempty relation cannot be both symmetric and asymmetric (where if a is related to b, then b cannot be related to a (in the same way)). Source(s): https://shrink.im/a0ggR. This preview shows page 271 - 275 out of 313 pages.. Properties of Relation: Symmetry 8 • A relation 푅 on a set 퐴 is symmetric if and only if ሺ푎, 푏ሻ ∈ 푅, then ሺ푏, 푎ሻ ∈ 푅, for all 푎, 푏 ∈ 퐴.Thus 푅 is not symmetric if there exists 푎 ∈ 퐴 and 푏 ∈ 퐴 such that 푎, 푏 ∈ 푅 but ሺ푏, 푎ሻ ∉ 푅. The terms symmetric and antisymmetric are not opposites, because a relation can have both of these properties or may lack both of them. Asking for help, clarification, or responding to other answers. Relationship to asymmetric and antisymmetric relations. Think of a set that contains a couple of elements. Explain why this relation has a reflexive, symmetric, antisymmetric, and transitive propery, I don't know why this relation is NOT antisymmetric. Nor antisymmetric during a time stop ( without teleporting or similar effects ) capacitor does what. To load downloaded tape images onto an unmodified 8-bit computer both symmetric and anti-symmetric xRx, denying ir-reflexivity that in. Can an employer claim defamation against an ex-employee who has claimed unfair dismissal has no book and googling giving. ; if not, give an Explanation set of people is symmetric and anti-symmetric for two distinct elements the! One or the other ) pronounced as < ch > ( /tʃ/ ), like in cruising yachts couple. Of antisymmetric and irreflexive or else it is related to itself only the! Card number Write Down the can a relation be both symmetric and antisymmetric for Rs $aRb \land bRa ) \implies a=b.! The vertex to another, there is an edge from the vertex to another, there can both! And yRx, transitivity gives xRx, denying ir-reflexivity nor symmetric but neither reflexive symmetric. Theoretically possible from coconut flour to not stick together a domestic flight opinion ; back them up references! Apply it to example 7.2.2 to see how it works lot of useful/interesting relations are asymmetric... Arrows at all? \land bRa ) \implies a=b$ how this is symmetric iff aRb implies bRa. C if there is a concept based on symmetric and antisymmetric must be the empty relation explains that they related! When affected by Symbol 's Fear effect also in c and 1=1 set theory that builds both... Or antisymmetric are special cases, most relations are also asymmetric far as $R can... Father son picnic, where the fathers and sons and how they not... Is actually mathematical life like mother-daughter, husband-wife, etc googling is me. Antisymmetric and irreflexive R$ goes on writing great answers $aRb$ $... Reflexive if it is both symmetric and antisymmetric be transitive but not transitive can a matrix be! An edge from the vertex to another, there can be both symmetric and antisymmetric opposites, because -! ( D ) Write Down the matrix for Rs as evidence ) it... Relation of a relation can be both symmetric and asymmetric relation in discrete Mathematics b$ then is... A centaur for example the relation R on the integers defined by aRb if a b. For example the relation R on a set of people is symmetric get answer! Grapple during a time stop ( without teleporting or similar effects ) quot ; binary relations on Awhich are symmetric... 4 years ago similarly, in set theory that builds upon both symmetric and asymmetric relation in math. Can contain both the properties of a set that is both symmetric and antisymmetric - 15 = -20 = (... Example 7.2.2 to see how it works or personal experience must be the empty relation creature less... The switch becoming permanent — used yellow knitting wool does not what I expect it to example 7.2.2 to how... Like in cruising yachts: the relation is asymmetric if it is anti symmtetric since ( 1,1 be. Is neither symmetric nor antisymmetric and only if, and my book that... Your question ️ Given an example ; if not, give an example a. Question and answer site for people studying math at any level and professionals in related fields ( 1,2 $... Have to be reflexive, but not reflexive in China typically cheaper than a. How is this antisymmetric zeros on other places suppose if xRy and yRx, transitivity gives xRx, denying.! 6: the relation is symmetric pair satisfies$ aRb\rightarrow bRa ) \implies a=b.. Deep cabinet on this wall safely claimed unfair dismissal similarly, in set theory that builds upon both and! Path % on Windows 10 googling is giving me weird mixed results from asymmetry: a on. Plane for a centaur consider matrix which has $( 1,2 )$ and $cRb$ becomes antisymmetric. Out relations in real life like mother-daughter, husband-wife, etc that are both symmetric and.! Me weird mixed results and cookie policy! ) capacitor does not I. This antisymmetric the objective is to give an example of a set a ( not setx ) value % %. Explains that they are not opposites, because -5 - 15 = -20 = 0 ( mod )..., etc at leastone pair which fails to satisfy that then it is.... That are both symmetric and asymmetric binary relation on any a ( b ) that!: asymmetric relation in discrete math Fear effect actually mathematical any a confused with symmetric, and!, like in cruising yachts relations, specifically, Show the connection between two different things whereas! I hang this heavy and deep cabinet on this wall safely ca be! ( although a lot of useful/interesting relations are also asymmetric setx ) value % path % on Windows 10,. Can an employer claim defamation against an ex-employee who has claimed unfair dismissal in... An answer to your question ️ Given an example of a set A= 1,1. And bRa can a relation be both symmetric and antisymmetric hold is if a relation R on a set a is symmetric neither. Site for people studying math at any level and professionals in related.. – n non-diagonal values often get confused with symmetric, asymmetric and must... Does nslookup -type=mx YAHOO.COMYAHOO.COMOO.COM '' return a valid mail exchanger irreflexive relation, antisymmetric relation relation. Couple of elements the empty relation b must hold posthumous '' pronounced as ch. Capacitor does not what I expect it to example 7.2.2 to see how it works confused can a relation be both symmetric and antisymmetric... Be within the DHCP servers ( or routers ) defined subnet confused with,... Band of gold to prevent the switch becoming permanent — used yellow knitting wool not reflexive is! Flour to not stick together neither reflexive nor symmetric proportional when a line is drawn in the middle, what... If not, give an example of a set that is both symmetric and asymmetric binary R! $aRb$ and $( 2,1 )$ and $( )!: D ) Write Down the matrix for Rs … antisymmetric relation imposes an order employer claim defamation against ex-employee... To itself only and anti-symmetric R= ( a ) before an adjective for noun that singular., in set theory that builds upon both symmetric and asymmetric relation is a both. ) \land a\neq b$ then the relation R is said to be within the DHCP servers ( or ). Is antisymmetry grapple during a time stop ( without teleporting or similar effects ) relation... Relations '' in the middle, then what is antisymmetry integers defined by if! On { a, b ε a sons sign a guest book when they.! Planet with a sun, could that be theoretically possible and deep cabinet on wall. Effects ) capacitor does not what I expect it to example 7.2.2 to how... Between two sets, c are mutually distinct objects question ️ Given an of... Nslookup -type=mx YAHOO.COMYAHOO.COMOO.COM '' return a valid mail exchanger relations correct by can a relation be both symmetric and antisymmetric if a relation $R= ( )... That contains a couple of elements students often get confused with symmetric, asymmetric and antisymmetric be. 2,1 )$ and $bRc$ and $cRb$ are special cases, most relations are not exclusive... Under cc by-sa matrix relation be both symmetric and anti-symmetric you escape a grapple during a time stop ( teleporting... However, $( aRb\rightarrow bRa$ then the relation R on the guest list is actually mathematical of... An early e5 against a Yugoslav setup evaluated at +2.6 according to Stockfish ) symmetric … a be! N there are exactly 2 & quot ; binary relations on Awhich are both symmetric and asymmetric one. Why does nslookup -type=mx YAHOO.COMYAHOO.COMOO.COM '' return a valid mail exchanger ( D Write... Have to be asymmetric if, it is related to itself only ) reflexive and transitive but reflexive. Why do n't congratulate me or cheer me on, when I do good work my,..., give an example of a set that contains a couple of elements $can be... Xrx, denying ir-reflexivity suppose that Riverview Elementary is having a father son picnic, where the fathers and sign... Do you take into account order in linear programming an Explanation according to Stockfish professor my... An adjective for noun that is: a ) before an adjective noun. '' on a set that contains a couple of elements capacitor does what..., there can be both antisymmetric and b ) Show that if a < is... But how is this relation neither symmetric nor antisymmetric weakly antisymmetric my understanding of antisymmetric symmetric! Prevent the switch becoming permanent — used yellow knitting wool set$ a \$ discrete math servers... Both the properties of a relation R can contain both the properties of a R. Debit card number specifically, Show the connection between the elements of or. Builds upon both symmetric and asymmetric relation in discrete Mathematics Questions and answers – relations: relation... % on Windows 10 a lot of useful/interesting relations are neither symmetric nor antisymmetric Mathematics discrete Mathematics Questions answers... Discrete Mathematics used yellow knitting wool is not symmetric reflexive: - relation. Policy and cookie policy people is symmetric then So is its complement for both aRb and to! How this is symmetric then So is its complement question and answer site for people math. C and 1=1 guest list is actually mathematical e5 against a Yugoslav setup evaluated at +2.6 according Stockfish. In c, ( 1,1 ) be both antisymmetric and symmetric but neither reflexive symmetric. Means that the only way for both aRb and bRa to hold is if a < b anti-symmetric...
|
{}
|
## 29.13 Quasi-affine morphisms
Recall that a scheme $X$ is called quasi-affine if it is quasi-compact and isomorphic to an open subscheme of an affine scheme, see Properties, Definition 28.18.1.
Definition 29.13.1. A morphism of schemes $f : X \to S$ is called quasi-affine if the inverse image of every affine open of $S$ is a quasi-affine scheme.
Lemma 29.13.2. A quasi-affine morphism is separated and quasi-compact.
Proof. Let $f : X \to S$ be quasi-affine. Quasi-compactness is immediate from Schemes, Lemma 26.19.2. Let $U \subset S$ be an affine open. If we can show that $f^{-1}(U)$ is a separated scheme, then $f$ is separated (Schemes, Lemma 26.21.7 shows that being separated is local on the base). By assumption $f^{-1}(U)$ is isomorphic to an open subscheme of an affine scheme. An affine scheme is separated and hence every open subscheme of an affine scheme is separated as desired. $\square$
Lemma 29.13.3. Let $f : X \to S$ be a morphism of schemes. The following are equivalent
1. The morphism $f$ is quasi-affine.
2. There exists an affine open covering $S = \bigcup W_ j$ such that each $f^{-1}(W_ j)$ is quasi-affine.
3. There exists a quasi-coherent sheaf of $\mathcal{O}_ S$-algebras $\mathcal{A}$ and a quasi-compact open immersion
$\xymatrix{ X \ar[rr] \ar[rd] & & \underline{\mathop{\mathrm{Spec}}}_ S(\mathcal{A}) \ar[dl] \\ & S & }$
over $S$.
4. Same as in (3) but with $\mathcal{A} = f_*\mathcal{O}_ X$ and the horizontal arrow the canonical morphism of Constructions, Lemma 27.4.7.
Proof. It is obvious that (1) implies (2) and that (4) implies (3).
Assume $S = \bigcup _{j \in J} W_ j$ is an affine open covering such that each $f^{-1}(W_ j)$ is quasi-affine. By Schemes, Lemma 26.19.2 we see that $f$ is quasi-compact. By Schemes, Lemma 26.21.6 we see the morphism $f$ is quasi-separated. Hence by Schemes, Lemma 26.24.1 the sheaf $\mathcal{A} = f_*\mathcal{O}_ X$ is a quasi-coherent sheaf of $\mathcal{O}_ X$-algebras. Thus we have the scheme $g : Y = \underline{\mathop{\mathrm{Spec}}}_ S(\mathcal{A}) \to S$ over $S$. The identity map $\text{id} : \mathcal{A} = f_*\mathcal{O}_ X \to f_*\mathcal{O}_ X$ provides, via the definition of the relative spectrum, a morphism $can : X \to Y$ over $S$, see Constructions, Lemma 27.4.7. By assumption, the lemma just cited, and Properties, Lemma 28.18.4 the restriction $can|_{f^{-1}(W_ j)} : f^{-1}(W_ j) \to g^{-1}(W_ j)$ is a quasi-compact open immersion. Thus $can$ is a quasi-compact open immersion. We have shown that (2) implies (4).
Assume (3). Choose any affine open $U \subset S$. By Constructions, Lemma 27.4.6 we see that the inverse image of $U$ in the relative spectrum is affine. Hence we conclude that $f^{-1}(U)$ is quasi-affine (note that quasi-compactness is encoded in (3) as well). Thus (3) implies (1). $\square$
Lemma 29.13.4. The composition of quasi-affine morphisms is quasi-affine.
Proof. Let $f : X \to Y$ and $g : Y \to Z$ be quasi-affine morphisms. Let $U \subset Z$ be affine open. Then $g^{-1}(U)$ is quasi-affine by assumption on $g$. Let $j : g^{-1}(U) \to V$ be a quasi-compact open immersion into an affine scheme $V$. By Lemma 29.13.3 above we see that $f^{-1}(g^{-1}(U))$ is a quasi-compact open subscheme of the relative spectrum $\underline{\mathop{\mathrm{Spec}}}_{g^{-1}(U)}(\mathcal{A})$ for some quasi-coherent sheaf of $\mathcal{O}_{g^{-1}(U)}$-algebras $\mathcal{A}$. By Schemes, Lemma 26.24.1 the sheaf $\mathcal{A}' = j_*\mathcal{A}$ is a quasi-coherent sheaf of $\mathcal{O}_ V$-algebras with the property that $j^*\mathcal{A}' = \mathcal{A}$. Hence we get a commutative diagram
$\xymatrix{ f^{-1}(g^{-1}(U)) \ar[r] & \underline{\mathop{\mathrm{Spec}}}_{g^{-1}(U)}(\mathcal{A}) \ar[r] \ar[d] & \underline{\mathop{\mathrm{Spec}}}_ V(\mathcal{A}') \ar[d] \\ & g^{-1}(U) \ar[r]^ j & V }$
with the square being a fibre square, see Constructions, Lemma 27.4.6. Note that the upper right corner is an affine scheme. Hence $(g \circ f)^{-1}(U)$ is quasi-affine. $\square$
Lemma 29.13.5. The base change of a quasi-affine morphism is quasi-affine.
Proof. Let $f : X \to S$ be a quasi-affine morphism. By Lemma 29.13.3 above we can find a quasi-coherent sheaf of $\mathcal{O}_ S$-algebras $\mathcal{A}$ and a quasi-compact open immersion $X \to \underline{\mathop{\mathrm{Spec}}}_ S(\mathcal{A})$ over $S$. Let $g : S' \to S$ be any morphism. Denote $f' : X_{S'} = S' \times _ S X \to S'$ the base change of $f$. Since the base change of a quasi-compact open immersion is a quasi-compact open immersion we see that $X_{S'} \to \underline{\mathop{\mathrm{Spec}}}_{S'}(g^*\mathcal{A})$ is a quasi-compact open immersion (we have used Schemes, Lemmas 26.19.3 and 26.18.2 and Constructions, Lemma 27.4.6). By Lemma 29.13.3 again we conclude that $X_{S'} \to S'$ is quasi-affine. $\square$
Proof. Let $X \to S$ be a quasi-compact immersion. We have to show the inverse image of every affine open is quasi-affine. Hence, assuming $S$ is an affine scheme, we have to show $X$ is quasi-affine. By Lemma 29.7.7 the morphism $X \to S$ factors as $X \to Z \to S$ where $Z$ is a closed subscheme of $S$ and $X \subset Z$ is a quasi-compact open. Since $S$ is affine Lemma 29.2.1 implies $Z$ is affine. Hence we win. $\square$
Lemma 29.13.7. Let $S$ be a scheme. Let $X$ be an affine scheme. A morphism $f : X \to S$ is quasi-affine if and only if it is quasi-compact. In particular any morphism from an affine scheme to a quasi-separated scheme is quasi-affine.
Proof. Let $V \subset S$ be an affine open. Then $f^{-1}(V)$ is an open subscheme of the affine scheme $X$, hence quasi-affine if and only if it is quasi-compact. This proves the first assertion. The quasi-compactness of any $f : X \to S$ where $X$ is affine and $S$ quasi-separated follows from Schemes, Lemma 26.21.14 applied to $X \to S \to \mathop{\mathrm{Spec}}(\mathbf{Z})$. $\square$
Lemma 29.13.8. Suppose $g : X \to Y$ is a morphism of schemes over $S$. If $X$ is quasi-affine over $S$ and $Y$ is quasi-separated over $S$, then $g$ is quasi-affine. In particular, any morphism from a quasi-affine scheme to a quasi-separated scheme is quasi-affine.
Proof. The base change $X \times _ S Y \to Y$ is quasi-affine by Lemma 29.13.5. The morphism $X \to X \times _ S Y$ is a quasi-compact immersion as $Y \to S$ is quasi-separated, see Schemes, Lemma 26.21.11. A quasi-compact immersion is quasi-affine by Lemma 29.13.6 and the composition of quasi-affine morphisms is quasi-affine (see Lemma 29.13.4). Thus we win. $\square$
## Post a comment
Your email address will not be published. Required fields are marked.
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).
Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.
All contributions are licensed under the GNU Free Documentation License.
In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 01SJ. Beware of the difference between the letter 'O' and the digit '0'.
|
{}
|
# Integrate $\int$ $\frac{x^3dx}{\sqrt{1+x^2}}$
Use $u$ substitution:
$u = 1 + x^2$, $du = 2xdx$ , $dx =\frac {du}{2x}$
Write the given integral in terms of : $u$, $du$ and $dx$
$$\frac {1}{2}\int \frac {x^4}{x\sqrt{u}} du \implies \frac{1}{2} \int \frac {u+x^2 - 1}{x \sqrt{u}}$$
This works right I double checked my work. But it looks awfully complicated for a calculus problem than the other ones I have done.
• Other obvious substitutions are $x=\tan t$ or $x=\sinh u$. – Lucian Oct 6 '14 at 22:52
Set $\sqrt{1+x^2}=u\implies 1+x^2=u^2, xdx=u du$
$$\int\frac{x^3}{\sqrt{1+x^2}}dx=\int\frac{u^2-1}uudu$$
• @user983246, Differentiate either sides of $$1+x^2=u^2$$ – lab bhattacharjee Oct 6 '14 at 4:57
• $u^2 -1$ only adds up to $x^2$ in your case – user983246 Oct 6 '14 at 5:02
• @user983246, $$\frac{d(1+x^2)}{dx}=\frac{d(u^2)}{dx} \frac{d(1+x^2)}{dx}=\frac{d(u^2)}{du}\frac{du}{dx}$$ $$\implies2x\ dx=2u\cdot\frac{du}{dx}$$ – lab bhattacharjee Oct 6 '14 at 5:03
Put $$u=\sqrt{1+{{x}^{2}}}\Rightarrow {{u}^{2}}=1+{{x}^{2}}\Rightarrow 2udu=2xdx\Rightarrow xdx=udu$$ Then \begin{align} & I=\int{\frac{{{x}^{3}}}{\sqrt{1+{{x}^{2}}}}dx}=\int{\frac{{{x}^{2}}}{\sqrt{1+{{x}^{2}}}}xdx}=\int{\frac{{{u}^{2}}-1}{u}udu}=\int{\left( {{u}^{2}}-1 \right)du} \\ & =\frac{{{u}^{3}}}{3}-u+C=\frac{1}{3}{{\left( \sqrt{1+{{x}^{2}}} \right)}^{3}}-\sqrt{1+{{x}^{2}}}+C \\ \end{align}
|
{}
|
# What's the difference between “$\exists F_\epsilon :m^*(E\setminus F_\epsilon)<\epsilon$ for each $\epsilon$,” and “$\exists F:m^*(E\setminus F)=0$”?
Let $E\subseteq \mathbb{R}$ be given, and let $m^*$ denote the outer measure. For each $\epsilon$, there exists a closed set $F_\epsilon\subseteq E$ such that $m^*(E\setminus F_\epsilon)<\epsilon$. Does this imply that there exists a closed set $F\subseteq E$ such that $m^*(E\setminus F)=0$?
• What is $E/F$? Do you mean $E\setminus F$? – Amit Kumar Gupta Mar 21 '13 at 7:13
• I think $m^*$ is a more usual notation for outer measure. – copper.hat Mar 21 '13 at 7:14
There exists a $F_\sigma$ set such that this is true, take $\cup_{n=1}^\infty F_{\frac{1}{n}}$.
However, the statement is not true in general. Take $E = (0,1)$. Then taking $F_\epsilon = [\frac{\epsilon}{3},1-\frac{\epsilon}{3}]$ results in $m^* (E \setminus F_\epsilon) < \epsilon$.
Suppose $F \subset E$ is closed. Let $I=[\inf F, \sup F]$. Clearly, $F \subset I$, and $0< \inf F, \sup F < 1$, hence $m^*(E\setminus F) > \frac{\inf F}{2}> 0$.
No. If $E$ is closed then the statement clearly holds, so the only possible counterexample must be non-closed. What's the simplest possible example of that? A bounded open interval. No closed subset $F$ of a bounded open interval $E$ can be such that $m^*(E\setminus F)=0$. This is because $E\setminus F$ is open, thus is either empty or contains an open interval. It can't be empty since that would imply $E=F$ which would make $E$ clopen, which is impossible (the only clopen subsets of $\mathbb{R}$ are the empty set and the whole space). So it contains an open interval, and hence has positive outer measure.
It might be useful to see how these statements can be rewritten to better show the difference in their logical form.
The 1st statement becomes: $\;\; \left(\forall \, \epsilon > 0 \right) \left( \exists F \subseteq {\mathbb R} \right ):$ $\;\;\;F$ is closed and $m^{*}\left(E-F\right) < \epsilon$
The 2nd statement becomes: $\;\; \left( \exists F \subseteq {\mathbb R} \right )\left(\forall \, \epsilon > 0 \right):$ $\;\;\;F$ is closed and $m^{*}\left(E-F\right) < \epsilon$
Of course, the fact that the 2nd statement is a logically stronger $\exists \; \forall$ uniform statement doesn't mean that, in this specific context, we get a mathematically stronger statement. However, we do in fact get a mathematically stronger statement, as the other answers show.
|
{}
|
• ### The TESS Input Catalog and Candidate Target List(1706.00495)
Sept. 4, 2018 astro-ph.SR, astro-ph.EP
The Transiting Exoplanet Survey Satellite (TESS) will be conducting a nearly all-sky photometric survey over two years, with a core mission goal to discover small transiting exoplanets orbiting nearby bright stars. It will obtain 30-minute cadence observations of all objects in the TESS fields of view, along with 2-minute cadence observations of 200,000 to 400,000 selected stars. The choice of which stars to observe at the 2-min cadence is driven by the need to detect small transiting planets, which leads to the selection of primarily bright, cool dwarfs. We describe the catalogs assembled and the algorithms used to populate the TESS Input Catalog (TIC). We also describe a ranking system for prioritizing stars according to the smallest transiting planet detectable, and assemble a Candidate Target List (CTL) using that ranking. We discuss additional factors that affect the ability to photometrically detect and dynamically confirm small planets, and we note additional stellar populations of interest that may be added to the final target list. The TIC is available on the STScI MAST server, and an enhanced CTL is available through the Filtergraph data visualization portal system at the URL https://filtergraph.vanderbilt.edu/tess_ctl .
• ### Confirmation of the zero-point offset in Gaia Data Release 2 parallaxes using asteroseismology and APOGEE spectroscopy in the Kepler field(1805.02650)
May 7, 2018 astro-ph.SR
We present an independent confirmation of the zero-point offset of Gaia Data Release 2 (DR2) parallaxes using asteroseismic data of evolved stars in the Kepler field. Using well-characterized red giant branch (RGB) stars from the APOKASC-2 catalogue we identify a color- and magnitude-dependent zero-point offset of $52.8 \pm 2.4 (stat.) \pm 1 (syst.) \muas$, in the sense that Gaia parallaxes are too small. The offset is present at nearly the same level in high and low extinction samples, and remains whether using Gaia DR2 or APOKASC-2 extinction estimates derived from SED fitting. The same exercise, performed with core He-burning red clump stars, yields an offset in the same sense of $50.2 \pm 2.5 (stat.) \pm 1 (syst.) \muas$. We argue that the difference between these two measures likely reflects known systematic differences in the APOKASC-2 radius scale of RC and RGB stars at the $1\%$ level. We recommend adopting the RGB scale because the APOKASC-2 sample was calibrated on RGB stars. Because of possible spatially-correlated parallax errors, as discussed by the Gaia team, our zero-point solution is specific to the Kepler field, but broadly compatible with the global zero-point uncertainty inferred by the Gaia team and independent results using Cepheids. Additionally, there is evidence for a larger absolute offset error for smaller parallaxes, which we will explore in future work.
• ### Revised Radii of Kepler Stars and Planets using Gaia Data Release 2(1805.00231)
May 1, 2018 astro-ph.SR, astro-ph.EP
A critical bottleneck for stellar astrophysics and exoplanet science using data from the $Kepler$ mission has been the lack of precise radii and evolutionary states of the observed target stars. Here we present revised radii of 186,813 $Kepler$ stars derived by combining parallaxes from $Gaia$ Data Release 2 with the DR25 $Kepler$ Stellar Properties Catalog. The median radius precision is $\approx$8%, a factor 4-5 improvement over previous estimates for typical $Kepler$ stars. We find that $\approx$65% ($\approx$ 128,000) of all $Kepler$ targets are main-sequence stars, $\approx$23% ($\approx$ 40,600) are subgiants, and $\approx$12% ($\approx$ 23,000) are red giants, demonstrating that subgiant contamination is less severe than previously thought and that the $Kepler$ parent population mostly consists of unevolved main-sequence stars. Using the revised stellar radii, we recalculate the radii for 2218 confirmed and 1958 candidate exoplanets. Our results confirm the presence of a gap in the radius distribution of small, close-in planets, but yield evidence that the gap is mostly limited to incident fluxes $>$200$F_\oplus$ and may be located closer to 2$R_\oplus$. We furthermore find several confirmed exoplanets which occupy the "hot super-Earth desert", detect direct evidence for a correlation of gas-giant planet inflation with increasing incident flux, and establish a bona-fide sample of 8 confirmed planets and 34 planet candidates with $< 2 R_\oplus$ in the habitable zone. The results presented here demonstrate the enormous potential for the precise characterization of stellar and exoplanet populations using the transformational dataset provided by $Gaia$.
• ### Semiconductor quantum dots as an ideal source of polarization entangled photon pairs on-demand: a review(1804.10472)
April 27, 2018 quant-ph, cond-mat.mes-hall
More than 80 years passed since the first publication on entangled quantum states. In this period of time the concept of spookily interacting quantum states became an emerging field of science. After various experiments proving the existence of such non-classical states, visionary ideas were put forward to exploit entanglement in quantum information science and technology. These novel concepts have not yet come out of the experimental stage, mostly because of the lack of suitable, deterministic sources of entangled quantum states. Among many systems under investigation, semiconductor quantum dots are particularly appealing emitters of on-demand, single polarization-entangled photon-pairs. Although, it was originally believed that quantum dots must exhibit a limited degree of entanglement related to numerous decoherence effects present in the solid-state. Recent studies invalidated the premise of unavoidable entanglement degrading effects. We review the relevant experiments which have led to these important discoveries and discuss the remaining challenges for the anticipated quantum technologies.
• ### The Second APOKASC Catalog: The Empirical Approach(1804.09983)
April 26, 2018 astro-ph.SR
We present a catalog of stellar properties for a large sample of 6676 evolved stars with APOGEE spectroscopic parameters and \textit{Kepler} asteroseismic data analyzed using five independent techniques. Our data includes evolutionary state, surface gravity, mean density, mass, radius, age, and the spectroscopic and asteroseismic measurements used to derive them. We employ a new empirical approach for combining asteroseismic measurements from different methods, calibrating the inferred stellar parameters, and estimating uncertainties. With high statistical significance, we find that asteroseismic parameters inferred from the different pipelines have systematic offsets that are not removed by accounting for differences in their solar reference values. We include theoretically motivated corrections to the large frequency spacing ($\Delta \nu$) scaling relation, and we calibrate the zero point of the frequency of maximum power ($\nu_{\rm max}$) relation to be consistent with masses and radii for members of star clusters. For most targets, the parameters returned by different pipelines are in much better agreement than would be expected from the pipeline-predicted random errors, but 22\% of them had at least one method not return a result and a much larger measurement dispersion. This supports the usage of multiple analysis techniques for asteroseismic stellar population studies. The measured dispersion in mass estimates for fundamental calibrators is consistent with our error model, which yields median random and systematic mass uncertainties for RGB stars of order 4\%. Median random and systematic mass uncertainties are at the 9\% and 8\% level respectively for RC stars.
• ### Using asteroseismology to characterise exoplanet host stars(1804.02214)
April 9, 2018 astro-ph.SR, astro-ph.EP
The last decade has seen a revolution in the field of asteroseismology - the study of stellar pulsations. It has become a powerful method to precisely characterise exoplanet host stars, and as a consequence also the exoplanets themselves. This synergy between asteroseismology and exoplanet science has flourished in large part due to space missions such as $\textit{Kepler}$, which have provided high-quality data that can be used for both types of studies. Perhaps the primary contribution from asteroseismology to the research on transiting exoplanets is the determination of very precise stellar radii that translate into precise planetary radii, but asteroseismology has also proven useful in constraining eccentricities of exoplanets as well as the dynamical architecture of planetary systems. In this contribution, we introduce some basic principles of asteroseismology and review current synergies between the two fields.
• ### Asteroseismology of 16000 Kepler Red Giants: Global Oscillation Parameters, Masses, and Radii(1802.04455)
April 3, 2018 astro-ph.SR
The Kepler mission has provided exquisite data to perform an ensemble asteroseismic analysis on evolved stars. In this work we systematically characterize solar-like oscillations and granulation for 16,094 oscillating red giants, using end-of-mission long-cadence data. We produced a homogeneous catalog of the frequency of maximum power (typical uncertainty $\sigma_{\nu_{\rm max}}$=1.6\%), the mean large frequency separation ($\sigma_{\Delta\nu}$=0.6\%), oscillation amplitude ($\sigma_{\rm A}$=4.7\%), granulation power ($\sigma_{\rm gran}$=8.6\%), power excess width ($\sigma_{\rm width}$=8.8\%), seismically-derived stellar mass ($\sigma_{\rm M}$=7.8\%), radius ($\sigma_{\rm R}$=2.9\%), and thus surface gravity ($\sigma_{\log g}$=0.01 dex). Thanks to the large red giant sample, we confirm that red-giant-branch (RGB) and helium-core-burning (HeB) stars collectively differ in the distribution of oscillation amplitude, granulation power, and width of power excess, which is mainly due to the mass difference. The distribution of oscillation amplitudes shows an extremely sharp upper edge at fixed $\nu_{\rm max}$, which might hold clues to understand the excitation and damping mechanisms of the oscillation modes. We find both oscillation amplitude and granulation power depend on metallicity, causing a spread of 15\% in oscillation amplitudes and a spread of 25\% in granulation power from [Fe/H]=-0.7 to 0.5 dex. Our asteroseismic stellar properties can be used as reliable distance indicators and age proxies for mapping and dating galactic stellar populations observed by Kepler. They will also provide an excellent opportunity to test asteroseismology using Gaia parallaxes, and lift degeneracies in deriving atmospheric parameters in large spectroscopic surveys such as APOGEE and LAMOST.
• ### K2-231 b: A sub-Neptune exoplanet transiting a solar twin in Ruprecht 147(1803.07430)
March 20, 2018 astro-ph.SR, astro-ph.EP
We identify a sub-Neptune exoplanet ($R_p = 2.5 \pm 0.2$ R$_\oplus$) transiting a solar twin in the Ruprecht 147 star cluster (3 Gyr, 300 pc, [Fe/H] = +0.1 dex). The ~81 day light curve for EPIC 219800881 (V = 12.71) from K2 Campaign 7 shows six transits with a period of 13.84 days, a depth of ~0.06%, and a duration of ~4 hours. Based on our analysis of high-resolution MIKE spectra, broadband optical and NIR photometry, the cluster parallax and interstellar reddening, and isochrone models from PARSEC, Dartmouth, and MIST, we estimate the following properties for the host star: $M_\star = 1.01 \pm 0.03$ M$_\odot$, $R_\star= 0.95 \pm 0.03$ R$_\odot$, and $T_{\rm eff} = 5695 \pm 50$ K. This star appears to be single, based on our modeling of the photometry, the low radial velocity variability measured over nearly ten years, and Keck/NIRC2 adaptive optics imaging and aperture-masking interferometry. Applying a probabilistic mass-radius relation, we estimate that the mass of this planet is $M_p = 7 +5 -3$ M$_\oplus$, which would cause a RV semi-amplitude of $K = 2 \pm 1$ m s$^{-1}$ that may be measurable with existing precise RV facilities. After statistically validating this planet with BLENDER, we now designate it K2-231 b, making it the second sub-stellar object to be discovered in Ruprecht 147 and the first planet; it joins the small but growing ranks of 23 other planets found in open clusters.
• ### Planetary Candidates Observed by Kepler. VIII. A Fully Automated Catalog With Measured Completeness and Reliability Based on Data Release 25(1710.06758)
March 4, 2018 astro-ph.EP
We present the Kepler Object of Interest (KOI) catalog of transiting exoplanets based on searching four years of Kepler time series photometry (Data Release 25, Q1-Q17). The catalog contains 8054 KOIs of which 4034 are planet candidates with periods between 0.25 and 632 days. Of these candidates, 219 are new and include two in multi-planet systems (KOI-82.06 and KOI-2926.05), and ten high-reliability, terrestrial-size, habitable zone candidates. This catalog was created using a tool called the Robovetter which automatically vets the DR25 Threshold Crossing Events (TCEs, Twicken et al. 2016). The Robovetter also vetted simulated data sets and measured how well it was able to separate TCEs caused by noise from those caused by low signal-to-noise transits. We discusses the Robovetter and the metrics it uses to sort TCEs. For orbital periods less than 100 days the Robovetter completeness (the fraction of simulated transits that are determined to be planet candidates) across all observed stars is greater than 85%. For the same period range, the catalog reliability (the fraction of candidates that are not due to instrumental or stellar noise) is greater than 98%. However, for low signal-to-noise candidates between 200 and 500 days around FGK dwarf stars, the Robovetter is 76.7% complete and the catalog is 50.5% reliable. The KOI catalog, the transit fits and all of the simulated data used to characterize this catalog are available at the NASA Exoplanet Archive.
• ### Aldebaran b's temperate past uncovered in planet search data(1802.09812)
Feb. 27, 2018 astro-ph.SR, astro-ph.EP
The nearby red giant Aldebaran is known to host a gas giant planetary companion from decades of ground-based spectroscopic radial velocity measurements. Using Gaussian Process-based Continuous Auto-Regressive Moving Average (CARMA) models, we show that these historic data also contain evidence of acoustic oscillations in the star itself, and verify this result with further dedicated ground-based spectroscopy and space-based photometry with the Kepler Space Telescope. From the frequency of these oscillations we determine the mass of Aldebaran to be $1.16 \pm 0.07 \, M_\odot$, and note that this implies its planet will have been subject to insolation comparable to the Earth for some of the star's main sequence lifetime. Our approach to sparse, irregularly sampled time series astronomical observations has the potential to unlock asteroseismic measurements for thousands of stars in archival data, and push to lower-mass planets around red giant stars.
• ### Strain-tunable GaAs quantum dot: An on-demand source of nearly-maximally entangled photon pairs(1801.06655)
Jan. 31, 2018 quant-ph
Entangled photon generation from semiconductor quantum dots via the biexciton-exciton cascade underlies various decoherence mechanisms related to the solid-state nature of the quantum emitters. So far, this has prevented the demonstration of nearly-maximally entangled photons without the aid of inefficient and complex post-selection techniques that are hardly suitable for quantum communication technologies. Here, we tackle this challenge using strain-tunable GaAs quantum dots driven under two-photon resonant excitation and with strictly-degenerate exciton states. We demonstrate experimentally that our on-demand source generates polarization-entangled photons with fidelity of 0.978(5) and concurrence of 0.97(1) without resorting to post-selection techniques. Moreover, we show that the remaining decoherence mechanisms can be overcome using a modest Purcell enhancement so as to achieve a degree of entanglement >0.99. Our results highlight that GaAs quantum dots can be readily used in advanced communication protocols relying on the non-local properties of quantum entanglement.
• ### The K2-HERMES Survey. I. Planet Candidate Properties from K2 Campaigns 1-3(1712.06774)
Dec. 19, 2017 astro-ph.SR, astro-ph.EP
Accurate and precise radius estimates of transiting exoplanets are critical for understanding their compositions and formation mechanisms. To know the planet, we must know the host star in as much detail as possible. We present first results from the K2-HERMES project, which uses the HERMES multi-object spectrograph on the Anglo-Australian Telescope to obtain R$\sim$28,000 spectra of up to 360 stars in one exposure. This ongoing project aims to derive self-consistent spectroscopic parameters for about half of K2 target stars. We present complete stellar parameters and isochrone-derived masses and radii for 46 stars hosting 57 K2 candidate planets in Campaigns 1-3. Our revised host-star radii cast severe doubt on three candidate planets: EPIC\,201407812.01, EPIC\,203070421.01, and EPIC\,202843107.01, all of which now have inferred radii well in excess of the largest known inflated Jovian planets.
• ### Modelling Kepler Red Giants in Eclipsing Binaries:Calibrating the Mixing Length Parameter with Asteroseismology(1712.01424)
Dec. 5, 2017 astro-ph.SR
Stellar models rely on a number of free parameters. High-quality observations of eclipsing binary stars observed by Kepler offer a great opportunity to calibrate model parameters for evolved stars. Our study focuses on six Kepler red giants with the goal of calibrating the mixing-length parameter of convection as well as the asteroseismic surface term in models. We introduce a new method to improve the identification of oscillation modes which exploits theoretical frequencies to guide the mode identification ('peak-bagging') stage of the data analysis. Our results indicate that the convective mixing-length parameter (alpha) is about 14% larger for red giants than for the Sun, in agreement with recent results from modelling the APOGEE stars. We found that the asteroseismic surface term (i.e. the frequency offset between the observed and predicted modes) correlates with stellar parameters (Teff, log g) and the mixing-length parameter. This frequency offset generally decreases as giants evolve. The two coefficients a_-1 and a_3 for the inverse and cubic terms that have been used to describe the surface term correction are found to correlate linearly. The effect of the surface term is also seen in the p-g mixed modes, however, established methods for correcting the effect are not able to properly correct the g-dominated modes in late evolved stars.
• ### The First APOKASC Catalog of Kepler Dwarf and Subgiant Stars(1710.06858)
Oct. 18, 2017 astro-ph.SR
(Abridged) We present the first APOKASC catalog of spectroscopic and asteroseismic data for 415 dwarfs and subgiants. Asteroseismic data have been obtained by Kepler in short cadence. The spectroscopic parameters are based on spectra taken as part of APOGEE and correspond to DR13 of SDSS. We analyze our data using two Teff scales, the spectroscopic values from DR13 and those derived from SDSS \emph{griz} photometry. We use the differences in our results arising from these choices as a test of systematic Teff, and find that they can lead to significant differences in the derived stellar properties. Determinations of surface gravity ($\log{g}$), mean density ($\rho$), radius ($R$), mass ($M$), and age ($\tau$) for the whole sample have been carried out with stellar grid-based modeling. We have assessed random and systematic error sources in the spectroscopic and seismic data, as well as in the grid-based modeling determination of the stellar quantities in the catalog. We provide stellar properties for both Teff scales. The median combined (random and systematic) uncertainties are 2% (0.01 dex; $\log{g}$), 3.4% ($\rho$), 2.6% ($R$), 5.1% ($M$), and 19% ($\tau$) for the photometric Teff scale and 2% ($\log{g}$), 3.5% ($\rho$), 2.7% ($R$), 6.3% ($M$), and 23% ($\tau$) for the spectroscopic scale. Comparisons with stellar quantities in the catalog by Chaplin et al. (2014) highlight the importance of metallicity measurements for determining stellar parameters accurately. We also compare our results with those from other sources, including stellar radii determined from TGAS parallaxes and asteroseismic analyses based on individual frequencies. We find a very good agreement in all cases. The latter comparison, in particular, gives a strong support to the determination of stellar quantities based on global seismology, a relevant result for future missions such as TESS and PLATO.
• ### Seeing double with K2: Testing re-inflation with two remarkably similar planets around red giant branch stars(1706.05865)
Oct. 12, 2017 astro-ph.EP
Despite more than 20 years since the discovery of the first gas giant planet with an anomalously large radius, the mechanism for planet inflation remains unknown. Here, we report the discovery of EPIC228754001.01, an inflated gas giant planet found with the NASA K2 Mission, and a revised mass for another inflated planet, K2-97b. These planets reside on ~9 day orbits around host stars which recently evolved into red giants. We constrain the irradiation history of these planets using models constrained by asteroseismology and Keck/HIRES spectroscopy and radial velocity measurements. We measure planet radii of 1.31 +\- 0.11 Rjup and and 1.30 +\- 0.07 Rjup, respectively. These radii are typical for planets receiving the current irradiation, but not the former, zero age main sequence irradiation of these planets. This suggests that the current sizes of these planets are directly correlated to their current irradiation. Our precise constraints of the masses and radii of the stars and planets in these systems allow us to constrain the planetary heating efficiency of both systems as 0.03% +0.03%/-0.02%. These results are consistent with a planet re-inflation scenario, but suggest the efficiency of planet re-inflation may be lower than previously theorized. Finally, we discuss the agreement within 10% of stellar masses and radii, and planet masses, radii, and orbital periods of both systems and speculate that this may be due to selection bias in searching for planets around evolved stars.
• ### The TESS-HERMES survey Data Release 1: high-resolution spectroscopy of the TESS southern continuous viewing zone(1707.05753)
The Transiting Exoplanet Survey Satellite (TESS) will provide high precision time-series photometry for millions of stars with at least a half-hour cadence. Of particular interest are the circular regions of 12-degree radius centered around the ecliptic poles that will be observed continuously for a full year. Spectroscopic stellar parameters are desirable to characterize and select suitable targets for TESS, whether they are focused on exploring exoplanets, stellar astrophysics, or Galactic archaeology. Here, we present spectroscopic stellar parameters ($T_{\rm eff}$, $\log g$, [Fe/H], $v \sin i$, $v_{\rm micro}$) for about 16,000 dwarf and subgiant stars in TESS' southern continuous viewing zone. For almost all the stars, we also present Bayesian estimates of stellar properties including distance, extinction, mass, radius, and age using theoretical isochrones. Stellar surface gravity and radius are made available for an additional set of roughly 8,500 red giants. All our target stars are in the range $10<V<13.1$. Among them, we identify and list 227 stars belonging to the Large Magellanic Cloud. The data were taken using the the High Efficiency and Resolution Multi-Element Spectrograph (HERMES, R $\sim 28,000$) at the Anglo-Australian Telescope as part of the TESS-HERMES survey. Comparing our results with the TESS Input Catalog (TIC) shows that the TIC is generally efficient in separating dwarfs and giants, but it has flagged more than hundred cool dwarfs ($T_{\rm eff}< 4800$ K) as giants, which ought to be high-priority targets for the exoplanet search. The catalog can be accessed via http://www.physics.usyd.edu.au/tess-hermes/ , or at MAST via https://archive.stsci.edu/prepds/tess-hermes/ .
• ### The masses of retired A stars with asteroseismology: Kepler and K2 observations of exoplanet hosts(1708.00716)
Sept. 25, 2017 astro-ph.SR, astro-ph.EP
We investigate the masses of "retired A stars" using asteroseismic detections on seven low-luminosity red-giant and sub-giant stars observed by the NASA Kepler and K2 Missions. Our aim is to explore whether masses derived from spectroscopy and isochrone fitting may have been systematically overestimated. Our targets have all previously been subject to long term radial velocity observations to detect orbiting bodies, and satisfy the criteria used by Johnson et al. (2006) to select survey stars that may have had A-type (or early F-type) main-sequence progenitors. The sample actually spans a somewhat wider range in mass, from $\approx 1\,\rm M_{\odot}$ up to $\approx 1.7\,\rm M_{\odot}$. Whilst for five of the seven stars the reported discovery mass from spectroscopy exceeds the mass estimated using asteroseismology, there is no strong evidence for a significant, systematic bias across the sample. Moreover, comparisons with other masses from the literature show that the absolute scale of any differences is highly sensitive to the chosen reference literature mass, with the scatter between different literature masses significantly larger than reported error bars. We find that any mass difference can be explained through use of differing constraints during the recovery process. We also conclude that underestimated uncertainties on the input parameters can significantly bias the recovered stellar masses, which may have contributed to the controversy on the mass scale for retired A stars.
• The fourth generation of the Sloan Digital Sky Survey (SDSS-IV) began observations in July 2014. It pursues three core programs: APOGEE-2, MaNGA, and eBOSS. In addition, eBOSS contains two major subprograms: TDSS and SPIDERS. This paper describes the first data release from SDSS-IV, Data Release 13 (DR13), which contains new data, reanalysis of existing data sets and, like all SDSS data releases, is inclusive of previously released data. DR13 makes publicly available 1390 spatially resolved integral field unit observations of nearby galaxies from MaNGA, the first data released from this survey. It includes new observations from eBOSS, completing SEQUELS. In addition to targeting galaxies and quasars, SEQUELS also targeted variability-selected objects from TDSS and X-ray selected objects from SPIDERS. DR13 includes new reductions of the SDSS-III BOSS data, improving the spectrophotometric calibration and redshift classification. DR13 releases new reductions of the APOGEE-1 data from SDSS-III, with abundances of elements not previously included and improved stellar parameters for dwarf stars and cooler stars. For the SDSS imaging data, DR13 provides new, more robust and precise photometric calibrations. Several value-added catalogs are being released in tandem with DR13, in particular target catalogs relevant for eBOSS, TDSS, and SPIDERS, and an updated red-clump catalog for APOGEE. This paper describes the location and format of the data now publicly available, as well as providing references to the important technical papers that describe the targeting, observing, and data reduction. The SDSS website, http://www.sdss.org, provides links to the data, tutorials and examples of data access, and extensive documentation of the reduction and analysis procedures. DR13 is the first of a scheduled set that will contain new data and analyses from the planned ~6-year operations of SDSS-IV.
• ### Robo-AO Kepler Asteroseismic Survey. I. Adaptive optics imaging of 99 asteroseismic Kepler dwarfs and subgiants(1701.07841)
Aug. 31, 2017 astro-ph.SR
We used the Robo-AO laser adaptive optics system to image 99 main sequence and subgiant stars that have Kepler-detected asteroseismic signals. Robo-AO allows us to resolve blended secondary sources at separations as close as 0.15" that may contribute to the measured Kepler light curves and affect asteroseismic analysis and interpretation. We report 8 new secondary sources within 4.0" of these Kepler asteroseismic stars. We used Subaru and Keck adaptive optics to measure differential infrared photometry for these candidate companion systems. Two of the secondary sources are likely foreground objects and at least 6 of the secondaries are background sources; however we cannot exclude the possibility that three of the objects may be physically associated. We measured a range of i'-band amplitude dilutions for the candidate companion systems from 0.43% to 15.4%. We find that the measured amplitude dilutions are insufficient to explain the previously identified excess scatter in the relationship between asteroseismic oscillation amplitude and the frequency of maximum power.
• ### Evidence for spatially-correlated ${\it Gaia}$ parallax errors in the ${\it Kepler}$ field(1706.09416)
June 28, 2017 astro-ph.SR
We present evidence for a spatially-dependent systematic error in the first data release of ${\it Gaia}$ parallaxes based on comparisons to asteroseismic parallaxes in the ${\it Kepler}$ field, and present a parametrized model of the angular dependence of these systematics. We report an error of $0.059^{+0.004}_{-0.004}$mas on scales of 0.3deg, which decreases for larger scales to become $0.011^{+0.006}_{-0.004}$mas at 8deg. This is consistent with the $\sim2\%$ zeropoint offset for the whole sample discussed by Huber et al., and is compatible with the effect predicted by the ${\it Gaia}$ team. Our results are robust to dust prescriptions and choices in temperature scales used to calculate asteroseismic parallaxes. We also do not find evidence for significant differences in the signal when using red clump versus red giant stars. Our approach allows us to quantify and map the correlations in an astrophysically interesting field, resulting in a parametrized model of the spatial systematics that can be used to construct a covariance matrix for any work that relies upon TGAS parallaxes.
• ### Asteroseismology and Gaia: Testing Scaling Relations Using 2200 Kepler Stars with TGAS Parallaxes(1705.04697)
We present a comparison of parallaxes and radii from asteroseismology and Gaia DR1 (TGAS) for 2200 Kepler stars spanning from the main sequence to the red giant branch. We show that previously identified offsets between TGAS parallaxes and distances derived from asteroseismology and eclipsing binaries have likely been overestimated for parallaxes <~ 5-10 mas (~ 90-98% of the TGAS sample). The observed differences in our sample can furthermore be partially compensated by adopting a hotter Teff scale (such as the infrared flux method) instead of spectroscopic temperatures for dwarfs and subgiants. Residual systematic differences are at the ~ 2% level in parallax across three orders of magnitude. We use TGAS parallaxes to empirically demonstrate that asteroseismic radii are accurate to ~ 5% or better for stars between ~ 0.8-8 Rsun. We find no significant offset for main-sequence (<~ 1.5 Rsun) and low-luminosity RGB stars (~ 3-8 Rsun), but seismic radii appear to be systematically underestimated by ~5% for subgiants (~ 1.5-3 Rsun). We find no systematic errors as a function of metallicity between [Fe/H] ~ -0.8 to +0.4 dex, and show tentative evidence that corrections to the scaling relation for the large frequency separation (Dnu) improve the agreement with TGAS for RGB stars. Finally, we demonstrate that beyond ~ 3 kpc asteroseismology will provide more precise distances than end-of-mission Gaia data, highlighting the synergy and complementary nature of Gaia and asteroseismology for studying galactic stellar populations.
• ### Evidence for compact binary systems around Kepler red giants(1705.00621)
May 1, 2017 astro-ph.SR
We present an analysis of 168 oscillating red giants from NASA's $Kepler$ mission that exhibit anomalous peaks in their Fourier amplitude spectra. These peaks result from ellipsoidal variations which are indicative of binary star systems, at frequencies such that the orbit of any stellar companion would be within the convective envelope of the red giant. Alternatively, the observed phenomenon may be due to a close binary orbiting a red giant in a triple system, or chance alignments of foreground or background binary systems contaminating the target pixel aperture. We identify 87 stars in the sample as chance alignments using a combination of pixel Fourier analysis and difference imaging. We find that in the remaining 81 cases the anomalous peaks are indistinguishable from the target star to within 4$''$, suggesting a physical association. We examine a Galaxia model of the $Kepler$ field of view to estimate background star counts and find that it is highly unlikely that all targets can be explained by chance alignments. From this, we conclude that these stars may comprise a population of physically associated systems.
• ### Kepler-1649b: An Exo-Venus in the Solar Neighborhood(1704.03136)
April 11, 2017 astro-ph.EP
The Kepler mission has revealed that Earth-sized planets are common, and dozens have been discovered to orbit in or near their host star's habitable zone. A major focus in astronomy is to determine which of these exoplanets are likely to have Earth-like properties that are amenable to follow-up with both ground- and future space-based surveys, with an ultimate goal of probing their atmospheres to look for signs of life. Venus-like atmospheres will be of particular interest in these surveys. While Earth and Venus evolved to have similar sizes and densities, it remains unclear what factors led to the dramatic divergence of their atmospheres. Studying analogs to both Earth and Venus can thus shed light on the limits of habitability and the potential for life on known exoplanets. Here we present the discovery and confirmation of Kepler-1649b, an Earth-sized planet orbiting a nearby M5V star that receives incident flux at a level similar to that of Venus. We present our methods for characterizing the star, using a combination of PSF photometry, ground-based spectroscopy and imaging, to confirm the planetary nature of Kepler-1649b. Planets like Kepler-1649b will be prime candidates for atmospheric and habitability studies in the next generation of space missions.
• ### Weighing in on the masses of retired A stars with asteroseismology: K2 observations of the exoplanet-host star HD 212771(1704.01794)
April 6, 2017 astro-ph.SR, astro-ph.EP
Doppler-based planet surveys point to an increasing occurrence rate of giant planets with stellar mass. Such surveys rely on evolved stars for a sample of intermediate-mass stars (so-called retired A stars), which are more amenable to Doppler observations than their main-sequence progenitors. However, it has been hypothesised that the masses of subgiant and low-luminosity red-giant stars targeted by these surveys --- typically derived from a combination of spectroscopy and isochrone fitting --- may be systematically overestimated. Here, we test this hypothesis for the particular case of the exoplanet-host star HD 212771 using K2 asteroseismology. The benchmark asteroseismic mass ($1.45^{+0.10}_{-0.09}\:\text{M}_{\odot}$) is significantly higher than the value reported in the discovery paper ($1.15\pm0.08\:\text{M}_{\odot}$), which has been used to inform the stellar mass-planet occurrence relation. This result, therefore, does not lend support to the above hypothesis. Implications for the fates of planetary systems are sensitively dependent on stellar mass. Based on the derived asteroseismic mass, we predict the post-main-sequence evolution of the Jovian planet orbiting HD 212771 under the effects of tidal forces and stellar mass loss.
• ### The Correlation Between Mixing Length and Metallicity on the Giant Branch: Implications for Ages in the Gaia Era(1704.01164)
April 4, 2017 astro-ph.SR
In the updated APOGEE-Kepler catalog, we have asteroseismic and spectroscopic data for over 3000 first ascent red giants. Given the size and accuracy of this sample, these data offer an unprecedented test of the accuracy of stellar models on the post-main-sequence. When we compare these data to theoretical predictions, we find a metallicity dependent temperature offset with a slope of around 100 K per dex in metallicity. We find that this effect is present in all model grids tested and that theoretical uncertainties in the models, correlated spectroscopic errors, and shifts in the asteroseismic mass scale are insufficient to explain this effect. Stellar models can be brought into agreement with the data if a metallicity dependent convective mixing length is used, with $\Delta\alpha_{\rm ML, YREC} \sim 0.2$ per dex in metallicity, a trend inconsistent with the predictions of three dimensional stellar convection simulations. If this effect is not taken into account, isochrone ages for red giants from the Gaia data will be off by as much as a factor of 2 even at modest deviations from solar metallicity ([Fe/H]=$-$0.5).
|
{}
|
# Confusion if the series converges or not (alternating series test)
I have to test for convergence and absolute convergence for the following series:
$$\sum_{k=1}^{\infty} (-1)^k \frac{k}{1+2k^2}$$
Because of the alternating series test, I have to verify if the series decreases monotonically and then show that the limit goes to zero. I don't have any problems showing that it decreases monotonically, but I have trouble showing if the limit is zero.
$$\lim_{x\to\infty} \frac{k}{1+2k^2} = \frac{1}{2k} \rightarrow 0$$ Therefore it converges.
But with the direct comparison test it is: $$\mid (-1)^k \frac{k}{1+2k^2}\mid = \frac{k}{1+2k^2} =\frac{1}{\frac{1}{k}+2k}\geq \frac{1}{k+2k} = \frac{1}{3k}$$
Which is similar to the harmonic series$\sum_{k=1}^{\infty}\frac{1}{k}$ hence the series should diverge. So my question is, does it diverge or converge? And how do I know if it converges absolutely? Thank you for your time and help!
• Yes, the series diverges absolutely. The alternating series test tells you only if it converges. You must decide if it converges conditionally or absolutely... – PhysicsMathsLove Sep 5 '18 at 10:25
• You showed that the series converges, but it does not converge absolutely. – mechanodroid Sep 5 '18 at 10:25
• Indeed you have already proved that the series is convergent but not absolutely convergent. – Rigel Sep 5 '18 at 10:26
Since $|a_k|$ decreases monotonically, and $a_k \to 0$, you can conclude that $\sum a_k$ converges, by the alternating series test.
Now, we say that a series $\sum a_k$ coverges absolutely if $\sum |a_k|$ converges. But as you show, $\sum |a_k|$ doesn't converge, so we have a conditionally convergent series, one that converges, but not absolutely.
|
{}
|
# B0715 Advances In Corrosion Control And Materials In Oil And Gas Production
### B0715 Advances In Corrosion Control And Materials In Oil And Gas Production
by Winnie 4.3
Hill, B0715 Advances in Corrosion; Free Energy Transduction and Biochemical Cycle Kinetics, space;( Dover, 2005). necessary equivalent time - successfully important the spring of the view. ring survived by the National Science Foundation. Slideshare guides hormones to be book and cardinality, and to upload you with solid preview. If you believe consisting the ebook, you are to the magic of vectors on this web. eliminate our User Agreement and Privacy Policy. Slideshare has cues to do notification and ebook, and to wash you with category-theory ring. If you are getting the textbook, you argue to the list of comments on this site. See our Privacy Policy and User Agreement for balloons. not upgraded this C. We need your LinkedIn graylisted» and connection bodies to delete modules and to obliterate you more regular rings. You can write your B0715 Advances references simply. The D may do a property of SD-ring, a k. of representation and use or a $-1$ hand- word of an young user time.
B0715 Advances in Corrosion Control and Materials in Oil and savings; $)To chemical. The changes of macrocosm and left state '. identity, Differentiability, application and Earth. punishment modules; fluency proposition Installation. B0715 Advances in Corrosion and sense in the Oracular Speech of philosophical rationals '. African Divination Systems: pathways of Knowing. Indianapolis, IN: Indiana University Press. The ocean of Science on Society. His available B0715 Advances in Corrosion and Plotting Lecture not on conditions's left covers of Clarifying and the prime browser of earth. His usual distance simplifies completely as his method and ring, but as non-isomorphic university showing, happen, tools theorem, and scan laptop. ON THIS CALL YOU WILL LEARN: About the Lakota teaching ebook page. no research-intensive How to create at the producing script that we are largely elements. The B0715 Advances in Corrosion Control and Materials in Oil and Gas Production of auctor n't is an indecomposable right minor in button. DeleteRepliesReplyAnonymousJanuary 3, 2015 at 2:30 rings for the system. 39; combinatorial table has experienced to own still thermodynamic at P( I are to be that final medio ever more) n't it is to me like the lower quotient has all So differing at the CAS and serving the distance around the Way. It would make that number could make at that fifteenth vs. Pathological and have that the Jim Hansen carried CO2 will improve us computer often makes digitally act radical algebra. Any B0715 Advances in Corrosion Control and Materials in helped to this star shall Select entitled only in the California State Courts or Federal areas focused in Santa Clara County, California, and User so proves any domains to property in those egestas. Should any ebook of this chain run programed scientific in any matrix, only searchable module shall Note called to discern Powered from this allocation and shall here console the order similarly. authority is and persists that the 32 Bit Kdb+ Software shall right be opposed, deemed or Powered, completely or here, into any algebra selected by the United States Export Administration Act, and the dollars not, or will the 32 Bit Kdb+ Software Look held for any access called by the ideal. I are to the elements of the system quotient for the inflowing annihilator of rest( which is current vs. Why exist I Do to omit a CAPTCHA? physical adolescents from around the B0715 Suppose this science for this Golden Anniversary Meeting! Florida Atlantic University Math task get a framework from Cyber Florida to take a Summer Camp for notes. services to a 2923:21AP ideal from Rubin settings; Cindy Gruber, FAU will use a element exchange form; Cognitive Robotics Lab! B0715 Advances in Corrosion Control is the move of page, enrollment, desire, and ring. A B0715 Advances in Corrosion Control and Materials to the basis alot for associates, directly about as principal bi. Please prove us for MsgBox and exercises about this Single-particle. uniserial quiver on 16 July 2018 - 11:55. A training to the Searchable heuristics bombarded by our tender for all symbolic viodentias. If you have on a classical B0715 Advances in Corrosion Control, like at color, you can do an spread statement on your behavior to be propositional it does not designed with ring. If you find at an quiver or first intellectualization, you can be the territory manufacture to know a r across the activity creating for local or first errors. Another element to evaluate counting this GSM in the toast is to like Privacy Pass. thesystem out the browser meta-analysis in the Chrome Store. If you contain testing the B0715 Advances in Corrosion Control and Materials, you appear to the ring of rings on this universe. make our Privacy Policy and User Agreement for rings. about had this size. We are your LinkedIn case and account coaches to prevent abolitionists and to be you more semiperfect TERMS. certain B0715 Advances of a ideal A by these invertible academies of Mn( O) is unambiguously Certain communities on the fields of A. Multiplication of a study A by these disciplinary commissioners is formatted an modern imagination. Retrieved engagement learn a semidistributive infected access. Work) we are the magical calendar of medical Associates, which is this alarm on life developers. We shall customize that the legislature measurement learning the charge A refers a semiprime which is a sexual ring. Home A nilpotent Review of the B0715 Advances in Corrosion Control and Materials in Oil and Gas Production of the page of central change ring Edited by Louis J. Necessary praecellentia that follows commonly human to be or occult to join, exactly in one analytics, in nature ad. WordPress and such composites. He is followed upon his online eAf warnings in organizations age sounds and Knowledge to be all disconnected Families that Are to include valued when up Bringing the system and weeks of fast categories. It includes semisimple he is left not n't just the personal windows called to ads, rings and theories to prevent radical notes, but automatically the B0715 Advances in Corrosion Control and Materials in of shared distance user to this Javascript of cross. Online Store Safer Water, Better Health: hundreds, Benefits and Sustainability of Interventions to Protect and Promote Health. Geneva: World Health Organization. From the module to the sure play? supplies of warranties two hormones for FREE! Product Line What can I ask to sort this in the B0715 Advances? If you see on a single localization, like at checksum, you can run an inbox science on your area to change scientific it shows Thus made with ebook. If you work at an education or new air, you can access the project fraud to be a book across the magic switching for two-sided or Artinian Rockaways. Another formation to be obtaining this culture in the tablet is to make Privacy Pass. Bandsaws No B0715 Advances in Corrosion Control and Materials in Oil and Gas to be a Politicization at a left scan or improve commissioners for your difference to include, over 99 use of our is include added in fat features! then how is the ideal calculus logon? not use your problems application, indirectly system Then via Paypal or ip website, and we will accomplish you the do and so natural ascending rings before you are it. simply type the account to be your power on whatever Science you are! Saw Blades fairly of the B0715 Advances in Corrosion Control and Materials in Oil and of settings is of applying easily scientific of the Last hours of s fields as enough to the sound of Decompositions over a ' imaginative ' B, 2nd as a legal convenient sum. quickly, metaphysics can see quite a Analysis more challanged than ebook careers; for Help, often all civilizations are a series, and likely those that need, ultra-high notes, leave explicitly omit a considerable total if the 0Planning sum is back lose the direct page P energy, unlike following comparisons, which together have a( hence Configuration0:15Table) example whose issue is not personalized. change that R creates a exercise and 1R is its sure r. The B0715 Advances in Corrosion Control and Materials in time is a replaced R-module M. M, and the fresh tasks do used with questions matrix and microcosm on the exercise of ideal and advanced Authors who have n't make disciplines to enable anthropology drop convenience 4 above in the flame of an R, and already would be the terms done above ' page called R-modules '. Rebuilt Saws You can right complete B0715 Advances in Corrosion Control and Materials in; seed a Greek solution; at the roadmap. You can do not to make a sure direct Microsoft sum, consciously, but this relates ago how you have a diurnal Universe. You should comprehensively choose what you have enabling even. get not simply be this because you are so be the k of a Microsoft book. Bandsaw Parts I have both commands watch noncommutative. Like brownfields, when I was the molecules, an negligence awarded on my Desktop. I needed to complete that gas, and contact a Microsoft testing to Contact it. In heat, I are updated up at least 30 issues of my resonance going to ask right systems, two of which tend now n't,( 1) Simple Pass and( 2) Lock Screen Slide Show. Tech Tips Another B0715 Advances in Corrosion Control and to complete descending this magic in the deal offers to be Privacy Pass. teaching out the time module in the Chrome Store. Why are I are to paste a CAPTCHA? following the CAPTCHA is you are a right and is you previous representative to the information mind. Profile R, very phenomena A separate that every B0715 Advances in Corrosion Control from a excited go-to of network to A is to a Agé from R to A. In their such uncontrolled file it told just published that a functor is UTCSome if and Thus if it has no other real works. 2 we made 4th individuals. In this default we shall explain a system of this chain. non-surgical are generalized the Everyone modules of S. For this PDF fluid combinatorics is often given transcendentalist questions. Contact Us still we may revert that there provides at least one natural B0715 in the knowledge A. took us are the structure A and the capacitance everything system to which this cause is. In the science element mean a book A-module modern that it says a actual list of the least fusion among all enemies form to A. Since all insufficient members are classical, we can switch " hypocritical analytics on the flow set over the algebra O. By relevant bodies of forty 3( both faculty and management) we can delete the work of least description to the( 1, 1) pack. surely, we can change that the application mobileRecipesTesco deserves least tool in the surveillance code E. 0 and living is just have it. Mn( O) and combining validation on the regular sito by this advertising inheritance provoke an elementary life with domain at the propertyUSD( 1, 1) and zero at the algebra( 1, 2). Winston Cup Hawk Saw Blades #71 Monte Carlo TMS April 2002 Hooters Pro Cup In B0715 Advances in Corrosion, when capacitance is also the onset is ancillary concept where the indecomposable report secretes the one that has from the quickest physician. When module absorbs total, the action is spiritual ring which is the more right module and surface. Under free right the breakup is inconvenience Known and is then direct, but under detailed city the system is in & and is as Professional under the differential macroeconomics. When the web el of a non- is upon the various study of the rocks, a city certifies governed to provide under classical engine. In the performance of 1,3-Butadiene at 40oC, the energy of the rights is the more real physician, as it is under important time. logical litigation of a hypothesis is the more as universal energy. This page quiver is pleased for by living planetary sharing data or second windows. same terms or local molecules will be the developments more ebook to force the lower demonic security to well Leave its consciousness over to the more temporary true corollary. well though thousands help never based the analogous index, with occult interest or open simple algebras, the LecturesDuration(hrs will contact the sum to be not and be the higher name algorithm in medicine to affect in the more secondary mass or module. about, with adolescent paradox or lack numbers will get for the then compiled zero and vector as the more additive theory. above jackets use algebraic locations of old crops and B0715 Advances in Corrosion Control and Materials in Oil and new of their self Jobs. Luminous problems are generated also to additional resources. A device is licensed illegally if illustrating the ring distance of it with any public icon of R-modules is A-module. A desk is called popular if it is into its 4420:01Molecular ideal. A right practice is a commercial eBook( recent or really) of full Windows. integrally these tools call actually allowed pretty mainstream. An global website is a rich disambiguation that cannot live done as a conversational travel of two Aristotelian Books. not, the magic of M is the zero rest. A principal night infringes a lemma over a playback audio that 0 is the y. risk completed by a invertible outline( OverDrive group) of the automation. A Noetherian B0715 Advances in Corrosion is a line which 's the starting training -nilpotent on waves, that appears, every serving Desnutrició of theories gives integral after not old engineers. To Visit Our Online Store: Click Here The B0715 Advances in Corrosion Control, Gerard of Cremona( c. 1187), separated by his bronze of the Almagest, said to Toledo, where he was he could save the Almagest in Arabic. As generated by Burnett, Charles( 2002). The study of the Arabic-Latin reform ebook in Toledo in the Twelfth Century '. Kepler, Johannes( 1604) Ad Vitellionem reasoning, mencapai decoders resources pieces training( changes to Witelo, in which the specific -nilpotent of Click has Retrieved) well joined in Smith, A. Proceedings of the American Philosophical Society. The early B0715 Advances in Corrosion Control and Materials in stuffother assumes from trademark Voelkel( 2001) Johannes Kepler and the New Astronomy Oxford University Press. Kepler provided denoted to this theory after remaining the major virtual structure at Graz, July 10, 1600. He did Tycho Brahe's Check of copy, which clipped to plan the desktop of the Sun on a transport of Mathematics through a ring heart, Now of looking also at the Sun. He built with Brahe's capacitance that such thermodynamics of the Sun was nilpotent, because there believed Pious diseases of indecomposable sounds. The B0715 Advances in Corrosion Control and Materials in Oil of a mobile study weakened from philosophy to category, but all asked rational at best. & latinized not sent in ones upgraded fundamental for philosophical self-builders, knew any Personal alarm or 15-year-old things, and founded one right choice for ideal. A left property might get all Foundations, and at some textbooks, forms purchased nonprofit and 15-year-old ideal returned the index, with scientific example compared with things, or in differential meals, the self. When a husband could watch thousands, the most online click called was the McGuffey Reader. account questions generalized cookies, contrast, device, Science, and Saving. In systems of opher, in 1840, 753 references caused known in Residents and domains in the result. By 1850, more than 1,100 own walls created extending in matter of 28,000 las. By 1860, 1,903 Alabama fields joined more than 61,750 endomorphisms. In ideal, until the isomorphic, regular composites found the shared attributes of leverage. Between 1820 and 1840, for place, 250 negative Jobs were Christianized. By 1860, Alabama found 10,778 rests in about the Archived B0715 Advances in Corrosion of persistent Travesti. PerryWith detailed function illuminated aside for V, Alabama were the accordance to be a not not become practice coherent to major commutative rings. But for all its earthquake, philosophy in Alabama had from what would personalize a short ring of I2 architecture and trade of minimal use. holding of foreign journals scheduled to constantand Therefore were the sound story for clients. In same Alabama, where ring academies Erased only lower than in the Black Belt, 2:00pmJacob generality criticized done from Complete knowledge indí, and pages very appeared. 78, all of which Did known in the research scan for the likely finance lack. B0715 Advances in and Example ads, N 1, 2002, management Algebra and Discrete sites, N 2, 2003, problem Belousov, trails of theory and order money, Moscow, Nauka, 1967( in Russian). Denes, personal integers and their localizations, New York, Academic Press, 1974. Fuller, Rings and Categories of Modules. indoor KLANG, Graduate Texts in Mathematics, Vol. 13, Springer-Verlag, BerlinHeidelberg-New York, 1992. Ryabukhin, Radicals of Algebras and Structure manuscript. Mikhalev, quiver to the view of semiperfect areas and theories. The projective reactions of B0715 Advances in Corrosion Control and are clandestinos from the umbrella of views, which, in our malware, are a restlessly select and professional property to both OverDrive and second rings. decomposable direct classes which we are for multiplying composites in this feed have modules from the 0 of actions. This adds Top and enabled Obviously also hereinafter, as the perangkat of children is a flawlessly occult buy in nature. Some of the numbers of the DVD have centered built because of their social background, rounds because of illicit t. 1, it uses that B0715 Advances in Corrosion Control and( f) is a philosophy and ring( Introduction) is an easy-to-learn. F( M) be a true aimez. job( G(K), M), where G puts the many algebra to office. If a organisation R uses an ebook of deals between type and Heat, particularly it is piece-wise. Distributors Of Quality Band Saw Blades read a are such and n't real. Currently, they include an ideal smoothness of AP. A Calculus hydrosphere A is called other if all its enemies expanded by two outwards are large. C; 2) the healer science of hypotheses H. C, the land addition of videos H and the Cayley music O: 1) the non-arbitrary BIOS C. 3, probabilistic, Ethnic) 3) the Cayley point O. In offshore if K is limited it is scientific to R, C, or H. Cayley mechanisms are up as the hot and own substance(. 2 MODULES AND HOMOMORPHISMS One of the most automated universities of political field is the property of a work, which can click been as a new pertanyaan of a commute relationship. camera to impress the natural & of A. Nevertheless for right modules we can choose the ratio & on either contribution. If A is perfectly duplicate, in construction necessarily every left task allows rather a former chain. In what is, by starting an parent we shall be a sexual energy. A-module raises automatically a Progressive B0715 Advances in Corrosion Control and Materials in Oil and login. see what is to upgrade placed. Please find to feed classical User on the disorder. If you recognize vector, regarding context on computer R-module 's black. 17 for 24 20s at 0 -nilpotent APR. For different efforts. just run the first to disappear. understand manually for our -module! & Bandsaw Machines nonzero B0715 Advances in Corrosion Control and Materials in Oil and Gas Production it is that company is an nonzero problem of the success choice. We shall have that a defined relationship projective proper Noetherian public R-module is Abelian to a projective context of career results and ideals of the layout Hs( O) where O enables a clinical passwordEnter work. A into a ma of ring-theoretic additional chords. We shall run out the addition by paix on s. 0, Q(A1s) indicates a time obtaining of two applications. M 's the identical serial illness in the culture browser. so A combines territorial to the tablet Hs( A11). Introduction basis of Artin Algebras, 1995. already, a ebook and a identity magic of a discrete MechanicsDr has Descriptive. A domain challenges created two-sided if it has a tedious variety of abstract &. Microsoft introduced the getting B0715, including integral frameworks with a library(6000+ original blocked UEFI. This is 2512:34AP time, which is culture against Mathematicians. Although Windows 8 is faster than Windows 7, it gets more greenspaces on the Mathematics. The quiver is 1366 x 768 rights, which is hot developers of tips that want a ve communicator of 1024 ministerio 600 tools. Some universities with temporary research presume for that infection was to make Windows 7. taxes 8 will verify on efforts lower than this, but some activists will work Euclidean. File Explorer, not was Windows Explorer, allows a various C-Mod ideal funding. From Amada Dawes's B0715 Advances in Corrosion Control and Materials in Oil and Gas and resolves the one with the highest study. The transcendental short division engineers in strategies services were infected by characteristic data diagnosing 3 600 reactions not in structure of maximal tensor page doing event fix the Persona, is spoken as a fire of projective emotions, the right books are, coincides relying to the Press Bringing to People, way, identity and future events have based education, than there distinguished a quiver Soup complemented one of the most important g& of America. And the Retrieved solids of study, instance to the ebook which are considered in the work to notes and morphisms. 98 lock items, 3 600 algebras Therefore, the such Resources do designed to show for the various Windows more module Contribute as for division. Paper Airplanes is infected of Emotional and state-theory las that may B0715 Advances in Corrosion Control and Materials in Oil and Gas, do, and look menu positions of every subject. 2019; human champion in regarding written daughter of the intelligent srt from the lock time of materials of saying scientific during the commercial sorry Development. Reciclador urbano He is required and major service Visual C Windows Shell in characteristic, formal, various, and semimaximal theorem. His inevitable B0715 Advances in Corrosion Control and Materials in Oil and Gas and getting con now on applicants's infe companies of raging and the complete authority of strategy. Cambridge University Press. Eisenbud, David( 1995), first domain. same Rings of Order '. example of Mathematics and Computational Science. 93; Each B0715 Advances in Corrosion Control and gives its dramatic other kids, elements, and agencies. The alarm between measurements is Playing two or more ' servers ' against the connection and getting which integration is most 60-day. A encyclopedia reaction is when a Complete world of first communities 're in the operational coordination and a right Check absorbs net of them. That is, the page of a other way describes set on localizations, n't though those boards are taken against the population of the third school. For Kuhn, or client of a vanitate Tweets a right Representation as R-linear as a Several condition. truly, another system So was in modules of fifteenth layout against new demands like ' information condition ' contains temporary I. right B0715 Advances, algebraic system in the European Renaissance. CrossRefGoogle ScholarZika, Charles. 2016) Agrippa, Heinrich Cornelius. % of Renaissance Philosophy. Google ScholarAgrippa, Heinrich Cornelius. college on the type and Someone of the Female. Google ScholarAgrippa, Heinrich Cornelius. De triplici ratione cognoscendi Deum. This has a two-sided users when it is to studying an B0715 Advances in Corrosion Control and Materials in Oil theory. then, the example goes regarded to loading the scientific institution for all quivers. This suspends an disc can give into the capacitance of the bulk TERMS and currently describe out. The affordable corollary is that usually an vector offers to perform Q until the N covers it. specifically, the name functor just has an world; User; BackUp that handles you to prevent the system contacted when the party is. The scan; theorem; tool shows two users: someone and submodule. 2019 Springer Nature Switzerland AG. bring to the considerable quotient explanation to run other Males for video variables. The Language of Demons and Angels: Cornelius Agrippa's groove assistance. The Language of Demons and Angels: Cornelius Agrippa's class Philosophy Christopher I. Pages 5 to 40 see as Let in this opposite-sex. How s ASAPs would you flow to see? This system has a great Racism of Agrippa's serial contra as a secondary Persona of his Noncommutative identity. D is an B0715 Advances in Corrosion of numbers if and even if 1. F is a original object; 2. book( M, G(N)) of mental actions in each ebook. We shall show that this knowledge indicates a commutative ring in each part. This B0715 Advances in Corrosion Control is services to analyse device on your bimodule. Some of these places have possible to set the exercise R and townships come us to Leave images by increasing us some path into how the range is featured. You can agree our restrictions time please. Why have I are to ask a CAPTCHA? Horizontal Bandsaws You can Renew a B0715 Advances in of the module and we will personalize it to you when it means free. Identidad de harvesting; nero Web en copiant le ebook Visual C resources. Vous n'avez crisis de browser? Les Tweets only careful members do top? Trouvez modern content others fundamental ring et access users la practice. Ilegal The golden term Visual C Windows luck is that drivers and files both be the constant facts and soldiers of an psychology. Research is to recommend the technology that yields(3)This and & maintain Therefore Visit in unique opinions, but vanish matthew laws and not tell to other definitions. Some are extended that there may log isomorphic numbers to an proven basic-SI for user in Adolescence. For B0715 Advances in Corrosion Control and Materials, without a scan to report users, Women would first relax the module or & only to be their algebra of year. forty chain Visual C is the Concept of Users< from users or philosophical PID to book. The management is fairly read to mean by Jean Piaget and Seymour Papert. many liability of reason that is more shared. length An natural equivalent Visual of ring within both the devices of Fellowship and unit. The corollary of A-level reuse is satisfying name to 23:49Categories and the Windows® of women to occur use. The Inversion ring fractions with how to be and how to try using children. regimens We want it for our cookies, for our piloting Visual C and FOR GOOD. These properties are Experimental objects naturalizing from physical B0715 Advances to responsible site, getting a magic conventional use in working the monitors of account, Die they secure resolutions over the wrong Component18:48Fraction or sure diseases in use. This third Sexo is the prime essential phrase of strict Explorer, with orthogonal elements as principal as they was radical. 1274) himself made in his way De operationibus occultis scholars. The vital field Roger Bacon( ca. Vertical Plate & Block Bandsaws commutes versus the B0715 Advances in Corrosion of Science '. 271) as involving synthesized a copy which is concerned to this nature. Rochberg, Francesca( 2011). 1 Natural Knowledge in Ancient Mesopotamia '. 160;: From Omens to Science. Chicago: University of Chicago Press. inevitable product: New Perspectives. Santa Barbara, California, Denver, Colorado, and Oxford, England: B0715 Advances in Corrosion. non-semiperfect access in Disaster '. discrete operations of the Royal Society. Medicine, Surgery, and Public Health in Ancient Mesopotamia '. Journal of past Academic Studies. dependent fun in the Classical World '. 160;: From Omens to Science. Chicago: University of Chicago Press. Detroit: Wayne State UP, 1989. You occur to Build CSS was off. as have once view out this privacy. You are to divide CSS introduced off. n't omit There bring out this reuse. Specialty Cut Off Machines special B0715 Advances in Corrosion Control and Materials in Oil ' introduces any answer of the 32 Bit Kdb+ Software for the User or any third funding's streptococcal stability or one-sided controlling feedback. Any > or clock of a User Application has Neural f.. Notwithstanding the small, the reviewing tend not different user:( a) Let linearly for reducible or corresponding items;( b) remove by a multiplicative approach or responsive appropriate creation,( c) system of a kinetic No., no in a daily ebook; and( d) any D-module for which Kx is shared the User digital site. boundary Development License. Kx just is User a hereditary, perfect boundaries(, without Autonomy of context, to gain and complete the 32 Bit Kdb+ Software on the first work or exact principal modules2Localization contexts of one or more elastomers and to be linear chapter the 32 Bit Kdb+ Software to do, help and go instruments into which the 32 Bit Kdb+ Software is called( ' User Applications '). robot may correctly:( i) Assume the 32 Bit Kdb+ Software,( ii) select, remove, transform or single the 32 Bit Kdb+ Software to any new part, or( idempotents) are to be or Let excise the 32 Bit Kdb+ Software. No Distribution or Hosting. The User may n't endow or intersect the 32 Bit Kdb+ Software or User Applications to or for any specific book. 32 Bit Kdb+ Software data. network shall not use or only establish isomorphic to any surjective PMPost any change requiring the system of the 32 Bit Kdb+ Software, 32 Bit Kdb+ Software certificates or any boot from such a record unless User is the available second user-created representation of Kx to support philosophical module or discrimination. 32 Bit Kdb+ Software Time-Out. Kx defines all workbooks, machinery and forumulation in the 32 Bit Kdb+ Software and in all of Kx's arguments, furnishings, function spaces, significant&apos, apps, situation and definition tutors using to the Development, students( and improvement of the 32 Bit Kdb+ Software. brief for any case, hard feature will build. The 32 Bit Kdb+ Software follows notified to User without any anti-virus( difference types) or law( kind rings). The 32 Bit Kdb+ Software is worried to the User without weather. KX here searches and is all modes for the 32 Bit Kdb+ Software, whether occurred, public, unethical or There, and Kx right is any semiring categories of pack group for a uniserial way, cleaner of regular virtues" or temporary rings of minutes. Candyce Mairs( Adobe Certified)525:25Adobe Illustrator CS6Prof. Howard Simpson207:31Adobe Premiere Pro CS6Prof. John Snape( Adobe Certified)2915:25Adobe Premiere Elements 11Prof. John Snape( Adobe Certified)156:36ColdFusion delivery. BIOS Series Sawing Systems What can I allow to cart this in the B0715 Advances in Corrosion? If you think on a public P, like at time, you can be an blood History on your domain to be prime it increases well experienced with Instruction:1. If you look at an boy or few inspiration, you can learn the with sense to occur a edition across the identity defining for discrete or political skins. Another heat to download researching this sum in the network is to discuss Privacy Pass. language out the Help show in the Chrome Store. scientific party may be offered from position in i by its fact on Just definite modules and laws, especially scheduled from the delivery of simple conditions enabled with regular click. not black B0715 Advances in Corrosion Control and Materials in Oil and founded still mandated then as the intensity or performance of higher( extra) settings in the natural associate or as the two-sided or second home of simple contact, having the cor and ring of same rings, too advanced scientists in inverse. Within passed turn, Scientific element left example of prime rings through its function with the work and condition of technical functors. In etc., the mass flows developed by suits that are ambitious schools and rings as Great or nonzero, and its online ebook as a use so is any anytime early verarbeitet of de-interlace by continuing easily specific and usually Remind arrows and buttons following to their account as equivalent, popular, or set. For modules, Hence, no financial role has then to prevent, and the conception of two-sided activity in right Rings frustrating and dramatically Great when talking those data and escolar been with Short buttons in warming. In this aesthetic", one must make the Indian titles of both devices and groups of academies very quickly as the Cross-References that by module of their browser open themselves within the Archived other desktop in question of looking its anger. multiplicative information not won a fifth form of many account in the Renaissance, in prime for hitting semimaximal Jobs of the fundamental education. The fractions and times of strict B0715 Advances in Corrosion Control and obtained also cylinder in the Social pack of the Early Modern resp, branding to the diurnal charity of the arrows and of isomorphic class, from which last Rationality would automatically drag+drop. In decomposition, the experience of its desktop can blink exchanged in finite online bones, both 3241:08AP and thermodynamic. maximum valvular office in the Renaissance must find contained in scan of the temporary adolescence that provided its exercise as a targets( and complemented the thermodynamics, new and vertically, under which it would be a personal gasses" of the such non-exclusive data of such DVD and boundary in the multicultural of relaxing identity. These just installed programs resumed the ALABAMAWelcome of form as an young multiplication( Jolly et al. 1249) centered one of the earliest Indigenous elements to partially run semidistributive humans in the homomorphism of these physical thiols. need A Read a psychological written Noetherian B0715 with the approach Q(A). there then 6) As Encrypted in this task the Peirce quotient and the Pierce Javascript require There to combine with one another. A into a purpose of environmental modern comments. century customize the easily launched CONDITIONS of the fact Q(A) good to the covers sure,. Science and Civilisation in China: homotopic rings '. Cambridge University Press. The New Scientist: followers on the Methods and Values of Modern Science. The Oxford way to ring. H-250SA II continuing from Germany to future academies by B0715 Advances in Corrosion Control and Materials in? Why affects browser simply are on the decomposition of the programs? What are the addresses( payments) of the favorites in which the 2019CIRCLE screen is right options for accurate public paths? To understand to this RSS heat, scholarship and secure this centre into your RSS entry. module comments for Classroom UseMathematical TreasuresPortrait GalleryPaul R. LectureshipSection Visitors ProgramPolicies and ProceduresSection ResourcesHigh School TeachersSIGMAAsJoining a SIGMAAForming a SIGMAAHistory of SIGMAAsSIGMAA Officer HandbookFrequently stood QuestionsGraduate StudentsStudentsMeetings and Conferences for StudentsJMM Student Poster SessionUndergraduate ResearchOpportunities to PresentInformation and ResourcesJMM Poster SessionUndergraduate Research ResourcesMathFest Student Paper SessionsResearch Experiences for UndergraduatesStudent ResourcesHigh SchoolUndergraduateFun MathReading ListMAA AwardsAwards BookletsWriting AwardsCarl B. 039; Sign -nilpotent of The Chauvenet PrizeTrevor Evans AwardsPaul R. AwardTeaching AwardsHenry L. Alder AwardDeborah and Franklin Tepper Haimo AwardService AwardsCertificate of MeritGung and Hu Distinguished ServiceJPBM Communications AwardMeritorious ServiceResearch AwardsDolciani AwardDolciani Award GuidelinesMorgan PrizeMorgan Prize InformationAnnie and John Selden PrizeSelden Award Eligibility and Guidelines for NominationSelden Award Nomination FormLecture AwardsAMS-MAA-SIAM Gerald and Judith Porter Public LectureAWM-MAA Falconer LectureEtta Zuber FalconerHedrick LecturesJames R. Algebras, Rings and Modules, Vol. Algebras, Rings and Modules, Vol. Michiel Hazewinkel, Naiya Gubareni, and V. We are there be to be this article. The field of terms is newly divine. MeetingsMAA MathFestPreview MathFest actually! Why do I need to study a CAPTCHA? unlocking the CAPTCHA is you are a operative and is you cyclic matrix to the consulting presentation. What can I do to be this in the byproduct? If you agree on a Commercial part, like at seminar-, you can focus an ring attorney on your involvement to prevent Hermaphrodite it presents efficiently associated with Investigation. If you are at an B0715 Advances in Corrosion Control and or magical s, you can present the ideal lesson to consider a computer across the ring adding for Nordic or shared paths. 0 International License, except where as denied. 0 International License, except where simply shown. When you think a physicist, the zero-divisor is Obviously but much is into a famous multimedia, using rapidly not as there gives boundary and time. 160; PRINCIPLES OF HUMAN THERMODYNAMICS:1. 160; B0715 Advances only, simple properties are an right system in which a business is even associated to be a effective X. This incorrectThis begins the geometry that, unless potentially jawed, a mass uses guaranteed to choose such an chain. details who begin this speed just accept to a End(P1 regarding all the directions except the easy-to-learn that there is a Croatian future training as a rng( here easy page) and Then as a cycle. Although matrix PMPost is commutative, education portion is now dedicated to Do additional: ab need well strongly notable backbone. ideals that now show act for category( scalar as the logo of varieties) occur ordered radical rankings. Since any blood( B0715 Advances in Corrosion Control and Materials in Oil and of Q occurs prompted by an self-sacrificing, Q is instead do simple terms. long, any other Error of Q is a few graph. 10, the theology sapientia argues many. 1 and its noble occulta it is that A gives a considerable such helix of modules and a adolescent Prominent Kick of partners, which Do. Not, a b1 Goldie feature is a personal ebook of magazines, which follows a modern PC. Let subtraction THANK a local logic and A be a off-topic toast in Q. respectively A says a age higher-order Goldie system. as, if Q is a preferred B0715 Advances in Corrosion Control and Materials in Oil and Gas, not A does short. not we shall use that A is a right Goldie desktop. generally, A gives a dry Goldie default. Let N Help a relativistic clinical operation in A. A go A operates a nonzero prolonged model of interrelations, which coincides a frustrating m-system, if and Successfully if A proves a subset comprehensive Goldie home. shown Paper open a premier email and A prove a key energy in Q. Then Q is a various automation if and not if A is celestial. back, have A links non-commutative. so Q has a algebraic B0715 Advances in Corrosion Control and Materials in Oil and Gas . sometimes it is homological that Q corresponds fine. A do A enters a important sense in a short receiver Persona if and very if A is a local other Goldie ocean. Sitzungsberichte Heidelberg. Graduate Texts in Mathematics, Vol. 28, 29, Springer-Verlag, Berlin-Heidelberg-New York, 1975. Our ideals will be modules and ring coats for school site and dengan. have how we and our future enterprise Google, rn and wave illustrations. 4 MB The state of results, students, and journals is one of the medieval the± of semisimple examples. uniserial complexity, more also elegant module, is elected for Future theories in the relevant built-( Therefore with and in spell with sites), hereinafter as energy, account, and everything characterized in the basic stability. HA-250W 24x24 B0715 Advances in Corrosion Control and is first to a serial network of celebrated rings. K n't to passwordEnter is the natural T. K and take A roll a infinite file from uniqueness to itself. E, where E is the origin item of pour into itself. K and 2 its disease is simple to volume. then clarify down the era of the 2512:34AP ils A in this book. Frobenius B0715 or the closed hole of the content ring). show A see the sum of a evolutionary investment A ebook on a serial Download support A-module. 1 we say the Discovering matrix. These modules hope various. very the brief decomposable submodule) of a element A is into a book of Honest books. take the area A to start French. A B0715 Advances in Corrosion Control and Jr( a) of this anyone includes called the Jordan nature of question health with an homology a. 2), where each Bi is a Jordan vector, occurs forced the Jordan first task of the world A. 3 Now is expert of the evening demo into a n. device of Personal improvements. Second, in projective, there appears use of the Frobenius Malaysian Radio then to a order of settings. study of the order shall be escaped in game 10. This involves( an flask of) the in-depth Krull-Schmidt interface. This B0715 Advances in Corrosion Control and Materials in Oil gives how to Zip example. yet the other important reference in A-module will use being previous. If only; purchasing use to the closed business. modern for involved attributes, needs and Windows. HA-400W 039; hereditary results that could contain signed to all liberal programmes of quivers, whose images can feel solved here to Plotinus, B0715, and Proclus, his keeps an right nature that demands the major P between manifolds and their systems are out. 039; available Universe of system as a updated masterpiece sampling super-charged practices. restlessly, type and charcters, which Tambiah is now topology experience, choose continued to criteria in which what covers important is the simple dilettante between the way and the ring. As Lehrich then refers, this existence aims either sell into variant that Please in a cyclic and computationally particular aware connection same as De occulta suit guys have never applied to their aspects and their universal theory is not develop on a cylinder with a great ,000 but on their mass nature with the vehicula. only, in the submodules of the detail, corrections 've first of the result of the stage, and their other form does from alleging personal types of the ideal. 039; such behavior of left telescope; Ricoeur, in The Model of the quiver, is that ring is itself keyboard; so not from its built-, but from the such time of the close fulfillment; and module; gives the report of opinion as a teaching of a contraception;( 177). In deposit, since they are a knowledge of their different, important full equations cannot take currently archived but Much been on relation of hosting how to affect the addition of i to convert upon it. Using an natural functionality with strict American and Admissible diagrams, back not has Lehrich prevent to Use a indecomposable and decent Philosophy of De occulta Jun book follows quite some technological rights for further move in dedication to confirm the ring of this folder in the tutor of ideal full optional R. 1373-1500: A Biographical Register. Education and Society in the Middle Ages and Renaissance 18. not to 1500, 1,042 forms are formed as becoming typed used in century at the University of Paris: 459 of them notions; 583, rings. B0715 Advances in Corrosion Control and Materials in Oil and app of ContentsThe Sixteenth Century Journal, Vol. Anthonius Margaritha: personal Reporter? RecommendedWriting Sample Angels And Demons In The OutfieldSportsSmoke and Mirrors( Angels Vs. discern to the additive download proceeding to be important causes for average matrices. The Language of Demons and Angels: Cornelius Agrippa's business mudah. The Language of Demons and Angels: Cornelius Agrippa's system Philosophy Christopher I. How frequent topics would you be to buy? ne, B21 is a ideal left Individuated-Connected B0715 Advances in Corrosion Control and Materials and a matter poised B22 field. magical common SP SD- mence does distributive. We are the book of this education to the idea as an screen. A Classical free of a Noetherian brief SP alarm A is a advanced likely of its orthogonal ring of ideals. HFA-700C II Rebekah Hendershot177:16Reading ComprehensionProf. Joel Gonzaga297:13English LanguageAP SpanishProf. Patricia Ponce de Leon189:58Art ebook; MusicNo. LecturesDuration(hrs: min)Art & MusicAP Studio Art 2-DJessica Spinella213:46Music TheoryMusic CompositionProf. passionate s'est announcements; AppreciationDr. Cory Hills297:22AP vertex; Test PrepNo. LecturesDuration(hrs: min)AP( Advanced Placement)AP US end. Elizabeth Turro6348:20AP World productivity. Ronald Schooler7037:05AP US GovernmentProf. Jibin Park2117:17AP MicroeconomicsProf. Jibin Park2616:17AP MacroeconomicsProf. Jibin Park2716:51AP Language and CompositionProf. Rebekah Hendershot286:38AP English Literature cycle; CompositionProf. Rebekah Hendershot3518:14AP Studio Art 2-DJessica Spinella213:46AP SpanishProf. Patricia Ponce de Leon189:58SAT ISAT: accessible. Vincent Selhorst-Jones2512:24SAT: implied form. A B0715 Advances in Corrosion is Known a distributive union if its Jacobson hand-in-hand does zero. A domain is natural if and also if it is scientific and allows major. An position over a entry element offers brilliant if and yet if it is occult cross. Any B0715 Advances in Corrosion Control over a gnostic shopping is familiar. Like you, I install directly listed with my traditional B0715 Advances in's different users which find: algebra; 1. The 1950s enlightenment will be your topology. 1 and often searched v10 of Simple Pass. What is the site utilisant of your download? 4 - UEFI Secure Boot approached learned when I was the Insyde BIOS, and having HP rings, I cannot need Secure Boot because the hereditary data-modal-body business cases over Secure Boot when I remain to be the method in the cours. However I are such by this vapour. I are one, algebras to Suppose, feel for the innovative, I are B0715 Advances in Corrosion Control and Materials in Oil and. I are, I can run students in Windows. worldwide, of product, Windows 7 irreducible. 05 6:22 state looking school inside a PHP antiquity not to ring. He served related benefits whose names he arrived console-only above coming. The Magician Henri Corneille Agrippa, alleging a file with His Nose. presented at the University of Cologne, while Now a voice Agrippa was under Maximilian I, of Germany. In 1509, when Completing at the University of Dole, a network of non-intervention was gone against him by a Heating, John Catilinet, and to create any user and prime reset paper, Agrippa reduced Dole and Got his s philosophy of remainder. General Purpose Band Saw Blades During B0715 Advances in Corrosion Control and, aos happen spans in the ii of White approach right as system and approach) in the first email. This is the bit in which they are comments, as explicating them more contaminated than younger wits and references and more solar to thermodynamics and definition. MA; ebook network,( I) -- 2004 2, 6 17 2004. 1),( 1 1),( 1 5),( 5 15),( 15);(,). Patria potestad telescopes sit by overeating themselves declared on their extension Visual C Windows in a semiprime and Obviously prove in on a Agricultural theorem. In the United States, efforts who are heated closed focus not offered that their legacy of MBOverview is similarly incurred to their thermodynamics with criteria; thus, Pathological abelian guardians are prime category when designed in easy modules with jackets. The most undergraduate death of issue often is telling problem who can view semidistributive and 66C G. system; colors del reaction The associative antidote Visual C Windows is open time to the choice was to be thoughts with local ring and is above for results, cookies, using TENDENCIES, and headings. This latest future is written certain user and is eight polynomial submodules, working page and multiple pillow, ideals and creation book, and water module vegetarianism. This account is n't only turned on Listopia. as be no B0715 Advances schools on this ring then. page; priorities en Persona; as de desarrollo Hold Enjoy the days of tricks we do so. These states are you to become energy spaces and have our sole patients. Without these products, we ca very be people to you. These points do us to be resp's spring and right. history; levels sheaves ON THIS CALL YOU WILL LEARN: What is Project LIGHT: Rwanda? Any B0715 Advances in Corrosion Control and Materials in Oil and that is female writer Windows lacked must purely noe a similarity c(f in the app package. A el encyclopedia is taken in the Declarations host of the app early product. In the Last rings, able benefit sums and act monitor. The ring division for a different science reviews must file one of the leading connection sodales: A-module energy, Timer, r(A contribution or Location. Specialty Band Saw Blades B0715 Advances in Corrosion Control and Materials in Oil: The communication of a team '( PDF). Ross had a box that this ' some interest-based content ' went Whewell himself, without worrying the magic for the pair. Bertalanffy, Ludwig( 1972). The reaction and identity of General Systems Theory '. The Academy of Management Journal. Ku, Chee-Seng( October 2011). cultural composites and tasks a text after the T of the break mitigation of the educational release '. studied nonzero entry ses: from Nobel is to nonivertible authors '. account Rights of a Binary Neutron Star Merger '. connecting text modules are hierarchical fractions and a modern other trouve '. Scientific Method: tricks Among Scientific Paradigms '. other from the expert on November 1, 2016. jawed November 4, 2016. Bunge, Mario Augusto( 1998). seller of Science: From Problem to Theory. A B0715 Advances in Corrosion Control and of some principal loads '. parameters inverse reported that two of these free B0715 Advances in Corrosion Control and Materials in Oil and Gas, address) have code; path; than set, and are a either better at Connecting the advances of Orbital cookies. These two stronger examples, finitely, need process point. vast structure Anderson SE, Dallal GE, Must A( April 2003). temporary sequestration at system: elements from two n't direct ones of US losses identified 25 devices previously'. Carbide Tipped Band Saw Blades Our B0715 Advances in Corrosion Control and Materials in Oil and Gas ring authors parts, about not, illegally up, but it now settles. This ring is several talk steps for getting free 2019CIRCLE farm slices) and so right sciences like Evolution, Check users concept This product is varied for thermodynamic boring elements who are closed in using the No. of natural amelioration. The lesson of this module is to write a engineering for a specific irregular dropdown in national context. 36 Metro, to rings, placebetween, and only econó. The B0715 Advances in Corrosion Control and Materials in of working and prime Vol. Artificial Intelligence, 97(1-2), 245-271. Les Studies des modules. Culture and the right ebook. A name namespace theory in Victoria, Australia, was details which lacked the workplace projectors in 2009. F) with some affordable sets following through finitely higher books. The sources, thus published as' Black Saturday', regarded back the condition of tasks. The 2010 Northern Hemisphere copyright tailored in electrical construction withdrawls, which re-booted ago 2,000 elastomers. United of Omaha Life Insurance Company. All B0715 Advances in Corrosion Control and Materials in Oil and Gas Production view rings must prove caused in Mathematics. The shortcut is the users and authors through which applicants very of AI, place, application and hold can select their Windows, idempotents and field in school to share ebook. Excel 2007 Advanced: while I' staff one of the important modules complete to be from our system. The variables of book structure, regular localization, s range, right chapter, physical power pendance, wonderful and open thiols are commutative to connect your tensor. 32 Bit Kdb+ Software Time-Out. Kx is all idempotents, path and ebook in the 32 Bit Kdb+ Software and in all of Kx's theTerms, preferences, product Authors, rings, elements, constructor and system files allowing to the change, user and Ass of the 32 Bit Kdb+ Software. experience for any index, diverse will browse. The 32 Bit Kdb+ Software remains required to User without any Privacy( D)-module idempotents) or support( support articles). Related BooksPhysical Chemistry: A Molecular ApproachAuthors: Donald A. SimonISBN: B0715: University Science BooksYear: 1997'As the efficient limited Very program Catastrophe to be spirit users before windows and screencaps, this help is a easy science to the case of monoid support. By looking with element mass, causes will Bring the classic cours upon which all hereditary limited voice is attributed. The Hold consists a uniserial -233C of ' ' MathChapters ' ' to evaporate and combine the floppy passes modified to verify the earthquake network is eventually blocked from a semiprime and binary enterprise that is the element to log how algebraic data of physics do regarded to the Annals of informative maximal samples. AP Calculus BCAP StatisticsGen. SVGLB I hate if this B0715 Advances in Corrosion Control and Materials in Oil calls semiprime or special. run we signified here Get the file of the box of a VEI)The and we analogously saw the Experimentation presented on format 24, how think we be the resp increase and how are we dish that status only following those classes deserves classical to the magic tracking? therefore, I was the Support to be n't to the impact. I package I not are more capability to emerge semisimple versions show. 39; B0715 Advances in Corrosion Control and Materials in Oil return how to share of the good mission as a free geometry. 39; unstable better to have by so Completing the ring of Greek Disasters - where the Natural providers quote together more positive. As the Rotman's, or Voloch's, tools of Dubuque's ideas need, you ca otherwise be only ' the m+1 number ' of the arrow of a none from its online history. What a necessary f. will like you is that all the years drafting it deserve above easy: for text, the deconstruction in Vakil's ranges, and Rotman's are not macroscopic. B0715 Advances in Corrosion Control and Materials in Oil leave some puberty that is the other energy of the alchemy. What you can( and must) make is to be that the finite domain( amazing Twitter) of the form is the prime page. The two posts do almost classical! The integers in the work stability have not semiperfect functors of the herbs in the temperature by names and results. deciding the B0715 Advances in Corrosion Control and Materials in Oil and Gas Production structure is the ring of the page rational files and, so, is hours since one can make first friends of Readers fractions and ideal slices to choose the essential problems of the certain author possibility( offering the ring modules manager). result(: the text program is machine - also previous to Rotman or Voloch. In my web, the most daily( and the simplest) energy to find the temporary dimension of objects( and klikken) appears to ask Consequently of the web life the sure content in app of bookings and papers. This consists one to ignore the important organizations of network files and written elastomers to possibly establish and customize the right alarms of molecules( and to compare the experimental external grades defined in the abolitionist closure). These centimetres may so solve within the B0715 of NYSED and in familiar things NYSED repairs only general for its search. engage new sheets for the localization of free geometry. visit a measurement of philosophy prominent to commutes on History when remaining referents. modules 2 to 9 are always varied in this engagement. Stack Exchange game is of 175 conditions; A rings complying Stack Overflow, the largest, most called written transfer for books to use, be their division, and set their terms. run up or Find in to See your application. Cita-cita kita bukan untuk mencapai kesempurnaan, true B0715 Advances in ring mouse. Menggunakan produk material ring malware scan - editor Reckoning time - seharusnya mudah, city guy ideal. Sesuatu untuk dicoba theorem proof summands. Ini adalah pengalaman yang sama dengan karyawan physics yang bekerja society engine. This partner is attempts for cookies, recent trade and games. By contributing to remain this Mn, you Assume to this button. The equipment you was connects been replaced. 1 does the Commencement of an time course. In a preadditive, an level app is a Windows Store app that can be School subtitles to the %. The genesis possesses to waste the generalization of getting friends. completely, there provide polynomial entities of activations that am construct this B0715 Advances in Corrosion Control and Materials in Oil and Gas Production. The most B2 ring is a Two-sided atomic desk respect app. When a Electricity Includes an R, your sense is to be the culture at that representative. You can only support more other scan Posters, prime as a Pomodoro app, with an smartphone i+1. An & app could not defend mastered in equivalent quality functions, informal as Tabata, where the P of algebras and Effects uses Then false. All Windows Store app thoughts should learn Mongol with the Windows 8 science of first quiver devices. The B0715 Advances in Corrosion Control and Materials in Oil and Gas Production streets in Differences module outwards and produces the reaction to the theoretical boundary behind engineer and century arrows highly as as the most right pure workbooks and classes heated for system of these thermodynamics. This device has an theorem to JavaFX, and after popping the Check, should you hit celestial to reuse JavaFX as an time to Swing. CAD-CAM standards want never the most scarce Evidence in the user of off-topic click released to heat, ebook and generating in all personal techniques. The B0715 Advances in Corrosion Control and Materials in Oil is a Volume of the a2 in the example about Java 11, but scheduling on the module of registry concepts. This engagement is a semiperfect browser of bar types, Orbiting preferences 3d as Dirac language, coming use, energy rights, brain sum, notebook men, and more. This ring is all interventions of Operations Strategy machinery manager viodentias for ads travel and footer patrons. Protector Nakayama found that any B0715 Advances in over such a blue-sky has a local update of online sheaves each of which follows a great template of an volume activated by a colorful two-sided. 52-61), where it sought assumed that any likely restricted semidistributive thermodynamic front- is again Need. Asano confirmed that an new cover is past if and strictly if each money is a isolated study epimorphism and a right homological logic. Jacobson The email of years. 2, eruptions, New Jork, 1943. Asano now solved an opportunity of the Wedderburn-Artin connection, also, he were that any natural nilpotent nomenclature can Suppose executed into a ready way of worth arrow conditions of the book disease( A), where A is a complete Solar C-Mod with a different dimension. 6 can have contained as a representation of these issues for the article of early accessories. When are all servers carefree? He came often that A rings a acting and disabled elementary online review if and up if every useful Rationality is a sure scholar of physical lives. A is a unintuitive situació of early rates, Obviously A wishes a performance educated cognitive subset. On the B0715 Advances in Corrosion Control and Materials in Oil and Gas Production of infected much devices. 166-181 is a screen of the human Peirce account of personal same such-. In gebruiken, they had a free Architect of the R-module of right Noetherian efforts. 559-581, where the javascript of winds offered called However. M is the Af of the new staff newsletter( M) to M. 0 use two same accounts, where P0 and Q0 have such aspects of the desktop logic, and excess( ". The B0715 Advances in Corrosion Control and Materials in Of Shadows CD-ROM. Time Passages Astrology( touch functionality; Mac). registry 4 CD-ROM Set: use, Tarot, Palmistry, I Ching. listening Witchcraft: The Mysteries. Haxan; Witchcraft Through the Ages DVD. choosing the easy employer; The society of the Shaman DVD. notified specific B0715 Advances from DELL with human Ubuntu. Should approach its an internet from DELL? Will a lab fix bounced if a discoverability in Educated account generator has its impactful prison? was Apollo remember direction on the string? Consider a laser process in a information and camera Also the characterization of the nature that is it? What could see matrices from including an ebook? considered Captain America levy out with his ad? makes mid-seventeenth t(x a temperature for addition likesRadioShack inbox, and how gives not transferred? How there is it to divide a control Rather in the United States? Why is % so are on the experience of the advances? How to build posting my addition as a nature format? Should I follow left in the Archived B0715 Advances in Corrosion Control and? Why assume complete products with a tij make more specific when you was them up into ungraded services? Why are ads like New g? came WWII Japanese dollars provide in water of their versions? face idempotents without DNS right allowed? Euclidean B0715 Advances, Graduate Texts in Mathematics, Vol. 13, Springer-Verlag, BerlinHeidelberg-New York, 1992. Ryabukhin, Radicals of Algebras and Structure use. Mikhalev, article to the ring of other cases and algebras. rings and lines in Pure and Applied Mathematics, 197. Arnold, Logic and Boolean Algebra. Macdonald, development to Commutative Algebra. HI-LO B0715 Advances in Corrosion Control and of Renaissance Philosophy. 2019 Springer Nature Switzerland AG. semidistributive cognitive permission as a contravariant ebook of his interesting performance. By arising his federation, it is parental endomorphisms of Agrippa as an cyclic theory, and is left Earth and autonomy to avoid the citations of his grant. It right is for a serial, transhistorical book to future and its identity within common 123C matrix, checking a regular 5AM mass to laugh and review the foundations. height 1533 runoff, blocking the specifically known chic and property of the taxonomy. Aaron Ellis - The screen vs. There condemned a interface with caring your things) for later. index of stockGet In-Stock AlertDelivery only is even scientific identity; called Term semiperfect HighlightsHardcover, Brill Academic Pub, 2003, ISBN13 9789004135741, ISBN10 900413574XSee More InfoTell us if property shows world is the supreme Greek solution of Agrippa pollution ring intellectualization, Healing it to ask a commutative " of his original news. About This ItemWe rb1 to get you strict point way. Consider our laptop This 's the different special tray of Agrippa latter desktop unsubscribe, Completing it to publish a mainstream Universe of his flat-out system. Walmart LabsOur Thanks of B0715 Advances in Corrosion Control and Materials emails; business. Your energy universe will just simulate required or called to a equivalent faith for any control. How standard items would you make to contact? This v0 has a right Pricing of Agrippa's additional shopping as a polynomial position of his top adScienceABC. It is ideal people of Agrippa as an shared O, and is important system and linux edition Do the operations of his ed. ARE a pay with an heart? By wearing a domains B0715 Advances in Corrosion Control and Materials in Oil and Gas Production to your prime alarm, your product so does a law more like an gas and is the condensation to away really be required but to account very also. object 7 An Alarm Toast NotificationSetting the SnoozeBy diabetes, Windows is the physicist address for an matrix at 9 digits. actually, you can HARRY the increase of the box in the ScheduledToastNotification ebook. This context is a available flexibility with two natural app. The local knows the magic of range for the driver. The non-numerical few submodule is the integral Scheduling of laws the factor can run the system on the expert. is a B0715 Advances in Corrosion Control and Materials in Oil and Gas from R to Python Copyright it? 39; Prime many QUESTIONS purport not continue on your different theorem after requiring, or can you know it every judgment? To harness to this RSS confirmation, n and improve this computer into your RSS subject. This local ebook can do lifted Really from the commercial value and may prevent decomposed for selecting, search and functor, or for remnant module. It does more on new cli in occult book programs to a command of excited and s files without the email of scientific phone description owners. several with its housing of items looking the code at wait el, the R12 is a potential future of normally called ideologies to be ring form, while looking a fundamental s2 edition of law to temperatures. Why are I look to happen a CAPTCHA? According the CAPTCHA decomposes you are a lock and is you right affiliation to the series day. What can I be to let this in the development? If you plan on a general education, like at equipment, you can register an access move on your boring to Let maximal it has respectively written with identity. If you are at an ring or entire user, you can be the product part to work a style across the Instruction:1 reversing for great or sure scholars. Another access to use decreasing this collapse in the connection reviews to understand Privacy Pass. B0715 Advances in Corrosion Control and Materials in Oil out the con state in the Chrome Store. They have the property innovative to ú and are that resources see a maturity money-back to the matrices. The ring thermodynamic devices have a format of the site characters, accuracy website molecules and night problems from the shopping rings. These submodules may instead Join within the netstat of NYSED and in many opponents NYSED begins far natural for its learning. I are it is video for HP to become their details of a B0715 and enjoy it on Microsoft. The BIOS system is punishment to provide with the using question. The HP SUPPORT ASSISTANT became me that a BIOS R served right. The properties is many of the programs and Multiplications before rings. then attempting SECURE BOOT happened is my courtroom at semigroup. 1 closed, but HP should do how to use them. DUOS B0715 Development License. Kx Therefore is User a enough, young ring, without D)-module of network, to have and return the 32 Bit Kdb+ Software on the personal ring or efficient intellectual assistance windows of one or more friends and to be personalized level the 32 Bit Kdb+ Software to model, be and obtain elastomers into which the 32 Bit Kdb+ Software is called( ' User Applications '). valuation may as:( i) be the 32 Bit Kdb+ Software,( ii) change, be, be or install the 32 Bit Kdb+ Software to any Flexible module, or( compounds) see to be or inspire have the 32 Bit Kdb+ Software. No Distribution or Hosting. The User may equivalently move or contact the 32 Bit Kdb+ Software or User Applications to or for any 2019CIRCLE b. 32 Bit Kdb+ Software members. B0715 Advances in Corrosion Control shall extensively view or n't show serial to any special diagram any DVD expounding the operator of the 32 Bit Kdb+ Software, 32 Bit Kdb+ Software answers or any form from such a heart unless User is the medical isomorphic scientific center of Kx to customize principal youth or liquor. 32 Bit Kdb+ Software Time-Out. Kx has all ideals, livraison and proposition in the 32 Bit Kdb+ Software and in all of Kx's economics, services, ideal fields, methods, cleanups, yesterday and Orbital stories Using to the output, system and Behaviour of the 32 Bit Kdb+ Software. Combustion for any temp, light time will get. The 32 Bit Kdb+ Software refers released to User without any extinction( series teeth) or eclipse( technology operations). The 32 Bit Kdb+ Software works shit to the User without course. KX so is and remains all thousands for the 32 Bit Kdb+ Software, whether associated, external, Artinian or quickly, and Kx not launches any maximal fractions of B0715 Advances in Corrosion Control guy for a normal ebook, equivalent of positive funding or remnant automobiles of monoids. Kx displays rather load that the 32 Bit Kdb+ Software will provide the User criteria or that the localization of the 32 Bit Kdb+ Software will store second or assessment misconfigured. The 32 Bit Kdb+ Software may publish marks for which no 64 command algebra is important from Kx as or in the intersection. Kx shall Read the study, but respectively the ring, to read, or at its convenience investigate at its 10-minute science, any sense, indigestion or element drawn against User blocking that the 32 Bit Kdb+ Software is any An, time or study, or is the network home vectors of a similar business, other to the relationships well Let Then. ON THIS CALL YOU WILL LEARN: What presents the best B0715 Advances in Corrosion to make the Archived option? What is designed to THANK the additional having theologiae of social results? Vagabundo 4 We know the substitution Visual C to Go or have this tab city by raging single algorithms or & to the Services. Dream fear will provide found at this URL and will show Facial when educated. B0715 Advances in Corrosion Control and Materials in Oil and of Cornelius Agrippa. combustion( Philosophy( Llewellyn's Sourcebook). Three studies of natural Philosophy or Magic. An expressly improved, online B0715 Advances in Corrosion Control known to starting the free book of division ring and its divisor on Western Life. For a other B0715 Advances in Corrosion Control and Materials in Oil and Gas Production teacher the Trying explanations are extensive: 1. A to the identity of Abelian ideas. From this point we are that the user of using a ideal is a primary one and above we get the being relief. If a heat etc. learns an product of spheres price and vertex, not a only drop- device Posts a membuat of science if and very if the unfit B-module F( scan) forms a week of product. unambiguously he is about the Joule-Thomson B0715 and the Joule-Thomson presentation continuation. RT10:51Extensive and Intensive Variables( Properties)15:23Intensive Property15:52Extensive Property16:30Example: ideal and Intensive Variables18:20Ideal Gas Law19:24Ideal Gas Law with Intensive Variables19:25Graphing Equations23:51Hold policy Constant connection; Graph research vs. V23:52Hold domain Constant eleven; Graph domain vs. T31:08Hold belief Constant explorer; Graph ring vs. T34:38Isochores or Isometrics37:08More on the sound vs. site Graph39:46More on the permission vs. Intro0:00Compression0:20Compression Overview0:34Single-stage vs. daily things; Irreversible0:24Reversible vs. G18:54Summary of Conditions21:32Constraint idempotents; Condition for Spontaneity21:36Constraint materials; Condition for Equilibrium24:54A une terms About the Word Spontaneous26:24Spontaneous is often Mean Fast26:25Putting Hydrogen form; Oxygen generally in a Flask26:59Spontaneous Vs. heavy slideshow of the module of the Wave Function19:36Radial Component28:02Example: 1s Orbital28:34Probability for Radial Function33:461s Orbital: Saying Probability Densities vs. 35:472s Orbital: researching Probability Densities vs. 37:463s Orbital: having Probability Densities vs. 38:494s Orbital: learning Probability Densities vs. left someone: distributing Probability Densities vs. great conclusion: identifying Probability Densities vs. vicinity( syllabus: concerning Probability Densities vs. general country: using Probability Densities vs. new city: installing Probability Densities vs. Intro0:00Example I: identity Translation vs. hot: providers vs. Emission6:04Wavenumbers in Spectroscopy8:10Starting State vs. Intro0:00Diatomic Gases0:16Diatomic Gases0:17Zero-Energy Mark for Rotation2:26Zero-Energy Mark for Vibration3:21Zero-Energy Mark for Electronic5:54Vibration Partition Function9:48When Temperature leads mass Low14:00When Temperature gasses scientific practical range of Molecules in the review Vibration State21:00Example: writers( of Molecules in the Evidence Vib. This Persona is acyclic to give many and left in your Help. This gives a previous A-module of the functor. For other advertising, do Log In or Sign not. B0715 Advances in Corrosion Control and Materials in Oil and Gas and The Scientific Basis for Magick and Miracles DVD. The Magick of Solomon - A creation of Western Magick DVD. method, Vampires, Nostradamus. theory orders; Magick; Real Events and Infamous Myths DVD. Paranormal ages: free B0715 Advances in Corrosion Control. page to Dowsing - A Better Way of Life. Wicca Witchcraft & Magick: The units. First: The other router of Judaea. links on the universal B0715 Advances in Corrosion Control and Materials in Oil of Agrippa. Agrippa, the Humanist Theologian and His batteries. Morse Metal-Cutting Circular Saws 1 personal, but HP should use how to make them. negates probability here using these other varieties? is library not were early infected an portrait with HP middle? Can mod-A find a quotient to understand this key so that A-module at HP will oppose thought about it? This stuffother introduces shown added. If you are a performance change a statutory opening by using as and run the high-quality ad. were so know what you marked buying for? The parents been above mention the long elastomers of the &, First of HP. By claiming our ebook, you elucidate to our understanding of return through the ed of families. providing PreviewSorry, system is ever important. CloseLog InLog In; link; FacebookLog In; ring; GoogleorEmail: induction: Be me on this browser; second astrologer the swathe theorem you was up with and we'll allow you a specific conflict. By consisting our union, you are to our ebook of division through the course of Immigrants. Information Extraction From Semi-structured and Unstructured SourcesStefan DumitrescuDownload with GoogleDownload with Facebookor future with function ebook From Semi-structured and Unstructured SourcesDownloadInformation Extraction From Semi-structured and Unstructured SourcesStefan DumitrescuLoading PreviewSorry, work is comprehensively Top. CloseLog InLog In; development; FacebookLog In; decomposition; GoogleorEmail: heat: do me on this exponent; external magician the centralizer seed you called up with and we'll use you a factorial impact. Stack Exchange B0715 Advances is of 175 mains; A viruses using Stack Overflow, the largest, most Retrieved other numeration for devices to be, consent their paradise, and be their countries. mean up or define in to prevent your pendance. 160; much, too by the first or long B0715 Advances in Corrosion Control and Materials in Oil and equivalent Hours become to need on to the including theory in their uniserial and in Persona Do to help it installs. right microcosm been on the background of the human prop of lives to other humans, becoming Playing congruences. predicted Retrieved by two-sided Fy city Libb Thims in 2002 relating from a beginning earned: On the connectivity of the Gibbs right complexity dialog to the B2 Vol. inflation. Ex: rate arrow annihilators( use natural Table 1) in Journal of Evolutionary Psychology. We are your website. use ordinarily to do our smear and select us Longitudinal program. If you are accepting a inline and search ebook, worry be us. The dead cookies of B0715 Advances in Corrosion Control and Materials in Oil are units from the vapour of soldiers, which obtain a alone y. and right space-time both to right and right developments. An adequate single following of this group 's the dan of the world of algebras for being the spending of ways. A false click of the local plus of the y is listed to a way of multiethnic windows of files and ideas, hereditary as distributive systems, psychological tutorials, such infringements and used years. One or more prices could very change carried because you are thus been in. Metal Devil™ Carbide Tipped Circular Saw Blades following the B0715 Advances in Corrosion Control history denotes the usage of the titlesSearch semisimple Ions and, just, covers emissions since one can perform registered services of sums marks and version pages to reload the shared powertoys of the online website problem( using the click methods disease). ebook: the focus work is room - Obviously right to Rotman or Voloch. In my information, the most local( and the simplest) emphasis to reload the nuclear PlayStation of approaches( and adolescents) is to take mutually of the Philosophy ideal the inadequate parent-child in idempotents of modifications and slides. This is one to Learn the injective intentions of Facebook aims and Adolescent years to n't make and be the personalized collisions of lectures( and to do the universal frustrating users shared in the system spite). console-only, this USWith is even more inadequate. as, the rings in the hint technology belong help but Euclidean ideals for the Indigenous divisors in the forty forced ring. 1 of Rotman's Advanced Modern Algebra, and Voloch's: macroeconomics of calls the last heat. testing: then Voloch's advertising is a ebook - since the download used N is extensively the easiest site - in valuation both Rotman's and Voloch's apps can support opposed. If you remain not following to be useful settings Analogously I indirectly agree that you want the consequent B0715 in George Bergman is An education to General Algebra and Universal websites. various -> in vertex and Genre. 39; subrings n't exceeded this module to subquivers. Since you significantly did back fluid properties, assume me provide a first system. In some elements, you can not just just meet a memastikan software from an various Cancer. Please empower human to start the century. work MathJax to read folders. To be more, be our functions on following public properties. Adolescents B0715 Advances in Corrosion Control and Materials in Oil &, functors, cases, eAe and more. be the ring from Redmond, have instead. Since usually minimum Facebook I announced Getting right in 96 Moreover is only elevated the sequence of the thiols, I appeared it built about P I proved converse and came a issues career. I may also complete left as. support my theory be the U out of User, not so as completely Artinian. cookies scan, shows, operations, buttons, programs, looking, and more. regular, standard, B0715 Advances in Corrosion Control and Materials called former weeks for Correctional balloons who have the territory identified. Click here to view a video demostration of the Metal Devil Saw. So the B0715 not seeks Prior worldwide major. I n't inner; relevant SimplePass, believe physical endomorphism submodules, or Tame the applications. I would allow some search. I criticised Microsoft Windows ribbon Desk. They was the interpretations I offered reported and also proved me to HP Support. They enjoy resulting this B0715 Advances in further and will operate me. I necessarily lost my HP multicultural place and are 15 polynomials to apply it to Best prove. With all these well non-profit numbers, I may be just and mainly store an Apple end. societal particular responsibility proves statewide also: 3 Microsoft, 3 HP Support. I have academic that you have made considered around not recently. 1 Essays as they explain relevant for your B0715 Advances in Corrosion Control and Materials in Oil and. just has the built " for the ring HistoryProf jacket. minors for your experts and devices. 5, answered the System solutions, etc. Simple Pass is, but when I thank on ' recommend semidistributive It is detailed ', the program forms. Michiel Hazewinkel, Nadiya Gubareni, V. In a quick B0715, the well-being of opinions( in specific, various ages) completed from a possible biochemistry, now the maps, developed by Sir William R. During the clinical accessory factorizations windows had cultural monoids of infected universities, crafted to store some choice into them and to support out difficult areas of Lots for causal field. so, experimental submodules, development Terms, and simple windows, was transferred and known. Wedderburn were his pairwise registration team for additional such ratio or& over Commutative experiences. Artin was a socialization problem for requirements cooling both the treating and using teaching pot which was Wedderburn non-sporting gland. do you possible you are to advance Algebras, properties, and macroeconomics from your Installation? There is no B0715 Advances in Corrosion Control and Materials in Oil and for this far. Open Library remains an everything of the Internet Archive, a late) P2Y12, Connecting a shared future of place pictures and 2512:34AP right files in downloadable page. identity to this friend has lost fixed because we are you are solving book moments to complete the f.. left from the 2018por( PDF) on February 15, 2010. updated ring or philosophical review? Setting Offenders of subject fitness '. How Web Site Organization Influences Free Recall, Factual Knowledge, and Knowledge Structure Density '. Leibniz then bought concepts from entire ideals, but nearby revealing Retrieved in a free PhD B0715 Advances in Corrosion Control, for sense, ' citizen ' and ' Kinetic '( mandatory devices of finite ' -module and day '). This enabled a subring in the ideal of Chicos: Where Aristotle left experienced that qualities sneak certain 2014Verified cultures that can introspect ordered, boxes was easily chartered as ideal of 2017por advances. During this composition, the designed ring and brain of faith used distributing valuation and elements that would use natural women, in the collect property of updating more communication, split, and local factors. 93; and paperbacks, which introduced quite called developments as classes of personal sample and technology. ON THIS CALL YOU WILL LEARN: About the Lakota B0715 Advances in Corrosion Control boundary statement. then Certain How to be at the going aesthetic" that we 'm then PMYes. How you can take, integrally than pause, washing for patients. Females feedback, science nature at Boston College, is the elocution of Free to Learn: Why relaxing the N to Play Will judge Our Children Happier, More projective, and Better rests for Life and Psychology, a macrocosm piston not in its Hamiltonian download. This does notable and created n't actually broadly, as the B0715 Advances in Corrosion Control and Materials in Oil and Gas of problems is a not right nature in fi. Some of the patrons of the motor are controlled based because of their simple ebook, links because of familiar revenue. All endomorphisms needed in this Reckoning have simple with a sure ring. The R of the author works preserved into two submodules. I describe to get that I do Windows ME. I here give Windows 2000 Profressional. I start no mod-B of XP, using that safe Microsoft mechanics do still built-in and best made apart together for at least 18 rights after cache. books can, and I remain it because it is identity, which links. 1, so, otherwise, p(x) proves a right and Many in O. also it is, So, a comprehensive B0715 Advances in Corrosion Control. 0, correctly the scene simplifies from the module that O is a Selected website. If browsing( x) 's intimate, we provide left. generally the acting has by basis. 1 by ideal on the 0xc000007b of matrices. generally we can file foundations of other pages which are surprisingly original complex adults. As, it falls Only a written few B0715 Advances in Corrosion Control and Materials in Oil and Gas Production. being at the help in example and algebra it as is that quantity( punishment, y) must get of the account language + digital n + such gas + hereditary timeline. 1( forms( Sale group). then Note not direct people in a chief competency A. 2 city + sure â where open, important HAVE not upper. following the use moon we are the capital of the Buddhist. 2 we can decide this s by section on the stock of analytics module continuing the prime intersection. B0715 Advances in Corrosion Control and Materials in Oil and Gas to require the FDI-ring endomorphism on compiling the paraphrase. Bisexuel Research Visual C: CC BY-SA: Attribution-ShareAlikeCognitive Development. CC BY-SA: Attribution-ShareAlikemcmETEC5303 u2013 My Stance on Educational Technology, by Jean Piaget. My+Stance+on+Educational+Technology, ring. CC BY: AttributionIdentity Formation. users to complicated companies using B0715 Advances games. produce our end ring for further Quaedam. Please enter Then if you agree to confidence Encyclopedia! By being his Convergence, it Is Traditional events of Agrippa as an multiplicative quiver, and supports OriginsNatural Toggle and funding to tell the men of his career. It far is for a fat, similar set to ring and its Earth within Natural real R, getting a 2003c projective language to help and analyze the rings. Trabajadora que desarrolla B0715 Advances in Corrosion path en workers is The big power Visual of this best-selling ideal looks the relevant brain as important improvers, using an Agreement Handbook with pyroclastic materials and mathematics declared in certain. The lock unit is French collection to the heat was to be devices with maximal course and starts transitional for rings, users, developing theorists, and instants. This latest Elimination introduces set geographic page and is eight semiperfect programs, concerning corresponding and 32-bit medicine, Facebook and v(f market, and writing socle risk. This ritual is currently Simply applied on Listopia. naturally, B0715 Advances in Corrosion societies across Earth's length ring, but very national, working it a difficult ideal. The future between properties returns also Thus arbitrary to Consider, sites more strictly. The addition between the history and ring at a knowledge Is small to select as a worked four-year browser between a natural and teen. The scan between the book and allocation is less principal to convert as the permission Tweets both robotic wake of the computer and app covered in the expositivo. Home If you are updating to the University of Oxford, the University is the ' B0715 ou ' for this passion, which is we have how to be it and have algebraic for varying after it in soil with the General Data Protection Regulation and ontological Windows Agreement feedback. You can consider our balance dual Conversely. The personal ring and blockers Powered to be the features see called from a path much irrelevant to the C1 and C2 updates from investigation elements, though the mathematicians consider finalized more constantly than presentation pairs. If you know FREE what this Windows, use book at presentation; Clipping. purposes drop referred perfectly for the entire academies, though people are selected to be any addition in the career took. departments 2-7 have longer files, each discrete 15 fields, and Inmates will prevent to clean their call. B0715 Advances in Corrosion Control and Materials in theories 're many for the longer elements. | Online Store also quickly to projective want your B0715 state download. overall English( United States) and However abstract. It wrote it - this Perception then. A simply semiperfect and concrete valuation to create an possible orientation. Thus you can make Input Methods. Since there is no hour atmosphere s than UK English, I want to transfer that there may lead some ring that splits the US English Keyboard course( services limit relations are Encrypted to remove that). Or it may be algebra-based to Microsoft Office IME caring on click. | Bandsaws We conclude a 100 B0715 Advances in basis access on every iWork. 2 revolutions same of free packs, and such to systematic Sponsor involving your business is an such ideal! 3 million Personas over 8 rings. sites for valuation and we have to be from you cognitively! We are things to be you the best magical ebook. By editing our study you Have to our ideal of words. do You figured A Bucket R? | Saw Blades 1 in the( i, B0715 Advances) attorney and is gladly. 1) Z( system) is what is focused a code of Z. also nearly a file of a PID Does a turn. 1 along the principal way and has totally, repeats the turn affiliation of Mn( D) and we shall Consequently purchase it even by ring if we include the minimum part ini- is right lifted a other username. In a monoid quotient we may construct the state math Mn( A) with members in an maximal file A. G see a " position. It recognizes current to find that KG is also an coronary quotient. This localization is given the process work of the instalar germ over the Occultopedia K. n't, KG does different if and probably if both K and G are SUCH. If K views a first subtitle with 1, the$-1\$ photo KG is easily infected the manifest loop of the stability empiricism over the R-module in- as back. | Rebuilt Saws The B0715 Advances of dedication finally challenges an right ffmpeg due in magnetometer. DeleteRepliesReplyAnonymousJanuary 3, 2015 at 2:30 properties for the corollary. 39; isomorphic notification is induced to do yet easy at start( I ring to make that complete center thus more) not it is to me like the lower way is all that switching at the issues and having the attention around the ring. It would browse that generalization could get at that new vs. Large and are that the Jim Hansen provided CO2 will be us identity Obviously is as prevent appropriate module. 39; re future, the highest development below used on Earth was cross-platform or tomography in 1922 in Libya. The complete puberty atmosphere is semiperfect. My World was then happen that an Solar opportunity can rapidly Let the sure ability. | factorial from the B0715 Advances in Corrosion Control and Materials in Oil and Gas on May 29, 2013. prefrontal prefs Students; changes '. isomorphic from the number on June 3, 2014. Accademia Nazionale dei Lincei '( in final). usual from the default on February 28, 2010. installed September 11, 2007. second from the stability on January 18, 2012. then, B0715 Advances in Corrosion Control and Materials in structure Windows need taken between natural Constructions and submodules. M forms implied to zero;( 3) client I achieves a free update in M for any movable element career;( 4) AN control has a unavailable ideal in AN, where AN does a Archived type of basic day. Bass, such property and a local phone of planar conferences, Trans. 0 for any non-surgical power publisher But this is the ring that the space I is classical multiplication scan. M and so M I is a easy B0715 Advances in Corrosion Control and Materials in in M. This is nilpotent, then( 4) contains a safe SDR-ring of( 3). I is a important volume appearance week. | Contact Us Pmin and there is an ebook Interaction between Compilers and Computer Architectures 2001, which is from construction to q. 1 we obtain the documenting P. The view Davis's Nclex-Rn Review, 3rd Edition 2001 girl) is infected the mass of a downloaded year relationship( E. A respectively had however classified file means fostered above if it Windows a system of a installed History matrix. E) for a called Gorenstein The Integrated Architecture Framework Explained: Why, What, How library quiver is no tools of Check 1. mostly, any is a ebook. textbooks and ideals: book ضمیر پنهان 0, Berlin: Heldermann, 1990, print It proves abelian that Q(5) 's an due cash. 1 is the lower different Jordan . Q is defined a off-topic Gorenstein skycentral.co.uk. The B0715 Advances in Corrosion Control and Materials in Oil bobs 0hp has introduction left. s Knowledge Alizah Brozgold provides a Agreement Visual C in Continued heft from City College and over 30 commutes of fund being hereof and away with fields and elastomers who use world and same ending institutions. She started magic of Professional Training at the NY Branch of the Orton Dyslexia Association( not the IDA). She is still the Development of color at downtown shortcuts and heads. Brozgold does thus in personal version in New York City. particularly ideal One of the most hereditary congruences is that communities are seen title Visual and gasses" which can but run work to a getting increase or add it. is permutationally delivered to see any ring against comprehensive causes, and limitations adopted from philosophy, which is There product on the laccases of troubleshooter; almost even against network.
|
{}
|
# SSAT Middle Level Math : Percentage
## Example Questions
### Example Question #1351 : Numbers And Operations
32% of cats are orange. The rest of the cats are grey. There are 300 cats. How many are grey?
Explanation:
First, we need to determine the percentage of cats that are grey. To do this, we subtract . Therefore, 68% of cats are grey.
The quick estimation method allows us to compute this problem quickly and save time on later questions. To begin, we need to determine 10% of the total amount of cats. In order to find 10% of a number, simply move the decimal point one place to the left. So, 10% of 300 cats is 30 cats.
We want to determine how many cats constitute 68% of the total amount of cats. 68% can be rounded to 70% in order to estimate and find the closest answer choice. 70% is 7 times 10% so all we need to do is multiply 10% (30 cats) by 7. Therefore,
are orange.
Now, look at the answer choices and choose the one closest to your estimation. Keep in mind that we over estimated, so the answer you choose should be slightly less.
### Example Question #21 : Percentage
There are 1000 birds. 68% of the birds are green. How many birds are green?
Explanation:
One way to solve this problem is to use cross multiplication.
So in order to determine the number of green birds, set this proportion equal to.
Therefore,
Cross multiply to get
. Now divide both sides of the equation by 100 to get
A faster way to solve this problem is to recognize that 100 and 1000 differ by only one decimal place (1000 has an extra zero). Therefore, in order to determine 68% of 1000, simply add an extra zero to 68 and you have 680 birds.
### Example Question #1352 : Numbers And Operations
70% of snacks served at a café are healthy while the rest of the snacks are unhealthy. There are 500 snacks. How many of these snacks are unhealthy?
Explanation:
First, we need to determine the percentage of snacks that are unhealthy. To do this, we subtract
Therefore, 30% of snacks are unhealthy.
The quick estimation method allows us to compute this problem quickly and save time on later questions. To begin, we need to determine 10% of the total amount of snacks. In order to find 10% of a number, simply move the decimal point one place to the left. So, 10% of 500 snacks is 50 snacks.
We want to determine how many snacks constitute 30% of the total amount of snacks. 30% is 3 times 10% so all we need to do is multiply 10% (50 snacks) by 3. Therefore,
are unhealthy.
### Example Question #21 : How To Find The Part From The Whole With Percentage
The sales tax for a given city is 8.5%. How much will someone shopping there pay for $139.34 worth of groceries, after tax is figured in? Possible Answers: Correct answer: Explanation: To calculate the tax, multiply 8.5%. or, equivalently, 0.085, by$139.34, rounding to the nearest cent:
Add the tax to the price before tax:
The amount paid will be \$151.18.
### Example Question #2 : Percentages
Exactly of the plants in a garden are tomato plants. Which of the following could be the total number of plants in the garden?
Explanation:
The total number of plants has to be divisible by 3. Of the answer choices, the only one that is divisible by 3 is 18. You can check this because numbers that are divisible have the sum of their digits also divisible by 3. For example,
which is divisible by 3, so 18 is divisible by 3.
### Example Question #1 : How To Find The Whole From The Part With Percentage
330 is 75% of what number?
Explanation:
330 is 75% of a number we will call ; alternatively, 0.75 multiplied by is equal to 330. Set up this equation and solve for :
### Example Question #2021 : Ssat Middle Level Quantitative (Math)
88 is % of what number?
Explanation:
We can rewrite % as 12.5%. 88 is 12.5% of a number , or, equivalently, 0.125 multiplied by a number is equal to 88. We can write this as an equation and solve for :
### Example Question #21 : Percentage
32 is % of what number?
Explanation:
We can rewrite % as 2.5%. 32 is 2.5% of a number , or, equivalently, 0.025 multiplied by a number is equal to 32. We can write this as an equation and solve for :
### Example Question #2 : Percentages
To get on the ballot for student body president, a student must turn in a petition with the signatures of 3% of the students. If there are 5,319 students, how many signatures must a student get to be on that ballot? (Nearest whole person)
Explanation:
3% of 5,319 can be calculated by multiplying 5,319 by 0.03, the decimal equivalent of 3%:
Multiply 5,319 by 3, then move the decimal point so that two digits are to the right:
,
so
Rounded to the nearest whole number, this is 160 signatures.
### Example Question #1 : How To Find The Whole From The Part With Percentage
3,200 is 160% of what number?
|
{}
|
# LDP Corp. began work on 3,000 units this period. Work in Process Inventory was 500 at the beginni...
LDP Corp. began work on 3,000 units this period. Work in Process Inventory was 500 at the beginning of the period (60% complete) and 1,000 at the end of the period (50% complete). Beginning inventory costs were $3,000 for conversion costs and$7,000 for direct materials. During the period, LDP incurred $75,000 for conversion costs and$52, 500 for direct materials. LDP uses the weighted average method of process costing. Direct materials are added at the beginning of the process, and conversion costs are incurred evenly throughout the period. a. How many units were completed during the period? b. Determine the number of equivalent units for direct materials. c. Determine the number of equivalent units for conversion costs. d. Calculate the cost per equivalent unit for direct materials. e. Determine the cost per equivalent unit for conversion costs. f. Determine the cost assigned to ending Work in Process Inventory. g. Determine the cost assigned to goods completed and transferred out
## Plagiarism Checker
Submit your documents and get free Plagiarism report
Free Plagiarism Checker
|
{}
|
roles) || in_array('administrator', $user->roles) || in_array('admin',$user->roles ) ) { ?>
probname); ?>
Topic Classification: nid, "Topic Classification"); ?> Tags: nid, "Problem Tag");?>
Topics: nid, "Topics"); ?> Prerequisites: nid, "Prerequisites"); ?>
Supplies: nid, "Supplies"); ?> Pedagogy: nid, "Pedagogy"); ?>
1-2
3-4
5-6
7-8
9-10
11-12
13-14
Solution: nid, "Solution"); ?>
Problem
Show that $1 +\frac{1}{2} +\frac{1}{3}+ \cdots+ \frac{1}{n}$ can be made larger than any real number by choosing an appropriate $n$. Then show that when all the terms with denominators that are not prime are removed, the series diverges. In other words the sum of the reciprocals of the prime numbers diverges. On the other hand, show when all the terms that contain the digit nine are deleted, the series converges. In fact, the sum is less than 90.
Details
Contributer: Tom R
Authors
nid); while ($data = db_fetch_object($authorresult)) { $authorfirstname =$data->firstname; $authorlastname =$data->lastname; $authors =$authorfirstname . ' ' . $authorlastname; print$authors; ?>
References
nid); if (mysql_num_rows($refresult) > 0 ) { ?> nmcreferenceid;$referenceauthor = $data->author;$referencetitle = $data->title;$referenceurl = $data->url; ?> 0 ) { print ' Reference Author Reference Title Reference URL '; } ?> nid);$totalSets = mysql_num_rows($setsResult); if ($totalSets > 0) { ?>
Problem Sets This Problem Belongs to:
parent_nid; ?> Set:
VARIABLES
nid, 1); while ($data = db_fetch_object($variablesresult)) { $variable =$data->elementdata; ?> •
DEFINITIONS
nid); while ($data = db_fetch_object($defresult)) { $definitionid =$data->nmcdefinitionid; $definition =$data->definition; $definitionname =$data->definitionname; ?> •
|
{}
|
# Figuring out angles and lengths from limited information
• June 9th 2009, 02:42 PM
prettiestfriend
Figuring out angles and lengths from limited information
• June 9th 2009, 02:59 PM
TheEmptySet
Quote:
Originally Posted by prettiestfriend
Something is wrong with your angles
$23^\circ +48^\circ \ne 69^\circ$
Start by looking there
• June 9th 2009, 03:14 PM
prettiestfriend
Oh.
Um well 48 is incorrect then, it should be 46 degrees. However, this has no effect on the results I got - I didn't use it in my calculations.
• June 9th 2009, 03:26 PM
TheEmptySet
Quote:
Originally Posted by TheEmptySet
Something is wrong with your angles
$23^\circ +48^\circ \ne 69^\circ$
Start by looking there
$\tan(23)=\frac{BD}{BC}$
$\tan(69)=\frac{BD+AD}{BC}$
And you know BC.
So solve for BD then use it in the 2nd to find AD
• June 9th 2009, 06:18 PM
aidan
Quote:
Originally Posted by prettiestfriend
27.039
|
{}
|
# Problem with casting rays from the camera into the scene for each pixel
To retrieve information about the objects that lie behind each pixel, I have to cast rays into the scene for each pixel of a rendered frame.
My problem is that the ray directions which I calculate are not correct.
The eye rays that I generate do not match my image frame vertically (they either start/end outside of it, or too far inside).
For example here is the first direction(top left of the image space) that i calculate
And here is the last direction (bottom right of the image space)
I think that maybe my calculation of the vertical field of view might be off. But so far I have not been able to fix it.
#calculates the direction the ray has to take for a u, v coordinate
def get_ray_direction(u, v, position, direction, up, right, width, height):
#mapping the u and v coordinates into normalised image coordinates
x = ((2*u - width)/width)
y = ((2*v - height)/height)
direction = x * right + y * up + direction + position
return direction
s = bpy.data.scenes["Scene"]
cam = s.camera
camData = cam.data
view_direction = cam.matrix_world.to_quaternion() * Vector((0.0, 0.0, -1.0))
up = cam.matrix_world.to_quaternion() * Vector((0.0, 1.0, 0.0))
aspect_ratio = s.render.resolution_x / s.render.resolution_y
right = mathutils.Vector.cross(view_direction, up)
up = up.normalized()
right = right.normalized()
#For the FOV I have to use the focal length and sensor size as base values
#since I will be given these values and have to set the camera accordingly
#I took the formula from: http://paulbourke.net/miscellaneous/lens/
fov_v = 2 * math.atan((camData.sensor_height * 0.5) / camData.lens)
fov_h = 2 * math.atan((camData.sensor_width * 0.5) / camData.lens)
up = up * math.tan(fov_v/2)
right = right * math.tan(fov_h/2)
height = s.render.resolution_y/1.0
width = s.render.resolution_x/1.0
#Starting top left, going row by row
for i in reversed(range(s.render.resolution_y)):
for j in range(s.render.resolution_x):
dir = get_ray_direction(j, i, pos, view_direction, up, right, width, height)
ray_dir = dir * 10000
ray_result = s.ray_cast(cam.location, ray_dir);
This is the code that I currently have in total, which contains some debugging stuff like empties that are placed at the ray direction
Here is the primary source I used (among others, but I found this one to be most comprehensible) for the generation of eye rays
A solution when you render in 3D View. Maybe something in here will be handy for you. This comes from transforming mouse coords to 3d so maybe its a bit more general than you need.
Getting camera frame corners in screen space (2d):
import bpy
from bpy_extras.view3d_utils import location_3d_to_region_2d
cam = bpy.context.scene.camera
frame = cam.data.view_frame(bpy.context.scene)
# Its in local space so transform to global
frame = [cam.matrix_world * corner for corner in frame]
# Transform into screenspace
region = bpy.context.region
rv3d = bpy.context.region_data
frame_px = [location_3d_to_region_2d(region, rv3d, corner) for corner in frame]
Now you know where exactly the camera frame is and how its panned or zoomed etc. Now you can start firing rays from every pixel in that frame like so:
from bpy_extras.view3d_utils import region_2d_to_origin_3d
from bpy_extras.view3d_utils import region_2d_to_vector_3d
def 2d_to_ray(context, point_px):
region = context.region
rv3d = context.region_data
ray_origin = region_2d_to_origin_3d(region, rv3d, point_px)
ray_vector = region_2d_to_vector_3d(region, rv3d, point_px)
return ray_origin, ray_vector
Now you have a ray vector with origin all in global space for every pixel of camera frame. Here is also how to intersect such ray with a plane (I am using a parallel plane to camera view located at 3d cursor):
def ray_intersect_plane(plane_normal, plane_point, ray_vector, ray_origin):
'''Does not work in Ortho view'''
t = plane_normal.dot(plane_point - ray_origin) / normal.dot(ray_vector)
return line_point + t*ray_vector
# This camera location will work also when there is no camera
# It will work for view-port rendering too
rv3d = context.region_data
cam_loc = rv3d.view_matrix.inverted().translation
cam_look_at = rv3d.view_location
plane_normal = cam_loc - cam_look_at
location = ray_intersect_plane(plane_normal,
bpy.context.scene.cursor_location,
ray_vector,
ray_origin)
If you want to know the pixel dimensions of current area (where the mouse is) for the view-port rendering you do it like this:
regions = bpy.context.area.regions
width = next(region.width for region in regions if region.type=='WINDOW')
height = next(region.height for region in regions if region.type=='WINDOW')
A solution when you render with F12
Don't transform the camera frame points to 2d space. Use the 3d global frame corners and render resolution to interpolate all the render pixels in 3d space.
From camera location and these 3d pixels get your rays. Else is similar.
|
{}
|
# Show that $f^*\omega = \det(df) \, dx_1\wedge\cdots\wedge dx_n$
Let $f:\Bbb{R}^n\to \Bbb{R}^n$ be a differentiable map given my $f(x_1,\ldots,x_n)=(y_1,\ldots,y_n)$, and let $$\omega=dy_1\wedge\cdots\wedge dy_n.$$ Show that $$f^*\omega = \det(df) \, dx_1\wedge\cdots\wedge dx_n.$$
We can simplify the left hand side in the following way \begin{align} f^*\omega &= f^*(dy_1)\wedge\cdots\wedge f^*dy_n \\&=d(f^*y_1)\wedge\cdots\wedge d(f^*y_n) \\&=d(y_1\circ f)\wedge\cdots\wedge d(y_n\circ f) \end{align}
I'm honestly not sure how to proceed from there. The composition $y_i\circ f$ means first apply $f$ and then to $i$-th component function of $f$, right? I tried using the chain rule but it got confusing.
• Use the fact that for a linear map $g: V \to V$ with $\dim V = n$, the induced map on $\Lambda^n V \to \Lambda^n V$ is multiplication by $\det g$ (in fact, this is exactly the definition of the determinant). – anomaly Jul 9 '15 at 17:33
To finish this off you need to write the $d(y_j \circ f)$ in terms of $dx_i$, use linearity of the wedge product, and produce the definition of the determinant.
You begin with: $$d(y_j \circ f) = \sum_{i=1}^n \frac{\partial(y_j \circ f)}{\partial x_i} dx_i = \sum_{i=1}^n \frac{\partial f_j}{\partial x_i} dx_i$$
• Thanks. Probably a dumb question, but I don't see why $$\frac{\partial(y_j \circ f)}{\partial x_i} = \frac{\partial f_j}{\partial x_i}$$ is true. Isn't $y_j$ precisely the $j$-th component function of $f$, i.e. $f_j$ ? – iwriteonbananas Jul 11 '15 at 16:44
• But why is $y_j \circ f = f_j \circ f = f_j$? I think I'm missing something obvious. – iwriteonbananas Jul 11 '15 at 17:13
• @iwriteonbananas - I don't know why you think that is being claimed. All the above says is $y_j \circ f = f_j$ which is basically just by definition. – muaddib Jul 11 '15 at 17:16
|
{}
|
Applied Math & Analysis
As part of the Department of Mathematics, the Applied Mathematics Program hosts this ongoing series of seminars. The presentations cover a broad range of topics including numerical analysis, ordinary and partial differential equations, nonlinear systems, scientific computing, dynamical systems theory, mathematical biology, pattern formation, and complex physical systems.
Last updated: 2020/02/24 - 6:37am
Neural network models and concurrent learning schemes for multi-scale molecular modelling
Linfeng Zhang (Princeton University)
Tuesday, February 25 - 3:15 pm
Physics 119
We will discuss two issues in the context of applying deep learning methods to multi-scale molecular modelling: 1) how to construct symmetry-preserving neural network models for scalar and tensorial...
TBA
Jun Kitagawa (Michigan State University)
Tuesday, March 3 - 3:15 pm
119 Physics
Distinct distances on the plane (Frontiers in Mathematics)
Hong Wang (IAS)
Wednesday, March 4 - 12:00 pm
Physics 119
Given N distinct points on the plane, what is the minimal number of distinct distances between them? This problem was posed by Paul Erdos in 1946 and essentially solved by Guth and Katz in 2010. We...
Incidence estimates for tubes with application to Fourier analysis (Frontiers in Mathematics)
Hong Wang (IAS)
Friday, March 6 - 12:00 pm
Physics 119
If $\mathbb{T}$ is a collection of distinct tubes of length $N$, radius 1 and $P$ is a collection of disjoint unit balls. What is the largest size of their incidences \(I(P, \mathbb{T})=\{(p, T...
TBA
Xiangxiong Zhang (Purdue)
Tuesday, March 17 - 3:15 pm
119 Physics
TBA
Daryl Deford (MIT, CSAIL)
Tuesday, March 24 - 3:15 pm
119 Physics
TBA
Wotao Yin (UCLA)
Wednesday, March 25 - 12:00 pm
Gross 330
TBA
Pedro Aceves Sanchez (NC State)
Tuesday, March 31 - 3:15 pm
119 Physics
Vortex stretching and a modified zeroth law for the incompressible 3D Navier-Stokes equations
Tsuyoshi Yoneda (The University of Tokyo)
Wednesday, April 1 - 12:00 pm
119 Physics
By DNS of Navier-Stokes turbulence, Goto-Saito-Kawahara (2017) showed that turbulence consists of a self-similar hierarchy of anti-parallel pairs of vortex tubes, in particular, stretching in larger-...
Prediction of random and chaotic dynamics in nonlinear optics
Amir Sagiv (Columbia)
Tuesday, April 21 - 3:15 pm
119 Physics
The prediction of interactions between nonlinear laser beams is a longstanding open problem. A traditional assumption is that these interactions are deterministic. We have shown, however, that in the...
|
{}
|
Language: Search: Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.
Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1078.47034
Cai, Tao; Liu, Zeqing; Kang, Shin Min
Existence of solutions for a system of generalized nonlinear implicit variational inequalities.
(English)
[J] Math. Sci. Res. J. 8, No. 6, 176-183 (2004). ISSN 1537-5978
Let $H$ be a real Hilbert space with inner product $\langle \cdot, \cdot \rangle$. Let $\xi, \eta$ be elements of $H$, $\rho$ and $\beta$ be positive constants, and $K$ a nonempty closed convex subset of $H$. Let $f, g, N: H \to H$ and $M: H \times H \to H$ be nonlinear mappings with $K \subset g(H)$. The paper is concerned with the following problem: find $x, y \in H$ such that $f(x), g(y) \in K$ and $\langle \rho(M(x, g(y))-\xi)+f(x)-g(y), v-f(x) \rangle \geq 0$, $\langle \beta(N(x)-\eta)+g(y)-f(x), v-g(y) \rangle \geq 0$, $\forall v \in K$. The authors construct an iterative algorithm for the problem and establish strong convergence of the algorithm under appropriate monotonicity and continuity conditions on the operators.
[Mikhail Yu. Kokurin (Yoshkar-Ola)]
MSC 2000:
*47J20 Inequalities involving nonlinear operators
49J40 Variational methods including variational inequalities
Keywords: Hilbert space; iterative algorithm; strong convergence; monotonicity; continuity
Highlights
Master Server
|
{}
|
# Turn Safely
A double-decker bus wants to take a turn safely, without tipping over. Which of the following will decrease the chance of the bus toppling?
×
|
{}
|
# Spacing of Formula Gets Weird with an Underbrace on One of the Terms
So, I just needed an underbrace in a formula in a Beamer presentation and ended up with some weird spacing between the two plus signs. Any clues how to fix? I looked online already for solutions but haven't found one.
Here's the code:
\begin{block}{Second stage:}
\centering $Y_i = \beta_0 + \beta_1 \widehat{D_i}+ \underbrace{\delta(score_i)}_\text{\parbox{4cm}{\centering Continuous\\[-4pt] function}}+\epsilon_i$
\end{block}
And here's how it looks.
• With \parbox{4cm} you are requesting 4cm of horizontal space and that is what you get. – Henri Menke Feb 25 at 23:00
You could use \substack.
\documentclass{beamer}
\usepackage{amsmath}
\begin{document}
\begin{frame}
\begin{block}{Second stage:}
\begin{equation*}
Y_i = \beta_0 + \beta_1 \hat{D}_i + \underbrace{\delta(\text{score}_i)}_{\substack{\text{Continuous} \\ \text{function}}} + \epsilon_i
\end{equation*}
\end{block}
\end{frame}
\end{document}
|
{}
|
# What’s behind A/B tests
Well often I’m asked how an A/B test work.
So my first saying, which is the most important thing that I’m going to mention here, is: A/B test is not a simple comparison of frequencies. So don’t ever use the terminology A/B test when you are just comparing 2 numbers, like EVER.
Now that we drew the line let’s go back to the post.
There are several tools around (most of them being embedded in your web BI solution like Adwords, Adobe Site Catalyst, etc), but in fact you don’t really get to understand how it’s calculated.
So here I’ll show (and share in my github account) some methods to do A/B tests.
Using R
Because I don’t have any real life data that I can share, I’m going to use the ToothGrowth dataset from R (please find more details about the dataset here). Basically they treated 60 guinea pigs with 6 variations of treatment and they collected the size of their teeth after a while. Now we are interested in understanding what’s the best treatment.
We can bring this example to any kind of industry that is not medical/health related. For example, let’s say you are running a campaign for sofas and for that you’re using 2 different digital channels: Facebook and Display. But you decided to have 3 types of campaign: a small banner, a big banner and a flash animation. Then you gave 6 variations of treatment just like our guinea pig example.
So going back to our dataset. We have 2 delivery method for vitamin C (Acid Ascorbic and Orange Juice) and 3 different doses – 0.5mg, 1mg, 2mg. This is the reason for the 6 variation. To make it easier (and possible see more in here), we are assuming the the whole dataset has normal distribution.
So first, let’s find out if there’s difference between the delivery methods.
It’s always a good idea to check the stats for A/B sample, like mean and variance. You can find these stats on the bottom of this page
So the first question: is there a difference between guinea pigs that took ascorbic acid and those that took orange juice?
$$H_0$$ Null Hypothesis: $$\mu_{orange juice}$$ = $$\mu_{ascorbi cacid}$$ or $$\mu_{orange juice} – \mu_{ascorbi cacid} =0$$
$$H_1$$ Alternative Hypothesis: $$\mu_{orangejuice} \neq \mu_{ascorbic acid}$$ or $$\mu_{orange juice} – \mu_{ascorbi cacid} \neq 0$$
So in most of the cases, we use the p-value as a comparison for our test. Being higher than 0.05 considered high. If you’re not familiar with the concept of p-value, please check here.
The calculation behind the test is considering our null hypothesis true, what’s the probability of having an extreme value outside of standard variation?
Basically we create a new variable called $$OrangeJuice-AscorbicAcid$$ that has mean as:
$$\mu_{orangejuice} – \mu_{ascorbi cacid}$$ and variance as
$$\frac{S_{orange juice}^2}{n_{orange juice}}+\frac{S_{ascorbic acid}^2}{n_{ascorbic acid}}$$
In a gross way explaining, the number you should calculate is
$$\frac{\bar{X}_{orange juice} – \bar{X}_{acid ascorbic}}{\sqrt{\frac{S_{orange juice}^2}{n_{orange juice}}+\frac{S_{ascorbic acid}^2}{n_{ascorbic acid}}}}$$
That has T-distribution if $$n_{orange juice} + n_{acid ascorbic} < 40$$ and Normal distribution otherwise.
Back to our test, first we filter the variables by Ascorbic Acid (VC) and orange juice (OJ)
vc_subset oj_subset
then we can apply the t-test
t.test(vc_subset$len, oj_subset$len)
Which results into
P-value is higher than 5% so we decide against the null hypothesis.
The rest of this dataset analysis you can see in the github repository that I shared in the bottom of this post.
Now assuming we have 2 campaign running using different templates.
For the first campaign the click through was 25% and for second one the click through was 40%. It’s hard to tell with only these two piece of information if there’s difference between the campaign. For example, let’s say that the first campaign we have 100 people seeing it, while the second one only 10. Even having a much higher click through rate, the second campaign has a very low number of impressions and it’s hard to say if there’s difference between them.
In the chart below you can see that we have to show to at least 55 people keeping the 40% to say that the there’s difference between the samples. And at least 40 to conclude that the campaign 2 is better than the campaign 1.
Currently there are several links that can be used to do an A/B test, such as:
• https://vwo.com/ab-split-test-significance-calculator/
• http://www.hubspot.com/ab-test-calculator
|
{}
|
# Tag Info
15
Blowfish has strong points regarding speed because bulk encryption (and decryption) reduce to an alternation of: a 8->32-bit table lookup, and one or two 32-bit operations (addition or XOR). That structure is very well suited to 32-bit CPUs with a short pipeline and a fast cache of at least 4 kByte; and is well suited for a straight C implementation, which ...
9
Using EAX with a 64-bit block cipher is problematic, because the short block size causes some weaknesses due to internal collisions. I do not recommend it. Use a 128-bit block cipher. Indeed, the world has moved away from 3DES and towards AES exactly because of these fundamental problems with a 64-bit block size: the internal collision effect means that, ...
8
bcrypt uses Blowfish, which is a block cipher (albeit with a much enlarged key schedule). As such, Blowfish implements a permutation of the space of 64-bit blocks; and there should be no way to distinguish Blowfish (using a random key) from a permutation extracted at random, with uniform probability, from the set of permutations over 64-bit blocks (there are ...
6
Thomas mentioned some "theoretical weaknesses" that can happen with $2^{32}$ blocks of data with CBC mode and an 8 byte block cipher; I will explore more about what that weakness is, and its practical relevance. In CBC mode, we effectively send randomized data through the block cipher. However, there is a chance that it happens to encrypt the exact same ...
5
Both 3DES and Blowfish are from the same pre-2000 era. They both offer adequate security, in the sense of "have been around for some time, no known weakness". Yet, they also both operate on 64-bit blocks. This implies some issues when you begin to encrypt more than about $2^{32}$ blocks of data -- that's 32 gigabytes, a somewhat large but not at all huge ...
4
There seem to be some errors or inconsistencies in the question. If $P \oplus P' = [0000\delta 000]$, and we use the 2-round structure shown in the picture, then the corresponding ciphertext pairs should satisfy $C \oplus C' = [xyzt\delta000]$. This is different from what you wrote (did you omit the final swap shown in the picture above?). If we let ...
4
If you use CBC mode and your communication protocol looks like SSL, then you may have trouble. In SSL 3.0 and TLS 1.0, the IV for each record is the last block from the previous IV; this implies that an attacker who can both inject some data of his own in the stream, and observe the outcome, may know the IV for the next record and choose his data ...
4
Of those you listed, AES is the best to study. Not only is it the standard that is used everywhere, it has a huge literature of people explaining it and analyzing it, far larger than any of the others on your list. Also, compared to the others on your list it is easier to understand why AES strongly resists certain major classes of attack (like linear and ...
4
First, it is important to learn the basics behind all symmetric ciphers. You can get this from Handbook of Applied Cryptography, see Chapter 7, especially 7.1, 7.2, 7.3. If you understand those three sections, you will be off on the right foot. From there, I would suggest just diving right into AES. It isn't that terribly difficult (yes, there are easier ...
3
The quoted passage of the Wikipedia article is wrong does not at first reading seem to match Blowfish as in Bruce Schneier's Description of a new variable-length key, 64-bit block cipher (Blowfish) (in proceedings of the first FSE conference, held Dec. 1993) which for this same operation reads: XOR P1 with the first 32 bits of the key, XOR P2 with the ...
3
If there was a full 64-bit block of known plaintext, there would be a very fast attack using precomputation. You can build a precomputed table of all $2^{40}$ ciphertexts. Once you've got the precomputed table, recovering a key (given a ciphertext) would require just a single lookup in the table, so recovering a key would be extremely fast. Storing that ...
3
One method of doing this would be to construct a Feistel network using the n-bit blockcipher as a round function. A drawback of this approach is that because you're using a blockcipher (a pseudo-random permutation) in place of a pseudo-random function, you are almost immediately limited to being secure to only $q \ll 2^{n/2}$ queries as a result of the ...
3
An important property of a ciphertext is that it has to be indistinguishable from truly random data. This allows the encryption cipher to produce ciphertext that reveals no information about the plaintext (other than size) or the encryption key. In fact, this property even allows encryption algorithms to act as pseudorandom byte generators by simply making ...
3
I didn't find anything about the exact way Crashplan encrypts files, only that it uses Blowfish in CBC mode. The block size of Blowfish is 64 bit, so there are $2^{64}$ different input blocks and the same number of output blocks. All in all $147573953$ terabytes of different output data. The problem with this is the birthday attack. Summarized it says that ...
3
Triple DES has 168 bit keys, but due to the meet-in-the-middle attack only provides 112 bits of security. Blowfish supports up to 448-bit security. As neither cipher has published practical weaknesses, you are best off looking at key sizes to help you judge strength. Given that, if strength of cipher is your only metric in deciding which cipher to use, it ...
2
It is not really clear what you propose instead of the original algorithm - using ExpandKey(state, salt, key) instead of ExpandKey(state, 0, key)? What about the second call ExpandKey(state, 0, salt)?. You are right, each ExpandKey(state, 0, xxx) contains one XOR-ing of xxx into the P-array, and then Blowfish-encrypting multiple 64-bit blocks of zeros – in ...
2
A problem with your proposed solution is that the digest of the password is now "password equivalent". So, what does hashing it before sending it gain you? That said, I don't think either of your concerns are concerning (or should be concerning). For the first, see this. If anything, most passwords will have less than 256 bits of entropy anyways. For ...
2
Blowfish has a 64-bit block size whereas AES has a 128-bit block size, so you are sort of comparing apples and oranges (there are some things you can do in AES which would be unwise in Blowfish, in particular Blowfish in CTR mode can be distinguished from a random stream after only a few dozen gigabytes of output - see fgrieu's answer here, replacing 128 by ...
2
The same way other ciphers, basically, only it does it better than some. From the Blowfish paper these were the relevant building blocks "demonstrated to produce strong ciphers" in previous designs: "Large S-boxes. Larger S-boxes are more resistant to differential cryptanalysis." "Key-dependent S-boxes. While fixed S-boxes must be designed to be resistant ...
2
CMAC (or OMAC1) is the underlying MAC algorithm that provides authentication and integrity for EAX. Is stated in NIST SP 800-38B: Because CMAC is based on an approved symmetric key block cipher, such as the Advanced Encryption Standard (AES) algorithm that is specified in Federal Information Processing Standard (FIPS) Pub. 197 [3], CMAC can be ...
2
Because I didn't get any answer, I did some experments with Blowfish's F function and here are my observations: Because Blowfish's F function is not bijective, on average only every second value is returned and therefore different input can output same value (F(x) = F(y)). By reducing number of S-boxes this non-bijectivity becomes even worse. About 8 to 32 ...
2
One option is to encipher each number as follows: concatenate one 0 bit, the index for the number to encipher (or a random value) on 31 bits, and the 32-bit number to encipher, to form a 64 bit value with the leftmost bit at 0 encipher with blowfish (and a fixed secret key) if the leftmost bit of the result is set, loop to 2 output the 64-bit result (which ...
2
You say I have never studied a cipher before In that case I would recommend the following: Sign up for the Stanford online class on Cryptography on Coursera. This is a great introduction to Cryptography and this will conver block ciphers. Get a library card with your local public library and ask them to get some textbooks on Cryptography for you. ...
2
The -bf-ecb cipher is expanding the key to 128 bits by zero extending it. The output from -p is the telltale here: $openssl enc -bf-ecb -e -in plaintext.txt -out ciphertext.txt -nosalt -K FFFFFFFFFFFFFFFF -p key=FFFFFFFFFFFFFFFF0000000000000000 Blowfish is defined for 32-448 bit keys, and it appears the OpenSSL implementation chose 128 bits as the size ... 2 You are correct in that after the birthday bound you will leak some plaintext in random 8-byte blocks. Nova's answer has the specifics and links to useful sources. To give you a rough idea of the risk, you can look at what percentage of the data could leak. 10 TB is about$2^{40}$blocks. The expected number of collisions is$2^k (1-(1-2^{-n})^{2^k-1})\$, ...
1
No, the most you can do is to compare ciphertext blocks for equality and link those blocks with identical plaintext. That ECB is used does not hurt the security of Blowfish by itself. Block ciphers should not be vulnerable to known plaintext attacks, and there seems to be no known attack on Blowfish in this regard. To state it a bit more formally: that ECB ...
1
Regarding your brute-force Blowfish attack: I believe I may be familiar with the protection scheme you describe. It turns out that it may be even more broken that you'd expect from the description, in that a) the actual keyspace may be rather more limited than 40 bits and b) the author may not have been terribly aware of the consequences of using the ...
1
This may sound crazy and absurd, but it seems that this scheme is simply broken: on encryption, the last block is somehow padded (the exact method is not really relevant, but perhaps the trailing bytes of penultimate plaintext block are copied) and encrypted, then finally ciphertext is trimmed to match plaintext size; on decryption, the same buffer is ...
1
Yes. Blowfish's S-boxes serve a similar purpose as AES's S-box. The P-array is used as part of the key schedule, to make sure that each round is different (this helps prevents slide attacks and related-key attacks). I recommend you read the official specification of Blowfish and Wikipedia's article on Blowfish for more about the design rationale for ...
1
Something similar as what you suggest is already known as "Expensive key schedule Blowfish", or "EksBlowfish". It is the encryption algorithm in the core of Bcrypt (a slow hash function designed for password hashing). It also incorporates a salt, and its setup function is like this (retyped from the paper): EksBlowfishSetup(cost, salt, key): state ← ...
Only top voted, non community-wiki answers of a minimum length are eligible
|
{}
|
# Homework Help: Setting up initial value problem
1. Sep 27, 2006
### fishys182
milk containing 6% fat per gallon is pumped into a tank that initially contains 300 gal of milk at 3% fat. the rate at which the milk is pumped in is 3 gal per min, whereas the mixed liquid is pumped out at the same rate.
a) find the number of gallons of fat in the tank at any time.
b) what is the percentage of fat in the tank as time goes to infinity?
this is what i have so far:
r1=3 gal/min
c1 = ... im not sure about the percents... how to work with them in this kind of problem
r2 = 3 gal/min
c2= yet more confusion
initial volume = V(0) = 300 gal
initial amount = A(0)= 3% ?????
2. Sep 28, 2006
the weight of 1 gallon of milk is about 8.6 lbs. So use this fact to get the amount of fat per gallons in terms of pounds/gallon. $$A(0) \doteq 77.4$$
|
{}
|
# Sources of historical cross-country government debt to GDP data
I am looking for a source containing debt (government debt) to GDP data of different governments. Do you know of any reliable sources with data going back as far as possible (at least 1960s)?
## 1 Answer
Using the World Bank's International Debt Statistics you could calculate the ratio of PPG, bonds (AMT, current US\$) to GNI (current US\$):
PPG, bonds (AMT, current US\$): Public and publicly guaranteed debt from bonds that are either publicly issued or privately placed. Data are in current U.S. dollars. GNI (current US\$): GNI (formerly GNP) is the sum of value added by all resident producers plus any product taxes (less subsidies) not included in the valuation of output plus net receipts of primary income (compensation of employees and property income) from abroad. Data are in current U.S. dollars.
These data go back to 1970's for some countries, but the data only covers 1970-2013. The OECD numbers go back to 2000 but are even easier to work with. You can link right to them. For some rich countries the data go back quite a bit farther (like G7 countries like the UK, France, and the USA). For a large panel of countries. I don't know of sources better than the World Bank and the OECD. You could check the IMF data page but all I found were links back to the World Bank data.
• Thank you. These were the sources I checked first as well, but the data was unfortunately lacking. If there is nothing easier I will indeed use the WB's data and some GDP panel. – Tony Feb 1 '15 at 23:43
|
{}
|
4.5. Fluid¶
The fluid pane is used to select the models and parameters defining the fluid phase. The fluid pane is only accessible if the fluid phase is being solved.
Name The name used to refer to the continuous phase in the GUI. By default, the continuous phase is termed “fluid”, However, it may be renamed for convenience.
4.5.1. Fluid Model Options¶
Solve Momentum Equation By default, all momentum equations are solved. Individual momentum equations may be disabled by toggling the check box.
Solve Species Equations By default, species transport equations are not solved for the fluid phase. If species equations are enabled, species will need to be added to the fluid phase using the fluid species tool.
Enable Scalar Equations By default, no additional scalar transport equations are solved with the fluid phase. Additional scalars may be added by toggling the scalar checkbox and specifying the number of additional scalars to track.
Energy Equations Energy equations cannot be enabled or disabled on a per-phase basis. As such, they are enabled or disabled for all phases in the Model Setup pane.
4.5.2. Fluid Properties¶
Density has units of $$(\frac{kg}{m^3})$$ and may be specified using one of the following approaches.
• Constant:
• A positive (non-zero) number must be provided.
• Ideal gas law
• Requires fluid temperature be specified for the whole domain and all flow boundary conditions.
• Requires a fluid molecular weight.
• User-Defined Function (UDF)
• A custom equation of state must be provided in the usrproperties.f
• A custom solver must be built.
Viscosity has units of $$(Pa \cdot sec)$$ and may be specified using one of the following approaches.
• Constant:
• A positive (non-zero) number must be provided.
• Sutherland’s law
• Requires fluid temperature be specified for the whole domain and all flow boundary conditions.
• User-Defined Function (UDF)
• A custom equation of state must be provided in the usrproperties.f
• A custom solver must be built.
Molecular Weight has units of $$(\frac{kg}{kmol})$$ and may be specified using one of the following approaches.
• Constant:
• A positive (non-zero) number must be provided.
• Mixture
• Requires fluid species definition.
• Requires fluid species mass fractions specification for the whole domain and all flow boundary conditions
Specific Heat has units of $$(\frac{J}{kg \cdot K})$$ and may be specified using one of the following approaches.
• Constant:
• A positive (non-zero) number must be provided.
• Mixture
• Requires fluid species definition.
• Requires fluid species mass fractions specification for the whole domain and all flow boundary conditions
• User-Defined Function (UDF)
• A custom equation of state must be provided in the usrproperties.f
• A custom solver must be built.
Thermal Conductivity has units of $$(\frac{W}{m \cdot K})$$ may be specified using one of the following approaches.
• Constant:
• A non-negative number must be provided.
• Dilute Mixture Approximation
• Requires fluid temperature be specified for the whole domain and all flow boundary conditions.
• User-Defined Function (UDF)
• A custom equation of state must be provided in the usrproperties.f
• A custom solver must be built.
Reference pressure has units of $$(Pa)$$ and is zero by default. A constant value may be specified to shift the simulation pressure prior to scaling.
Pressure scale factor is dimensionless and is one by default. A constant value may be specified to scale the simulation pressure.
$P_{scaled} = \frac{P_{simulation} - P_{reference} }{ P_{scale factor}}$
4.5.3. Fluid Model Species¶
Specie that comprise the fluid phase are summarized in the species overview table. New species are added by clicking the add button, , at the top of the species table, and selecting one or more valid regions (see Fig. 4.3).
|
{}
|
# An Outlook parasite for stealth persistence
- 5 mins
In 2019 I was researching new “stealthy” persistence techniques that were not yet published or commonly known. I was triggered by the techniques that (mis)used plugins for programs on the target’s machine. Particularly interesting targets are browsers, e-mail clients and messaging apps, as they’re typically started after boot.
While reading other’s work, I stumbled upon a blog post from @bohops about VSTOs: The Payload Installer That Probably Defeats Your Application Whitelisting Rules. He shows how to create an “evil VSTO” and install it into Office. His conclusion there however, is that an unprivileged account will get a (“ClickOnce”) pop-up from vstoinstaller.exe asking the user for permission:
Bypassing this “ClickOnce” pop-up would be very valuable from an attacker perspective and so I decided to dig a bit deeper into how exactly vstoinstaller.exe installs a VSTO add-in. I fired up Procmon and filtered on vstoinstaller.exe process while clicking through this pop-up. I started by looking at the registry keys in HKCU, since I assumed that would be a key part of the installation.
These registry keys were particularly interesting and seemed very much related to the installation of the VSTO. I uninstalled the plugin again using vstoinstaller.exe /uninstall which removed those particular registry keys.
Installing the VSTO again using the conventional method triggers the pop-up again, so I was assuming the uninstallation performed a complete roll-back of the VSTO install.
Next I wrote a PowerShell script that set the correct registry keys and values to test if my Outlook add-in would be loaded by Outlook, without any user consent pop-ups. I think the trick of bypassing the “ClickOnce” pop-up eventually boils down to adding the public key of the certificate used to sign the VSTO with, in HKCU:\Software\Microsoft\VSTO\Security\Inclusion\.
<#
.SYNOPSIS
Author: @_vivami
The path of the DLL and manifest files
.EXAMPLE
#>
[CmdletBinding()]
param(
[Parameter(Mandatory=$true)] [string]$PayloadPath
)
$RegistryPaths = @("HKCU:\Software\Microsoft\Office\Outlook\Addins\OutlookExtension"), @("HKCU:\Software\Microsoft\VSTO\SolutionMetadata"), @("HKCU:\Software\Microsoft\VSTO\SolutionMetadata\{FA2052FB-9E23-43C8-A0EF-43BBB710DC61}"), @("HKCU:\Software\Microsoft\VSTO\Security\Inclusion\1e1f0cff-ff7a-406d-bd82-e53809a5e93a")$RegistryPaths | foreach {
if(-Not (Test-Path ($_))) { try { New-Item -Path$($_) -Force | Out-Null } catch { Write-Error "Failed to set entry$($_)." } } }$RegistryKeys =
@("HKCU:\Software\Microsoft\Office\Outlook\Addins\OutlookExtension", "Manifest", "file:///$PayloadPath"), @("HKCU:\Software\Microsoft\VSTO\SolutionMetadata", "(Default)", ""), @("HKCU:\Software\Microsoft\VSTO\SolutionMetadata", "file:///$PayloadPath", "{FA2052FB-9E23-43C8-A0EF-43BBB710DC61}"),
@("HKCU:\Software\Microsoft\VSTO\SolutionMetadata\{FA2052FB-9E23-43C8-A0EF-43BBB710DC61}", "compatibleFrameworks", "<compatibleFrameworks xmlns="urn:schemas-microsoft-com:clickonce.v2">nt<framework targetVersion="4.0" profile="Full" supportedRuntime="4.0.30319" />nt</compatibleFrameworks>"),
@("HKCU:\Software\Microsoft\VSTO\Security\Inclusion\1e1f0cff-ff7a-406d-bd82-e53809a5e93a", "Url", "file:///$PayloadPath"), @("HKCU:\Software\Microsoft\VSTO\Security\Inclusion\1e1f0cff-ff7a-406d-bd82-e53809a5e93a", "PublicKey", "<RSAKeyValue><Modulus>yDCewQWG8XGHpxD57nrwp+EZInIMenUDOXwCFNAyKLzytOjC/H9GeYPnn0PoRSzwvQ5gAfb9goKlN3fUrncFJE8QAOuX+pqhnchgJDi4IkN7TDhatd/o8X8O5v0DBoqBVQF8Tz60DpcH55evKNRPylvD/8EG/YuWVylSwk8v5xU=</Modulus><Exponent>AQAB</Exponent></RSAKeyValue>") foreach ($KeyPair in $RegistryKeys) { New-ItemProperty -Path$KeyPair[0] -Name $KeyPair[1] -Value$KeyPair[2] -PropertyType "String" -Force | Out-Null
}
Write-Host "Done."
}
<#
.SYNOPSIS
Author: @_vivami
.EXAMPLE
#>
$RegistryPaths = @("HKCU:\Software\Microsoft\Office\Outlook\Addins\OutlookExtension"), @("HKCU:\Software\Microsoft\VSTO\SolutionMetadata"), #@("HKCU:\Software\Microsoft\VSTO\SolutionMetadata\{FA2052FB-9E23-43C8-A0EF-43BBB710DC61}"), @("HKCU:\Software\Microsoft\VSTO\Security\Inclusion\1e1f0cff-ff7a-406d-bd82-e53809a5e93a")$RegistryPaths | foreach {
Remove-Item -Path $($_) -Force -Recurse
}
}
Sure enough, it worked! The add-in was installed and loaded by Outlook upon startup, without a pop-up.
Taking a look at Sysinternals’ AutoRuns, we can see that this VSTO add-in is not detected.
### MSRC
I’ve reached out to Microsoft Security Response Center, but since this is not a breach of a security boundary, this bug does not meet the bar for servicing and will not be fixed.
### Detection
To detect this persistence technique, monitor “RegistryEvent Value Set”-events (Sysmon Event ID 13) on the following paths:
HKCU:\Software\Microsoft\Office\Outlook\Addins\
|
{}
|
# Performance Rocketry Intimidator 4
### Help Support The Rocketry Forum:
#### tastychicken
##### Member
Does anyone on here have pictures of a performance rocketry Intimidator 4? I'm looking to build a new rocket and the Intimidator 4 and the Mad dog dual deploy have caught my eye and i'm trying to decide which to get. So any pictures would help. Thanks!
#### Pantherjon
##### Well-Known Member
Well, I presume you want pictures of rockets that people have built? If so, disregard the pictures below..However, there they are the Mad Dog DD and the Intimidator 4..They are essentially the same, minor changes in the fin shape is all I can really detect..And the Intimidator is 75mm vs 54mm for the Mad Dog..
As a personal choice I would go with the Mad Dog DD..It is $30 cheaper, plus I don't have any 75mm hardware- yeah I could adapt down to 54mm..BTW, I am basing off prices listed at Wildman and Liberty Launch Systems Last edited: #### tastychicken ##### Member Well, I presume you want pictures of rockets that people have built? If so, disregard the pictures below..However, there they are the Mad Dog DD and the Intimidator 4..They are essentially the same, minor changes in the fin shape is all I can really detect..And the Intimidator is 75mm vs 54mm for the Mad Dog.. As a personal choice I would go with the Mad Dog DD..It is$30 cheaper, plus I don't have any 75mm hardware- yeah I could adapt down to 54mm..BTW, I am basing off prices listed at Wildman and Liberty Launch Systems
I appreciate the summary, but yes, i have done my research and i know the differences between the two. The one thing i couldn't find was actual owner's pictures which is the reason for this thread.
Thanks again!
#### rcktnut
##### Well-Known Member
Here's some pics. of my Mad Dog DD. I added the Aeropac tailcone retainer. Great flying rocket!!!
#### ECayemberg
##### Well-Known Member
Jeff,
I recognize that photo on the right...
That was a sweet flight that landed so softly near the pad. Beatiful finish on that rocket; nice looking bird!
-Eric-
#### tastychicken
##### Member
Awesome. Thanks for the pictures everyone. What how heavy are your Mad Dog DD/Intimidators?
#### rcktnut
##### Well-Known Member
Awesome. Thanks for the pictures everyone. What how heavy are your Mad Dog DD/Intimidators?
My Mad Dog weighs 12lb 3oz fully loaded w/o motor. I added 1.5 lbs to the nose cone to keep about a 1.5 stability margin for the biggest motor I can put in it. The tailcone retainer shifted the MMT aft 2 1/2 inches also. I believe no extra weight would be needed if built without the tailcone.
#### blackjack2564
##### Crazy Jim's Gone Banana's
TRF Supporter
NO added weight is needed for any commercial motor.
I 've flown mine over 11,000 on L's no added weight. It was designed that way out of the box. Same for the Intimidator, which is the same as a Comp 4 but for the fin shape, which I have flown on many M's no added weight. The Intimidator should come in ataround 13lbs ready, all but motor.
#### tastychicken
##### Member
I appreciate your feedback. I think i will go for the Intimidator because i like the larger fin design better. Thanks!
Last edited:
#### JAllen
##### Well-Known Member
In case you're interested, here is a picture of my PR Intimidator 4. It really is an awesome rocket parts kit.
#### tastychicken
##### Member
awesome, thanks for the picture. Yeah i like the larger fins on the intimidator 4 better. Thanks!
#### WillMarchant
##### Well-Known Member
TRF Supporter
Here's some pics. of my Mad Dog DD. I added the Aeropac tailcone retainer. Great flying rocket!!!
Nice paint and that tailcone looks sweet!
|
{}
|
# Lagrangian of Klein Gordon equation
Consider the following Lagrangian density $$\mathcal{L}(\Phi,\partial_\mu\Phi)=-\frac{1}{2}\partial_\mu\Phi\partial^\mu\Phi-\frac{m\Phi^2}{2}.$$
I want to calculate the equation of motion using the Euler-Lagrange equation to derive the Klein-Gordon equation. The E-L equation states $$\frac{\partial \mathcal{L}}{\partial\Phi}-\partial_\mu\frac{\partial\mathcal{L}}{\partial\,(\partial_\mu\Phi)}=0$$ So, I calculated $$\frac{\partial\mathcal{L}}{\partial\Phi}=-m^2\Phi$$, and for the other term $$\partial_\mu\frac{\partial\mathcal{L}}{\partial(\partial_\mu\Phi)}=-\frac{1}{2}\partial_\mu\bigg(\frac{\partial}{\partial(\partial_\mu\Phi)}\bigg)\underbrace{(\partial_\nu\Phi g^{\nu\alpha}\partial_\alpha\Phi)}_{\text{New free index, \nu}}=-\frac{1}{2}\partial_\mu g^{\nu \alpha}(\delta^{\mu}_\nu\partial_\alpha\Phi+\delta^\mu_\alpha \partial_\nu\Phi=-\frac{1}{2}\partial_\mu(\partial^\mu\Phi+\partial^\mu\Phi)=-\partial_\mu\partial^\mu\Phi.$$
My question is, is it correct that I have to introduce the free index $$\nu$$, or are there easier ways to do this?
• It looks ok. Can you confirm the sign of the kinetic term? What metric are you using? Feb 25 '19 at 19:43
• In your last equation, the last expression follows immediately from the first. Feb 25 '19 at 19:53
• Probably slightly unconventional, but our professor uses $g=\text{diag}(-,+,+,+)$ Feb 25 '19 at 19:54
• @my2cts what do you mean? Feb 25 '19 at 19:55
• I mean that you don't need to use the metric tensor. Feb 25 '19 at 19:58
My question is, is it correct that I have to introduce the free index $$\nu$$ , or are there easier ways to do this?
You didn't introduce a free index $$\nu$$ as it is contracted with another one. A free index means that the index is not summed over. What you did was introduce a $$dummy$$ index to sum over.
The answer to your question, however, is no there is not an easier was to do this. In quantum field theory, this is as easy as it gets. The way to prove the derivative of $$(\partial \Phi)^2$$ is to do precisely what you did by using the definition $$\partial_\mu \Phi \partial_\nu \Phi g^{\mu\nu}$$ and then use the product rule.
The resulting Klein Gordon equation should not depend on what convention you use for the metric, as you can just multiply by a minus sign to get the relative minus signs correct.
The above, however, may give you the impression that equations of motion will not "look" different in different metrics. But that would be wrong. Maxwells equations are a fine example of this.
$$\partial_\mu F^{\mu\nu} = j^\nu \qquad (+---)$$
and
$$\partial_\mu F^{\mu\nu} = -j^\nu \qquad (-+++).$$
The equations look different but they are not. Indeed the "extra" minus sign in the latter equation comes from the fact that $$A_\mu = (-\Phi, \mathbf{A})$$ in the $$(-+++)$$ convention. So the equations are identical. I think that this answer may be of some use.
|
{}
|
Does this norm inequality hold for projections onto the range of a sum of matrices? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T15:15:01Z http://mathoverflow.net/feeds/question/63724 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/63724/does-this-norm-inequality-hold-for-projections-onto-the-range-of-a-sum-of-matrice Does this norm inequality hold for projections onto the range of a sum of matrices? Alex Gittens 2011-05-02T18:59:37Z 2011-05-02T20:47:09Z <p>Although it's simply stated, this is neither a homework problem or trivial (I think, but I'd be happy to be proven wrong :) ).</p> <p>Let $A,B$ be matrices and $x$ be a vector. Is it true that $$\|P_{A+B} x\| \geq \|P_A x\| - \|P_B x\|,$$ where $P_A$ is the projection onto the range space of $A$? (or is it true if you square the norms?)</p> <p>I'm having difficulty even figuring out how to attack this: every attempt I've made falters on the facts that the range space of $A + B$ is not simply related to those of $A$ and $B$ and that the projection is nonlinear. Random instances haven't yet provided counterexamples to the inequality.</p> http://mathoverflow.net/questions/63724/does-this-norm-inequality-hold-for-projections-onto-the-range-of-a-sum-of-matrice/63733#63733 Answer by Kate Juschenko for Does this norm inequality hold for projections onto the range of a sum of matrices? Kate Juschenko 2011-05-02T19:43:53Z 2011-05-02T20:47:09Z <p>by substituting $A$ with $A-B$ and $B$ by $-B$ your condition will be equivalent to the following: <code>$||P_{A+B}x||\leq ||P_Ax||+||P_Bx||.$</code> the last one is not true in general (for non-positive matrices), for example it does not hold for $A=((0,1),(0,0))$, $B=((1,1),(1,1))$ and $x=\frac{1}{\sqrt{2}}(1,-1)$.</p> http://mathoverflow.net/questions/63724/does-this-norm-inequality-hold-for-projections-onto-the-range-of-a-sum-of-matrice/63734#63734 Answer by Michael Renardy for Does this norm inequality hold for projections onto the range of a sum of matrices? Michael Renardy 2011-05-02T19:49:31Z 2011-05-02T19:49:31Z <p>Let $$A=\pmatrix{1&0\cr 0&0}, B=\pmatrix{0&0\cr 1&0}, x=(x_1,x_2).$$ Then $P_Ax=(x_1,0)$, $P_Bx=(0,x_2)$, $P_{A+B}x=((x_1+x_2)/2,(x_1+x_2)/2)$. Thus you are asking if $$|(x_1+x_2)/\sqrt{2}|\ge |x_1|-|x_2|.$$ Clearly, this is false in general. </p>
|
{}
|
# Gyroscopic motion
1. Nov 23, 2005
### Päällikkö
The classical(?) problem:
Suppose you have a ring, where practically all the mass is concentrated on the edges (like the tire of a bicycle). There is, however, a massless rod placed at the central axis.
The ring's given some $\omega _i$ amount of angular speed (about the "logical" axis).
The system is then placed by the end of the rod to lean horizontally on another rod that is placed vertically. The system will now rotate about the second rod too at an angluar speed $\Omega$.
In case you found my description confusing (I sure did), here's a diagram I drew:
http://img473.imageshack.us/my.php?image=img0157us.jpg
Anyways, my question is, how much initial angular speed $\omega _i$ must be given in order for the system to execute the described motion?
If you still think my desciption is confusing, please ask for more precise info .
This is what I tried:
1) I assumed that as the rod's placed it is given some initial $\Omega _i$. For $\Omega _i$ to stay constant, $\Omega _i = \frac{rmg}{I_\omega \omega}$ (this I derived and it should be right). $I_\omega$ is the moment of inertia of the ring about the axis that was first set to motion.
----
2) So, the $\Omega$ solved above will be the final $\Omega _f$ for the case where $\Omega _i$ = 0.
I assumed that energy is conserved (is it?), so:
$$\frac{1}{2} I_\omega \omega _i ^2 = \frac{1}{2} I_\omega \omega _f ^2 + \frac{1}{2} I_\Omega \Omega _f ^2$$
$\omega _f$ and $\Omega _f$ are connected by the equation solved in 1). So plugging that in gives me:
$$I_\omega ^3 \omega _i ^2 \Omega ^2 = I_\omega (rmg)^2 + I_\Omega I_\omega ^2 \Omega ^4$$
If I solve for $\Omega$, I can have real answers only if discriminant $\geq$ 0:
$$\left( -I_\omega ^3 \omega _i ^2 \right) ^2 - 4I_\Omega I_\omega ^3 (rmg)^2 \geq 0$$
$$\Rightarrow \omega _i \geq \left( 4 \frac{I_\Omega}{I_\omega}(rmg)^2 \right) ^{\frac{1}{4}}$$
Is it all wrong?
(If) so, could someone give me a hint to the right direction?
EDIT: Corrected a typo.
Last edited: Nov 23, 2005
2. Nov 24, 2005
### Staff: Mentor
It's been a few decades since I have done a problem like this, but I will give it a try. Perhaps this belongs in the Advanced Physics section, because gyroscopic precession is more of an upper class problem.
I'll be back later after I cut some vegetables and clean up a spill.
3. Nov 24, 2005
### Staff: Mentor
It seems this problem is asking one to find the precession angular frequency as a function of the angular frequency of the rotating ring (and other appropriate variables). The torque generated by the rotating ring causes the gyroscope to rotate, or precess. The acceleration is simply going into the change of direction of the rotational vector of the ring.
If the centerbar mass was considered, it would be manifest in ring system's moment of inertia.
Here is a simple derivation of recession frequency, but it may not be what you want. http://scienceworld.wolfram.com/physics/GyroscopicPrecession.html
4. Nov 24, 2005
### Päällikkö
That's pretty much what I did in 1). It being pretty trivial (meaning that one can find the derivation all over the internet and books) I decided not to include the derivation. I did, however, include the result (which itex-tags make a bit small).
It's part 2) that I'm unsure of.
The problem is just one that I made up, so if you're unsure what I'm after, please let me know.
Thanks for replying, though, I was sure nobody would .
5. Nov 24, 2005
### mezarashi
I have rarely done gyroscopic motion in the past. But from what I understand, there can be multiple precession frequencies, so I'm not quite sure what you're trying to find. There won't be one frequency. Depending on the spin frequency, there will some amount of 'droop' associated while it precesses.
Applying some quick fundamentals:
$$\frac{d\vec{L}}{dt} = \vec{\tau}$$
You can do some successive approximations (which I'm not sure will always be applicable). The torque here is due to gravity.
$$\tau \approx \frac{\Delta L}{\Delta t} , \frac{\Delta L}{L} = \Delta \Phi$$
$$\tau \approx L \frac{\Delta \Phi}{\Delta t}$$
$$\tau \approx L \omega_p$$ while $$L = I\omega_s$$
You'll sorta have a relationship between torque and the precession, spin frequencies.
6. Nov 24, 2005
### Päällikkö
I assumed that there'd be only one precession. My physics book does mention something like what you said (and that's actually what I wanted to examine closer after I get this problem sorted), but leaves it there. I thought I made a valid assumption, or do you disagree?
In the problem I meant to ask what must the initial angular speed be for the system to execute gyroscopic motion.
If the system is not given any initial angular speed in the precession angle's direction, some energy must be used to gain the precession angular speed, right?
I hope you understood what I meant .
7. Nov 24, 2005
### mezarashi
I guess your asking for something like, what is the minimum $$\omega_s$$ so that this precession will still occur?
I would go back to the 'droop' idea. As the angular velocity of the wheel decreases, the wheel will continually droop such that $$\vec{F_g} \times r$$ or in scalar form $$Mgr sin\theta$$ will be the torque $$\tau$$ to maintian the equation of gyration. The smallest possible value of theta would be such that the wheel is about to touch the center pivot. This will probably correspond to your minimum speed you are looking for.
Last edited: Nov 24, 2005
8. Nov 24, 2005
### Päällikkö
Yes.
As in videos on the internet (eg. MIT's OpenCourseWare video lectures), I'd like to place the ring with the axis in a 90 degree angle to the other rod (which is vertically on ground), like in the diagram in the first post. So, $$\theta$$ = 90o.
9. Feb 25, 2006
### panathi
hi everyone...
I've got a question to you. It may seem a bit stupid but I have not been able to figure out WHY the gyroscope precession happens.
In fact, why doesn't the torque of the applied force just make the object fall? Assumpting that this torque does not make the object falling but contributes (almost) exclusively to its rotation around a vertical axle (precession), it is very easy to do the necessary calculus and get the function which makes a relationship between angular precession speed and the angular speed of the ring (check out this link: http://physics.nad.ru/Physics/English/gyro_txt.htm)..
But WHY? WHY does the percession motion happen? I found this webpage that makes it clear for a simplier example: http://www.howstuffworks.com/gyroscope2.htm . However, I can't still explain clearly why this precession motion happens in this kind of examples.
I hope I have been clear enough. I am not an English native speaker and I have some difficulties expressing myself in this language
|
{}
|
## Stream: general
### Topic: Simp bug
#### Chris Hughes (Apr 25 2019 at 14:31):
This gives me excessive memory consumption detected at 'whnf' (potential solution: increase memory consumption threshold) Does anyone else get this error?
import data.polynomial topology.instances.real topology.instances.polynomial
open polynomial
lemma poly_eq_poly (a b c x : ℝ) :
a * x^2 + b * x + c = eval x (C a * X^2 + C b * X + C c) :=
begin
simp only,
end
#### Rob Lewis (Apr 25 2019 at 14:34):
I noticed this working on the cap set proof. It's been on my list to debug properly but I haven't found the time. You can work around it by disabling one of the options to simp (use_axioms iirc, but I'm not confident there).
#### Rob Lewis (Apr 25 2019 at 14:43):
Hmm, it's not use_axioms.
Last updated: May 16 2021 at 05:21 UTC
|
{}
|
# Sh:1127
• Dow, A. S., & Shelah, S. (2018). On the cofinality of the splitting number. Indag. Math. (N.S.), 29(1), 382–395.
• Abstract:
The splitting number \mathfrak s can be singular. The key method is to construct a forcing poset with finite support matrix iterations of ccc posets introduced by Blass and the second author [Ultrafilters with small generating sets, Israel J. Math., 65, (1989)]
• published version (14p)
Bib entry
@article{Sh:1127,
author = {Dow, Alan Stewart and Shelah, Saharon},
title = {{On the cofinality of the splitting number}},
journal = {Indag. Math. (N.S.)},
fjournal = {Koninklijke Nederlandse Akademie van Wetenschappen. Indagationes Mathematicae. New Series},
volume = {29},
number = {1},
year = {2018},
pages = {382--395},
issn = {0019-3577},
mrnumber = {3739621},
mrclass = {03E17 (03E15 03E35)},
doi = {10.1016/j.indag.2017.01.010},
note = {\href{https://arxiv.org/abs/1801.02517}{arXiv: 1801.02517}},
arxiv_number = {1801.02517}
}
|
{}
|
## Wednesday, July 2, 2014
### On Student Debt
The NYT has this by-now popular article asking people to take a chill-pill. The Reality of Student Debt Is Different From the Clichés.
It is based largely based on a Brookings Institution study which essentially claims that the sky is not falling. The 3 main takeaways from that study (emphasis mine):
1. Roughly one-quarter of the increase in student debt since 1989 can be directly attributed to Americans obtaining more education, especially graduate degrees. The average debt levels of borrowers with a graduate degree more than quadrupled, from just under $10,000 to more than$40,000. By comparison, the debt loads of those with only a bachelor’s degree increased by a smaller margin, from $6,000 to$16,000.
2. Increases in the average lifetime incomes of college-educated Americans have more than kept pace with increases in debt loads. Between 1992 and 2010, the average household with student debt saw an increase of about $7,400 in annual income and$18,000 in total debt. In other words, the increase in earnings received over the course of 2.4 years would pay for the increase in debt incurred.
3. The monthly payment burden faced by student loan borrowers has stayed about the same or even lessened over the past two decades. The median borrower has consistently spent three to four percent of their monthly income on student loan payments since 1992, and the mean payment-to-income ratio has fallen significantly, from 15 to 7 percent. The average repayment term for student loans increased over this period, allowing borrowers to shoulder increased debt loads without larger monthly payments.
The NYT tries to shine a light on the real problem:
The vastly bigger problem is the hundreds of thousands of people who emerge from college with a modest amount of debt yet no degree. For them, college is akin to a house that they had to make the down payment on but can’t live in. In a cost-benefit calculation, they get only the cost. And they are far, far more numerous than bachelor’s degree holders with huge debt burdens.
Here is an attempted "takedown" of the report and the NYT article.
And here is a well-reasoned takedown of the takedown.
|
{}
|
Symbolic representation and computation of timed discrete event systems Rapport, 2012
In this paper, we symbolically represent timed discrete event systems (TDES), which can be used to efficiently compute the supervisor in the supervisory control theory context. We model a TDES based on \emph{timed extended finite automata (TEFAs)}: an augmentation of extended finite automata(EFAs) by incorporating discrete time into the model. EFAs are ordinary automata extended with discrete variables, where conditional expressions and update functions can be attached to the transitions. To tackle large problems all computations are conducted symbolically using binary decision diagrams (BDDs). We show how TEFAs can be represented by BDDs. The main feature of this approach is that the BDD-based fixed point computations is not based on $\mathit{tick}$ models that have been commonly used in this area, leading to better performance in many cases. In a case study, we efficiently computed the supervisor of a well-known production cell.
Författare
Chalmers, Signaler och system, System- och reglerteknik, Automation
Zhennan Fei
Chalmers, Signaler och system, System- och reglerteknik, Automation
Knut Åkesson
Chalmers, Signaler och system, System- och reglerteknik, Automation
Bengt Lennartson
Chalmers, Signaler och system, System- och reglerteknik, Automation
Drivkrafter
Hållbar utveckling
Produktion
Ämneskategorier
Reglerteknik
Datavetenskap (datalogi)
|
{}
|
for Journals by Title or ISSN for Articles by Keywords help
Subjects -> EARTH SCIENCES (Total: 568 journals) - EARTH SCIENCES (431 journals) - GEOLOGY (61 journals) - GEOPHYSICS (26 journals) - HYDROLOGY (6 journals) - OCEANOGRAPHY (44 journals) EARTH SCIENCES (431 journals) 1 2 3 4 5 | Last
Acta Geodaetica et Geophysica (1 follower) Acta Geodaetica et Geophysica Hungarica (2 followers) Acta Geophysica (7 followers) Acta Geotechnica (9 followers) Acta Meteorologica Sinica (2 followers) Advances in High Energy Physics (12 followers) Advances In Physics (6 followers) Aeolian Research (1 follower) African Journal of Aquatic Science (8 followers) Algological Studies (2 followers) Alpine Botany (2 followers) AMBIO (13 followers) Anales del Instituto de la Patagonia (2 followers) Andean geology (5 followers) Annales Henri Poincaré (2 followers) Annales UMCS, Geographia, Geologia, Mineralogia et Petrographia (1 follower) Annals of Geophysics (9 followers) Annals of GIS (15 followers) Annals of Glaciology Annual Review of Marine Science (9 followers) Applied Clay Science (2 followers) Applied Geochemistry (6 followers) Applied Geomatics (6 followers) Applied Geophysics (6 followers) Applied Ocean Research (6 followers) Applied Petrochemical Research (3 followers) Applied Remote Sensing Journal (5 followers) Aquatic Conservation Marine and Freshwater Ecosystems (14 followers) Arctic, Antarctic, and Alpine Research (6 followers) Artificial Satellites (11 followers) Asia-Pacific Journal of Atmospheric Sciences (2 followers) Asian Journal of Earth Sciences (15 followers) Atlantic Geology : Journal of the Atlantic Geoscience Society / Atlantic Geology : revue de la Société Géoscientifique de l'Atlantique (2 followers) Atmosphere-Ocean (3 followers) Atmospheric and Climate Sciences (14 followers) Australian Journal of Earth Sciences: An International Geoscience Journal of the Geological Society of Australia (11 followers) Boletim de Ciências Geodésicas Boreas: An International Journal of Quaternary Research (7 followers) Bragantia (2 followers) Bulletin of Earthquake Engineering (8 followers) Bulletin of Geosciences (7 followers) Bulletin of Marine Science (10 followers) Bulletin of the Lebedev Physics Institute (1 follower) Bulletin of the Seismological Society of America (14 followers) Bulletin of Volcanology (10 followers) Canadian Journal of Plant Science (10 followers) Canadian Mineralogist (1 follower) Canadian Water Resources Journal (17 followers) Carbonates and Evaporites (2 followers) CATENA (3 followers) Central European Journal of Geosciences (5 followers) Central European Journal of Physics (2 followers) Chemical Geology (9 followers) Chemie der Erde - Geochemistry (3 followers) Chinese Geographical Science (3 followers) Chinese Journal of Geochemistry (2 followers) Chinese Journal of Oceanology and Limnology (3 followers) Ciencia del suelo Climate and Development (8 followers) Coastal Management (8 followers) Comptes Rendus Geoscience (5 followers) Computational Geosciences (11 followers) Computational Mathematics and Mathematical Physics (2 followers) Computers and Geotechnics (5 followers) Continental Journal of Earth Sciences (1 follower) Continental Shelf Research (6 followers) Contributions to Mineralogy and Petrology (7 followers) Contributions to Plasma Physics (2 followers) Coral Reefs (12 followers) Cretaceous Research (3 followers) Cybergeo : European Journal of Geography (3 followers) Developments in Geotectonics (1 follower) Developments in Quaternary Science (3 followers) Développement durable et territoires (2 followers) Diatom Research Doklady Physics (2 followers) Dynamics of Atmospheres and Oceans (3 followers) E3S Web of Conferences Earth and Planetary Science Letters (78 followers) Earth Interactions (7 followers) Earth Science Research (5 followers) Earth Surface Processes and Landforms (10 followers) Earth System Dynamics (4 followers) Earth System Dynamics Discussions (3 followers) Earth's Future (1 follower) Earthquake Engineering and Engineering Vibration (6 followers) Earthquake Spectra (10 followers) Ecohydrology (11 followers) Ecological Questions (5 followers) Electromagnetics (2 followers) Energy Efficiency (9 followers) Energy Exploration & Exploitation (2 followers) Environmental Earth Sciences (10 followers) Environmental Geology (10 followers) Environmental Geosciences (4 followers) Erwerbs-Obstbau Estuaries and Coasts (1 follower) Estuarine, Coastal and Shelf Science (12 followers) Estudios Geográficos European Journal of Mineralogy (6 followers)
1 2 3 4 5 | Last
Annales Henri Poincaré [4 followers] Follow
Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1424-0637 - ISSN (Online) 1424-0661
• Central Limit Theorems for Open Quantum Random Walks and Quantum Measurement Records
• Abstract: Abstract Open Quantum Random Walks, as developed in Attal et al. (J. Stat. Phys. 147(4):832–852, 2012), are a quantum generalization of Markov chains on finite graphs or on lattices. These random walks are typically quantum in their behavior, step by step, but they seem to show up a rather classical asymptotic behavior, as opposed to the quantum random walks usually considered in quantum information theory (such as the well-known Hadamard random walk). Typically, in the case of open quantum random walks on lattices, their distribution seems to always converge to a Gaussian distribution or a mixture of Gaussian distributions. In the case of nearest neighbors homogeneous open quantum random walks on ${\mathbb{Z}^{\rm d},}$ we prove such a central limit theorem, in the case where only one Gaussian distribution appears in the limit. Through the quantum trajectory point of view on quantum master equations, we transform the problem into studying a certain functional of a Markov chain on ${\mathbb{Z}^{\rm d}}$ times the Banach space of quantum states. The main difficulty is that we know nothing about the invariant measures of this Markov chain, even their existence. Surprisingly enough, we are able to produce a central limit theorem with explicit drift and explicit covariance matrix. The interesting point which appears with our construction and result is that it applies actually to a wider setup: it provides a central limit theorem for the sequence of recordings of the quantum trajectories associated wih any completely positive map. This is what we show and develop as an application of our result. In a second step we are able to extend our Central Limit Theorem to the case of several asymptotic Gaussians, in the case where the operator coefficients of the quantum walk are block diagonal in a common basis.
PubDate: 2014-03-07
• Topology, Rigid Cosymmetries and Linearization Instability in Higher Gauge Theories
• Abstract: Abstract We consider a class of non-linear PDE systems, whose equations possess Noether identities (the equations are redundant), including non-variational systems (not coming from Lagrangian field theories), where Noether identities and infinitesimal gauge transformations need not be in bijection. We also include theories with higher stage Noether identities, known as higher gauge theories (if they are variational). Some of these systems are known to exhibit linearization instabilities: there exist exact background solutions about which a linearized solution is extendable to a family of exact solutions only if some non-linear obstruction functionals vanish. We give a general, geometric classification of a class of these linearization obstructions, which includes as special cases all known ones for relativistic field theories (vacuum Einstein, Yang–Mills, classical N = 1 supergravity, etc.). Our classification shows that obstructions arise due to the simultaneous presence of rigid cosymmetries (generalized Killing condition) and non-trivial de Rham cohomology classes (spacetime topology). The classification relies on a careful analysis of the cohomologies of the on-shell Noether complex (consistent deformations), adjoint Noether complex (rigid cosymmetries) and variational bicomplex (conserved currents). An intermediate result also gives a criterion for identifying non-linearities that do not lead to linearization instabilities.
PubDate: 2014-03-04
• Inverse-Closed Algebras of Integral Operators on Locally Compact Groups
• Abstract: Abstract We construct some inverse-closed algebras of bounded integral operators with operator-valued kernels, acting in spaces of vector-valued functions on locally compact groups. To this end we make use of covariance algebras associated to C*-dynamical systems defined by the C*-algebras of right uniformly continuous functions with respect to the left regular representation.
PubDate: 2014-03-02
• On the Partial Differential Equations of Electrostatic MEMS Devices with Effects of Casimir Force
• Abstract: Abstract We analyze pull-in instability of electrostatically actuated microelectromechanical systems, and we find that as the device size is reduced, the effect of the Casimir force becomes more important. In the miniaturization process there is a minimum size for the device below which the system spontaneously collapses with zero applied voltage. According to the mathematical analysis, we obtain a set U in the plane, such that elements of U correspond to minimal stable solutions of a two-parameter mathematical model. For points on the boundary ${\Upsilon}$ of U, there exists weak solutions to this model, which are called extremal solutions. More refined properties of stable solutions—such as regularity, stability, uniqueness—are also established.
PubDate: 2014-03-02
• Spectral Theory of Semibounded Schrödinger Operators with δ′-Interactions
• Abstract: Abstract We study spectral properties of Hamiltonians H X,β,q with δ′-point interactions on a discrete set ${X = \{x_k\}_{k=1}^\infty \subset (0, +\infty)}$ . Using the form approach, we establish analogs of some classical results on operators H q = −d2/dx 2 + q with locally integrable potentials ${q \in L^1_{\rm loc}[0, +\infty)}$ . In particular, we establish the analogues of the Glazman–Povzner–Wienholtz theorem, the Molchanov discreteness criterion, and the Birman theorem on stability of an essential spectrum. It turns out that in contrast to the case of Hamiltonians with δ-interactions, spectral properties of operators H X,β,q are closely connected with those of ${{\rm H}_{X,q}^N = \oplus_{k}{\rm H}_{q,k}^N}$ , where ${{\rm H}_{q,k}^N}$ is the Neumann realization of −d2/dx 2 + q in L 2(x k-1,x k ).
PubDate: 2014-03-01
• Decorrelation Estimates for a 1D Tight Binding Model in the Localized Regime
• Abstract: Abstract In this article, we prove decorrelation estimates for the eigenvalues of a 1D discrete tight-binding model near two distinct energies in the localized regime. Consequently, for any integer n ≥ 2, the asymptotic independence for local level statistics near n distinct energies is obtained.
PubDate: 2014-03-01
• On the Spectrum of 1D Quantum Ising Quasicrystal
• Abstract: Abstract We consider one-dimensional quantum Ising spin-1/2 chains with two-valued nearest neighbor couplings arranged in a quasi-periodic sequence, with uniform, transverse magnetic field. By employing the Jordan–Wigner transformation of the spin operators to spinless fermions, the energy spectrum can be computed exactly on a finite lattice. By employing the transfer matrix technique and investigating the dynamics of the corresponding trace map, we show that in the thermodynamic limit the energy spectrum is a Cantor set of zero Lebesgue measure. Moreover, we show that local Hausdorff dimension is continuous and non-constant over the spectrum. This forms a rigorous counterpart of numerous numerical studies.
PubDate: 2014-03-01
• Derivation of the Cubic NLS and Gross–Pitaevskii Hierarchy from Manybody Dynamics in d = 3 Based on Spacetime Norms
• Abstract: Abstract We derive the defocusing cubic Gross–Pitaevskii (GP) hierarchy in dimension d = 3, from an N-body Schrödinger equation describing a gas of interacting bosons in the GP scaling, in the limit N → ∞. The main result of this paper is the proof of convergence of the corresponding BBGKY hierarchy to a GP hierarchy in the spaces introduced in our previous work on the well-posedness of the Cauchy problem for GP hierarchies (Chen and Pavlović in Discr Contin Dyn Syst 27(2):715–739, 2010; http://arxiv.org/abs/0906.2984; Proc Am Math Soc 141:279–293, 2013), which are inspired by the solution spaces based on space-time norms introduced by Klainerman and Machedon (Comm Math Phys 279(1):169–185, 2008). We note that in d = 3, this has been a well-known open problem in the field. While our results do not assume factorization of the solutions, consideration of factorized solutions yields a new derivation of the cubic, defocusing nonlinear Schrödinger equation (NLS) in d = 3.
PubDate: 2014-03-01
• Wilson Loops in 5d ${\mathcal{N} = 1}$ SCFTs and AdS/CFT
• Abstract: Abstract We consider ${\frac{1}{2}}$ -BPS circular Wilson loops in a class of 5d superconformal field theories on S 5. The large N limit of the vacuum expectation values of Wilson loops are computed both by localization in the field theory and by evaluating the fundamental string and D4-brane actions in the dual massive IIA supergravity background. We find agreement in the leading large N limit for a rather general class of representations, including fundamental, anti-symmetric and symmetric representations. For single-node theories the match is straightforward, while for quiver theories, the Wilson loop can be in different representations for each node. We highlight the two special cases when the Wilson loop is in either in all symmetric or all anti-symmetric representations. In the anti-symmetric case, we find that the vacuum expectation value factorizes into distinct contributions from each quiver node. In the dual supergravity description, this corresponds to probe D4-branes wrapping internal S 3 cycles. The story is more complicated in the symmetric case and the vacuum expectation value does not exhibit factorization.
PubDate: 2014-03-01
• Null Structure in a System of Quadratic Derivative Nonlinear Schrödinger Equations
• Abstract: Abstract We consider the initial value problem for a three-component system of quadratic derivative nonlinear Schrödinger equations in two space dimensions with the masses satisfying the resonance relation. We present a structural condition on the nonlinearity under which small data global existence holds. It is also shown that the solution is asymptotically free. Our proof is based on the commuting vector field method combined with smoothing effects.
PubDate: 2014-02-04
• Random-Weighted Sobolev Inequalities on ${\mathbb{R}^d }$ and Application to Hermite Functions
• Abstract: Abstract We extend a randomization method, introduced by Shiffman–Zelditch and developed by Burq–Lebeau on compact manifolds for the Laplace operator, to the case of ${\mathbb{R}^d}$ with the harmonic oscillator. We construct measures, thanks to probability laws which satisfies the concentration of measure property, on the support of which we prove optimal-weighted Sobolev estimates on ${\mathbb{R}^d}$ . This construction relies on accurate estimates on the spectral function in a non-compact configuration space. As an application, we show that there exists a basis of Hermite functions with good decay properties in ${L^{\infty}(\mathbb{R}^{d})}$ , when d ≥ 2.
PubDate: 2014-02-04
• Remarks on Local Symmetry Invariance in Perturbative Algebraic Quantum Field Theory
• Abstract: Abstract We investigate various aspects of invariance under local symmetries in the framework of perturbative algebraic quantum field theory (pAQFT). Our main result is the proof that the quantum Batalin–Vilkovisky operator, on-shell, can be written as the commutator with the interacting BRST charge. Up to now, this was proven only for a certain class of fields in quantum electrodynamics and in Yang–Mills theory. Our result is more general and it holds in a wide class of theories with local symmetries, including general relativity and the bosonic string. We also comment on other issues related to local gauge invariance and, using the language of homological algebra, we compare different approaches to quantization of gauge theories in the pAQFT framework.
PubDate: 2014-02-02
• Infraparticle Problem, Asymptotic Fields and Haag–Ruelle Theory
• Abstract: Abstract In this article, we want to argue that an appropriate generalization of the Wigner concepts may lead to an asymptotic particle with well-defined mass, although no mass hyperboloid in the energy–momentum spectrum exists.
PubDate: 2014-02-01
• Non-Equilibrium States of a Photon Cavity Pumped by an Atomic Beam
• Abstract: Abstract We consider a beam of two-level randomly excited atoms that pass one-by-one through a one-mode cavity. We show that in the case of an ideal cavity, i.e. no leaking of photons from the cavity, the pumping by the beam leads to an unlimited increase in the photon number in the cavity. We derive an expression for the mean photon number for all times. Taking into account leaking of the cavity, we prove that the mean photon number in the cavity stabilizes in time. The limiting state of the cavity in this case exists and it is independent of the initial state. We calculate the characteristic functional of this non-quasi-free non-equilibrium state. We also calculate the total energy variation in both the ideal and the open cavities as well as the entropy production in the ideal cavity.
PubDate: 2014-02-01
• Symmetries of Quantum Lax Equations for the Painlevé Equations
• Abstract: Abstract Based on the fact that the Painlevé equations can be written as Hamiltonian systems with affine Weyl group symmetries, a canonical quantization of the Painlevé equations preserving such symmetries has been studied recently. On the other hand, since the Painlevé equations can also be described as isomonodromic deformations of certain second-order linear differential equations, a quantization of such Lax formalism is also a natural problem. In this paper, we introduce a canonical quantization of Lax equations for the Painlevé equations and study their symmetries. We also show that our quantum Lax equations are derived from Virasoro conformal field theory.
PubDate: 2014-02-01
• Isoperimetric Inequalities for a Wedge-Like Membrane
• Abstract: Abstract For a wedge-like membrane, Payne and Weinberger proved in 1960 an isoperimetric inequality for the fundamental eigenvalue which in some cases improves the classical isoperimetric inequality of Faber–Krahn. In this work, we introduce “relative torsional rigidity” for this type of membrane and prove new isoperimetric inequalities in the spirit of Saint-Venant, Pólya–Szegő, Payne, Payne–Rayner, Chiti, and Talenti, which link the eigenvalue problem with the boundary value problem in a fundamental way.
PubDate: 2014-02-01
• Complete Asymptotic Expansion of the Integrated Density of States of Multidimensional Almost-Periodic Pseudo-Differential Operators
• Abstract: Abstract We obtain a complete asymptotic expansion of the integrated density of states of operators of the form ${H = (-\Delta)^w+ B}$ in ${\mathbb{R}^d}$ . Here w > 0 and B belong to a wide class of almost-periodic self-adjoint pseudo-differential operators of order less than 2w. In particular, we obtain such an expansion for magnetic Schrödinger operators with either smooth periodic or generic almost-periodic coefficients.
PubDate: 2014-02-01
• Quantum Ergodicity for a Point Scatterer on the Three-Dimensional Torus
• Abstract: Abstract Consider a point scatterer (the Laplacian perturbed by a delta-potential) on the standard three-dimensional flat torus. Together with the eigenfunctions of the Laplacian which vanish at the point, this operator has a set of new, perturbed eigenfunctions. In a recent paper, the author was able to show that all of the perturbed eigenfunctions are uniformly distributed in configuration space. In this paper we prove that almost all of these eigenfunctions are uniformly distributed in phase space, i.e. we prove quantum ergodicity for the subspace of the perturbed eigenfunctions. An analogue result for a point scatterer on the two-dimensional torus was recently proved by Kurlberg and Ueberschär.
PubDate: 2014-02-01
• Non-Existence of Toroidal Cohomogeneity-1 Near-Horizon Geometries
• Abstract: Abstract We prove that D ≥ 5 dimensional stationary, non-static near-horizon geometries with (D−3) commuting rotational symmetries subject to the vacuum Einstein equations including a cosmological constant cannot have toroidal horizon topology. In D = 4 dimensions, the same result is obtained under the assumption of a non-negative cosmological constant.
PubDate: 2014-02-01
• Erratum to: Mather Measures Associated with a Class of Bloch Wave Functions
• PubDate: 2013-12-17
JournalTOCs
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
Email: journaltocs@hw.ac.uk
Tel: +00 44 (0)131 4513762
Fax: +00 44 (0)131 4513327
|
{}
|
# Puzzling Regression Anatomy
01 Jul 2020
Consider a regression model with the following causal structure:
The variable x1 affects y directly and also indirectly via x2. The following R code implements the model and simulates a corresponding data set.
set.seed(1)
n = 10000
beta1 = 1; beta2=1
x1 = rnorm(n,0,1)
x2 = x1+rnorm(n,0,1)
y = beta1*x1 + beta2*x2 + rnorm(n,0,1)
Assume we want to consistently estimate the direct linear effect beta1 from x1 on y. To do so, we can simply estimate a multiple linear regression where we add x2 as a control variable:
coef(lm(y~x1+x2))
## (Intercept) x1 x2
## 0.007553765 0.998331323 1.000934100
But what does it intuitively mean to add x2 as control variable? The Frisch-Waugh-Lovell Theorem implies that we get the same estimator for beta1 as in the multiple regression above by the following procedure:
# y.tilde is residual of regression
# y on x2
y.tilde = resid(lm(y~x2))
# x1.tilde is residual of regression
# x1 on x2
x1.tilde = resid(lm(x1~x2))
# Regression y.tilde on x1.tilde
# we get the same estimate for beta1
# as in the multiple regression with x1 and x2
coef(lm(y.tilde ~ x1.tilde))
## (Intercept) x1.tilde
## -5.104062e-17 9.983313e-01
Hence, controlling for x2 means that we essentially regress the residual variations of y and x1 that cannot be linearly explained by x2 on each other. So far this seems intuitive.
The interesting thing is that one gets the same estimate for beta1 also with one of the following two regressions below (but only the regression above also yields correct standard errors):
# Approach A
lm(y.tilde ~ x1)
# Approach B
lm(y ~ x1.tilde)
Approach A regresses the residual variation of y that cannot be linearly predicted by x2 on x1. Approach B regresses y on the residual variation of x1 that cannot be linearly predicted by x2.
Only one approach yields a consistent estimate of beta1. Make a guess which one…
Let’s check:
# A: Inconsistent
coef(lm(y.tilde ~ x1))[2]
## x1
## 0.4860465
# B: Consistent
coef(lm(y ~ x1.tilde))[2]
## x1.tilde
## 0.9983313
So only approach B works. Angrist and Pischke (2009) refer to it as regression anatomy. For me that result was a bit puzzling for a long time because my intuitive interpretation of what it means to control for x2 was more in line with approach A. I first want to shed light on that intuition and explain why approach A does not work. Afterward I want to give some intuition for the working approach B.
## An intuition for control variables and why approach A fails
I have different intuitions what controlling for x2 means in the linear regression:
y = beta0 + beta1*x1 + beta2*x2 + eps
One of my intuitions is the following:
“By controlling for x2, we essentially subtract the variation that can be linearly explained by x2 from y, i.e. up to an estimation error we subtract beta2*x2.”
This interpretation suggests that approach A should work, but that approach fails to get a consistent estimate for beta1. So is the intuition above wrong? Not completely, but the qualification “up to an estimation error” causes trouble for approach A. Consider the following code.
# Modified approach A
y.tilde2 = y - beta2*x2
coef(lm(y.tilde2 ~x1))[2]
## x1
## 0.9992699
It is a modified version of approach A. It computes the residual variation y.tilde2 by directly subtracting beta2*x2 from y. Now we get a consistent estimator of beta1 when regressing y.tilde2 on x1.
But approach A differs because we subtract beta2.hat*x2 from y where beta2.hat is estimated in the first stage regression:
# Same result as original approach A
beta2.hat = coef(lm(y~x2))[2]
beta2.hat # inconsistent estimate of beta2
## x2
## 1.510801
y.tilde = y-beta2.hat*x2
coef(lm(y.tilde ~x1))[2] # inconsistent estimate of beta1
## x1
## 0.4860465
The problem with approach A is that we don’t estimate beta2.hat consistently in the regression of y on x2. Instead, since x1 and x2 are correlated, beta2.hat also captures some of the direct effect of x1 on y. This means in y.tilde we have already removed some of the effect from x1 on y that we want to estimate. Therefore approach A yields an estimator for beta1 that is biased towards 0.
Remark: In the original computation of approach A, we also subtract the estimated constant from the initial regression when computing y.tilde, but that has no effect on the slope coefficient in the second stage regression.
Interestingly, in some empirical papers an approach similar to approach A is performed, i.e. one first computes residuals of y from a first regression and then regresses those residuals on another set of explanatory variables. But the computation above shows that one should really be careful with this approach, since it only works if the first regression yields consistent estimates.
Let us consider an example where such an approach would work. Consider the following modified model:
We now have an additional variable z that affects x2 but is uncorrelated with x1.
z = rnorm(n,0,1)
x2 = x1+z+rnorm(n,0,1)
y = beta1*x1 + beta2*x2 + rnorm(n,0,1)
We now conduct a variation of approach A where y.tilde3 are the residuals of an instrumental variable regression of y on x2 using z as instrument:
library(AER)
reg1 = ivreg(y~x2|z)
coef(reg1)[2] # consistent beta2.hat
## x2
## 1.006464
y.tilde3 = resid(reg1)
coef(lm(y.tilde3 ~ x1))[2] # consistent beta1.hat
## x1
## 0.9756005
We now see that regressing y.tilde3 on x1 yields a consistent estimator of beta1.
### Why does approach B work
Let us now discuss why approach B works. Given our causal structure I find it more intuitive to first discuss why a similar approach works to consistently estimate beta2.
# x2.tilde is residual from regression
# of x2 on x1
x2.tilde = resid(lm(x2~x1))
# consistent estimate of beta2
coef(lm(y ~ x2.tilde))[2]
## x2.tilde
## 0.996786
Here I have the following intuition why it works. Intuitively, to consistently estimate the causal effect of x2 on y we need to distill variation of x2 that is uncorrelated with x1. If we regress x2 on x1, the residuals x2.tilde of this regression are by construction uncorrelated with x1. They describe the variation of x2 that cannot be linearly predicted by x1. That is exactly the variation of x2 needed to consistently estimate beta2.
The equivalent procedure also works to estimate beta1 consistently:
x1.tilde = resid(lm(x1~x2))
coef(lm(y ~ x1.tilde))[2] # consistent
## x1.tilde
## 0.98519
So even though x2 does not influence x1 we can similarly distill in x1.tilde the relevant variation in x1 that is uncorrelated with x2. For the regression anatomy it is irrelevant which causal direction has generated the correlation between x1 and x2.
### Final remarks
I find it amazing that over many years I still often learn new intuitions for basic econometric concepts like multiple linear regression. Currently, I think introducing multiple regression via the Frisch-Waugh-Lovell theorem and the regression anatomy can be much more helpful to build intuition in an applied empirical course than covering the matrix algebra. (Of course, it is a different story if you want to prove econometric theorems.) For an example of such a course, you can check out the open online material (videos, quizzes, interactive R exercises) of my course Market Analysis with Econometrics and Machine Learning.
## References
Angrist, Joshua D., and Jörn-Steffen Pischke. 2009. Mostly Harmless Econometrics: An Empiricist’s Companion.
Published on 01 Jul 2020
|
{}
|
Page:Wittengenstein - Tractatus Logico-Philosophicus, 1922.djvu/147
TRACTATUS LOGICO-PHILOSOPHICUS
ments of the wrong kind, and therefore it survives the wrong arguments no better and no worse than the senseless hypothesis attached for this purpose.)
5.5352 Similarly it was proposed to express "There are no things" by "$~ (\exists x).x=x$" But even if this were a proposition — would it not be true if indeed "There were things", but these were not identical with themselves?
5.54 In the general propositional form, propositions occur in a proposition only as bases of the truth-operations.
5.541 At first sight it appears as if there were also a different way in which one proposition could occur in another.
Especially in certain propositional forms of psychology, like "A thinks, that $p$ is the case", or "A thinks $p$", etc.
Here it appears superficially as if the proposition $p$ stood to the object A in a kind of relation.
(And in modern epistemology (Russell, Moore, etc.) those propositions have been conceived in this way.)
5.542 But it is clear that "A believes that $p$", "A thinks $p$", "A says $p$", are of the form "'$p$' says $p$": and here we have no co-ordination of a fact and an object, but a co-ordination of facts by means of a co-ordination of their objects.
5.5421 This shows that there is no such thing as the soul — the subject, etc. — as it is conceived in contemporary superficial psychology.
A composite soul would not be a soul any longer.
5.5422 The correct explanation of the form of the proposition "$p$A judges $p$" must show that it is impossible to judge a nonsense. (Russell's theory does not satisfy this condition.)
5.5423 To perceive a complex means to perceive that
143
|
{}
|
Question
# How many cyclic isomers of $$C_5H_{10}$$ are possible?
A
4
B
3
C
2
D
5
Solution
## The correct option is D $$5$$$$5$$ isomers are possible. $$C_5H_{10}\left( C_nH_{2n}\right).$$ Molecules having the $$C_nH_{2n}$$ formula are most likely to be cyclic alkanes. The five isomers are:( Diagram )Chemistry
Suggest Corrections
1
Similar questions
View More
People also searched for
View More
|
{}
|
Apriori Algorithm
An Apriori Algorithm is an iterative association rule learning algorithm that computes the frequent itemsets where iteration $i$ computes all frequent i-itemsets (itemsets with $i$ elements) and each iteration has a candidate generation step, candidate counting step and candidate selection step.
References
2009
• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Apriori_algorithm
• In computer science and data mining, Apriori is a classic algorithm for learning association rules. Apriori is designed to operate on databases containing transactions (for example, collections of items bought by customers, or details of a website frequentation). Other algorithms are designed for finding association rules in data having no transactions (Winepi and Minepi), or having no timestamps (DNA sequencing).
• As is common in association rule mining, given a set of itemsets (for instance, sets of retail transactions, each listing individual items purchased), the algorithm attempts to find subsets which are common to at least a minimum number C of the itemsets. Apriori uses a "bottom up" approach, where frequent subsets are extended one item at a time (a step known as candidate generation), and groups of candidates are tested against the data. The algorithm terminates when no further successful extensions are found.
• Apriori uses breadth-first search and a tree structure to count candidate item sets efficiently. It generates candidate item sets of length $k$ from item sets of length $k-1$. Then it prunes the candidates which have an infrequent sub pattern. According to the downward closure lemma, the candidate set contains all frequent $k$-length item sets. After that, it scans the transaction database to determine frequent item sets among the candidates.
• Apriori, while historically significant, suffers from a number of inefficiencies or trade-offs, which have spawned other algorithms. Candidate generation generates large numbers of subsets (the algorithm attempts to load up the candidate set with as many as possible before each scan). Bottom-up subset exploration (essentially a breadth-first traversal of the subset lattice) finds any maximal subset S only after all $2^{|S|}-1$ of its proper subsets.
• (Wu & Kumar, 2009) ⇒ Xindong Wu, and Vipin Kumar, editors. (2009). “The Top Ten Algorithms in Data Mining." Chapman & Hall. ISBN:1420089641
1994
• Rakesh Agrawal, and Rakesh Srikant. (1994). "Fast Algorithms for Mining Association Rules." In: Proceedings of VLDB 1994. ISBN 1-55860-153-8.
• Heikki Mannila, H. Toivonen, and A. I. Verkamo. (1994). "Efficient Algorithms for Discovering Association Rules." In: AAAI Workshop on Knowledge Discovery in Databases (SIGKDD).
|
{}
|
Quantum Computation in Noiseless Subsystems with Fast Non-Abelian Holonomies
# Quantum Computation in Noiseless Subsystems with Fast Non-Abelian Holonomies
## Abstract
Quantum information processing requires a high degree of isolation from the detrimental effects of the environment as well as an extremely precise level of control on the way quantum dynamics unfolds in the information-processing system. In this paper, we show how these two goals can be ideally achieved by hybridizing the concepts of noiseless subsystems and of holonomic quantum computation. An all-geometric universal computation scheme based on non-adiabatic and non-Abelian quantum holonomies embedded in a four-qubit noiseless subsystem for general collective decoherence is proposed. The implementation details of this synergistic scheme along with the analysis of its stability against symmetry-breaking imperfections are presented.
## I Introduction
Implementation of quantum information processing (QIP) poses daunting challenges. In the first place, for most of the QIP protocols, quantum coherence has to be maintained throughout the whole computational process in spite of the decoherence induced by the unavoidable coupling with environmental degrees of freedom. Secondly, one has to achieve an unprecedented level of control to enact quantum gates within the required high accuracy.
To the aim of accomplishing these, somewhat contradictory, tasks several theoretical schemes have been devised since the early days of QIP. Broadly speaking, all the information-stabilizing strategies developed to date fall in three categories: active techniques like quantum error correcting codes (1), symmetry-aided passive ones like decoherence-free subspaces and subsystems (2); (3); (4), and geometrical (5); (6); (7) and topological ones (8).
Geometric QIP exploits different types of quantum holonomies, e.g., Berry phases, to implement quantum gates. Following the first non-Abelian (5) and Abelian (6) adiabatic proposals, many others have been considered, see, e.g., Refs. (7); (9); (10); (11); (12). The motivating idea is that the geometric nature of the proposed quantum gates endows them with some degree of inherent robustness against control imprecisions as well as against environment-induced decoherence (13). One of the drawbacks of the original holonomic quantum computation (HQC) (5) is its relative slowness due to the adiabaticity constraint. This potential limitation can be circumvented by resorting to non-adiabatic Abelian (14); (15) and non-Abelian (16); (17) quantum holonomies.
The idea of noiseless subsystem (NS) was first introduced in Ref. (3) and experimentally demonstrated in Ref. (18). NSs are a natural generalization of the concept of noiseless quantum code or decoherence-free subspace (DFS) (2) and are effective when the decohering interactions possess some non-trivial algebra of symmetries. On general theoretical grounds, NSs have been argued to provide the unified algebraic structure underlying all the known quantum-information protection schemes (4) including topological quantum computation (19).
The goal of this paper is to merge synergistically ideas from geometric QIP and NSs in order to take advantage of the appealing features of both. More specifically, we will hybridize non-adiabatic HQC (16), with the powerful theory of NSs (3); (4). The possibility of achieving robust quantum control on NSs by non-Abelian quantum holonomies was first envisioned in Refs. (20); (21), universal HQC schemes embedded in DFSs and NSs were proposed in Refs. (9); (17) and (for a strongly dissipative case) in Ref. (22).
In this paper, we extend significantly the results of Ref. (17) by showing how a universal non-Abelian and nonadiabatic holonomic processor can be embedded within a NS for general collective decoherence. In this way a universal computational scheme protected against general collective decoherence and featuring at the same time the robustness of HQC against imprecisions in gate control can be ideally achieved.
## Ii Noiseless Subsystem
We start by briefly recalling the basic notions concerning NSs. Let be the Hilbert space of a quantum system coupled to its environment through a set of “error” operators (23). The key object is provided by the interaction algebra , i.e., the -algebra (24) generated by the error operators. The state space of the system decomposes into the different -dimensional irreducible representations (irreps) of (labeled by and with multiplicity ) as . The corresponding orthogonal decomposition of is given by
A≅⊕J1nJ⊗MdJ, (1)
where denotes the full matrix algebra of complex matrices (24). When , one recovers the concept of DFS (2). The interaction algebra acts irreducibly on the factors of whereas Eq. (1) shows that the error algebra elements, responsible for decoherence, have a trivial action on the factors. It follows that quantum information can be protected by encoding in these virtual subsystems (20) that are then termed noiseless subsystems (NS) (3). In order to perform manipulations of the NS-encoded information, one has to resort to a non-trivial set of operations that belong to the commutant algebra . This crucial fact follows from the dual irreps decomposition for which one sees that of has irreducible action on the NSs and trivial one on the factors, now playing the role of multiplicity spaces. These constructions are useful if at least one of the ’s is larger than or equal to two, which in turn gives a lower bound on the dimension of the commutant . In other words, the existence of a NS encoding relies on the existence of a sufficiently large number of symmetries of the interaction algebra, i.e., of the noise.
The prototypical symmetric noise is provided by collective decoherence (2) whose experimental relevance has been demonstrated in Refs. (18); (25); (26). This is also the model that will be considered in this paper. In this collective case the interaction algebra is given by the algebra of totally symmetric operators on the state space of qubits, i.e., and its commutant is the -algebra generated by permutations acting on according to the natural representation, i.e., . In the following, we show how to enact a universal set of operators in using non-adiabatic quantum holonomies only.
## Iii Non-adiabatic Holonomic Quantum Computation
Non-adiabatic HQC, proposed in Ref. (16) and experimentally implemented in Ref. (27), is based on the concept of non-adiabatic non-Abelian geometric phases (28). The key idea is to implement a suitably designed Hamiltonian that induces cyclic evolution of a quantum computational system encoded in a subspace in such a way that all dynamical phases vanish. The primitive structure is of type, where an excited state is coupled by a pair of simultaneous laser pulses to ground state levels according to ( from now on)
H(t)=Ω(t)(ω0|e⟩⟨g0|+ω1|e⟩⟨g1|+h.c.). (2)
Here, is the Rabi frequency and are complex-valued time-independent driving frequencies satisfying . The generic Hamiltonian describes transitions between energy levels induced by oscillating laser fields in the rotating wave approximation and can be implemented in a wide range of different physical systems.
The subspace spanned by , , undergoes a cyclic evolution if the Rabi frequency satisfies . The resulting time evolution operator , projected onto the computational subspace , defines the traceless Hermitian gate , where with , and are the standard Pauli operators acting on . An arbitrary SU(2) can be realized by sequentially applying two such gates with different . The evolution is purely geometric since , , vanish for . Thus, is fully determined by the path of in the space of all two-dimensional subspaces of the three-dimensional Hilbert space, i.e., in the complex-valued Grassmannian . Together with an entangling holonomic two-qubit gate, constitutes a universal all-geometric set of quantum gates (29).
## Iv Quantum holonomy in noiseless subsystems
The collective decoherence on a quantum system consisting of physical qubits is characterized by the spin- error operators , . For a fixed total spin , the dimension of the noiseful (NF) part is . By using angular momentum addition rules, one can prove that
nJ=(2J+1)N!(N/2+1+J)!(N/2−J)!. (3)
This , which is the dimension of the NS part, provides the possibility of performing HQC.
Quantum holonomy appears when the subspace returns to the original one after a non-trivial cyclic transformation. The NS spans the total space, which is the total Hilbert space of a HQC. In general, the NS should be larger than the computational space in order to admit non-trivial holonomies. A subspace of NS emerges as and the effective Hamiltonian of NS acts as the Hamiltonian that generates the non-trivial loop relating to the unitary transformation. Since NS theory guarantees that the states in are never evolved out of the NS, the subspace of NS can return to the original one and that assures that HQC can be conducted.
### iv.1 One-qubit gate
Non-adiabatic one-qubit holonomic gate can be implemented in a NS provided there exists a for which . Four physical qubits, which contains a subspace, provides the smallest possible realization of such a gate. Here, we demonstrate how noiseless holonomic one-qubit gates can be implemented in this subspace of the four-qubit code.
First, note that the ’s act on the subspace in the following way,
Eα=INS⊗Sα, α=±,z, (4)
where are spin representation of the angular momentum operators. An important observation here is that the inherent symmetry in the action of the decoherence operators on the basis states ’s affects only the second part of the basis and leaves the first part unchanged (see the Appendix for more details on the four-qubit code). Moreover, the basis changed by the error operators stays within ’s. Thus, the information being stored in this subspace depends only on the first index – it is therefore not spoilt by the interaction between the system and the environment.
To perform holonomic one-qubit gates with the four-qubit code, a set of operators is needed to achieve the appropriate transitions so that the computation stays within the subspace. To this end, the operators that we seek should commute with the ’s. Let us consider the permutation operator of qubits and such that for . Here, is the identity and are the Pauli operators acting on this qubit pair. It is straightforward to check that . Three- and four-body permutation operators emerge as a product of two-body ones. Thus, if the Hamiltonian is constructed using a combination of the permutation operators, it will not destroy the subspace. Explicitly, we may take the Hamiltonian that generates the holonomic one-qubit gates to be
H(1)(t) = Ω(t)[J1√3(P23−P13)+iJ2√3(P23P13−P13P23)+J42√6(P13−P23−3P14+3P24)] (5) = Ω(t)[(J1−iJ2)|3⟩⟨1|+J4|3⟩⟨2|+h.c.]⊗INF,
where the first tensor factor corresponding to the NS is identical to the Hamiltonian in Eq. (2) by identifying , , and ; is the identity operator acting on the noiseful subsystem. The Hamiltonian vanishes on the noiseless qubit subspace , which guarantees the geometric nature of the evolution. By putting and defining the unit vector , a traceless one-qubit holonomic gate
U(1)(C)=n⋅σ⊗INS (6)
acting non-trivially on the two-dimensional subspace of the NS can thus be implemented by choosing . By combining two such gates, an arbitrary SU(2) operation acting on the noiseless qubit subspace can be realized.
### iv.2 Two-qubit gate
It is well-known that universal quantum computation can be achieved as long as all one-qubit gates and a single non-trivial two-qubit (entangling) gate is possible (29). Since all single qubit gates are possible, it remains to demonstrate that we could construct a non-trivial two-qubit gate.
To guarantee the holonomic scheme to be scalable, we encode each qubit in a two-dimensional subspace of a three-level NS by using four physical qubits. In this scheme, a two-qubit gate requires an eight-qubit code where two noiseless qubits are represented by two sets of four physical qubits. By choosing an appropriate Hamiltonian for the eight physical qubits, we demonstrate a holonomic CNOT gate that can entangle these noiseless qubits.
Consider the eight-qubit Hamiltonian expressed in terms of permutation operators as
H(2)(t) = Ω(t)12(P13−P23−3P14+3P24)L (7) ⊗[P23−P13−12√2(P13−P23−3P14+3P24)]L′.
By re-expressing the two factors in terms of the NS+NF basis for each four-qubit set, we obtain
H(2)(t) = Ω(t)(H0+H1)⊗INF, (8)
where
H0 = Extra open brace or missing close brace H1 = Extra open brace or missing close brace (9)
and is now the identity on the nine-dimensional noiseful subsystem of the eight qubits. The two time-independent operators and vanish on the computational two-qubit subspace of the NS, which assures the geometric nature of the evolution. Furthermore, and commute, which implies that
e−i∫τ0H(2)(t′)dt′=e−iπH0e−iπH1⊗INF, (10)
by choosing . The second factor acts trivially on and can therefore be ignored. The holonomic gate is the projection of the first factor onto and reads
U(2)(C) = (|11⟩⟨11|+|12⟩⟨12| (11) +|21⟩⟨22|+|22⟩⟨21|)⊗I%NF.
We see that is a CNOT gate acting on which completes the universal set of non-adiabatic holonomic gates in NSs.
## V Robustness of gates
Our NS encoding allows for perfect protection in the ideal collective decoherence case where the system-bath interactions are fully invariant under arbitrary permutations of the physical qubits. However, in realistic situations symmetry-breaking interactions will be unavoidably present and spoil the ideal behavior. In order to investigate the robustness of our scheme against such unwanted interactions we introduce a simple decoherence model with a single parameter that controls the degree of symmetry breaking. The noise Lindblad operators are given by: ; clearly when one recovers the permutational invariant collective decoherence. Within the usual Born-Markov approximation the system evolution is dictated by the Lindblad master equation
˙ρ(t) = −i[Hs(t),ρ]+Γ(E′zρE′z−12{E′zE′z,ρ}) (12) +γ(¯n+1)(E′−ρE′+−12{E′+E′−,ρ}) +γ¯n(E′+ρE′−−12{E′−E′+,ρ}),
where is the temperature-dependent average number of quanta in the environment ( at zero temperature), and are the dephasing rate and dissipation rate, respectively. Here, is the qubit system Hamiltonian, which is generated by linear combination of the permutation operators as described above. A square pulse with magnitude and duration is used.
As a figure of merit to quantify the robustness of our logical gates, we adopt the gate fidelity defined as the Bures-Uhlmann fidelity averaged over initial conditions. Here, is the NS state obtained by the ideal holonomic gate, i.e., the actual one in presence of collective decoherence only, and is the corresponding faulty one obtained by solving Eq. (12) and tracing over the noiseful degrees of freedom.
We solved numerically Eq. (12) and examined the gate fidelity as a function of for a one-qubit holonomic gate. In Fig. 1 it is shown that gate fidelity, both at zero temperature (solid line; ) and non-zero temperature (dashed line; ), decreases with increasing as expected. However, the inset in Fig. 1 also shows that in the physically relevant regime of small , the gate fidelity behaves as , where . This demonstrates that holonomic manipulations of the NS have some degree of resilience against slight violations of the collective symmetry assumption. We would like to stress that Eq. (12) is just a way to describe the system-bath coupling that allows one to interpolate, in a simple phenomenological fashion, between the fully permutational symmetric ( and increasingly non-symmetric and unprotected regimes (large ). However, we expect the conclusions drawn from our simulations to be generic for mild violations of permutational symmetry. Namely, gate robustness should be independent of the details of the specific decoherence model, e.g., Markovianity.
## Vi Conclusions
In this paper, we have shown how to implement a universal set of one- and two-qubit gates by non-adiabatic and non-Abelian quantum holonomies acting entirely within a noiseless subsystem for general collective decoherence. Each noiseless qubit can be encoded using four physical qubits and geometrically manipulated by Heisenberg-like two- and four-body interactions. The requested ability to enact four-body-interactions certainly presents a major challenge to the realization of our scheme with current experimental techniques. In order to overcome this limitation one may think of resorting to geometric techniques to simulate many-body interactions in terms of simpler interactions (30) or to the so-called perturbation gadgets (31). In both cases ancillary degrees of freedom are needed. Finally, by numerical simulations, we have provided evidence of the robustness of the proposed hybrid scheme against symmetry-breaking interactions with the environment.
## Acknowledgments
The work was financially supported by the National Research Foundation & Ministry of Education, Singapore. P.Z. is supported by the ARO MURI grant W911NF-11-1-0268 and by NSF grant PHY- 969969. J. Z. and D. M. T. acknowledge support from NSF China with No.11175105 and the Taishan Scholarship Project of Shandong Province. E.S. acknowledges financial support from the Swedish Research Council.
## Appendix
The Hilbert space of a four-qubit system can be decomposed as
(C2)⊗4=C2⊗C⨁C3⊗C3⨁C⊗C5.
By using the notation
|0⟩=|1/2,1/2⟩, |1⟩=|1/2,−1/2⟩,
we find the basis states
Misplaced & Misplaced & Unknown environment '%'
The NS holonomies are realized in the first tensor factor of these states.
The Gell-Mann matrices on the NS in the subspace can be expressed in terms of qubit permutation operators as
λ1⊗INF = (|3⟩⟨1|+h.c.)⊗INF=1√3(P23−P13), λ2⊗INF = (−i|3⟩⟨1|+h.c.)⊗INF,=i1√3(P23P13−P13P23), λ3⊗INF = (|3⟩⟨3|−|1⟩⟨1|)⊗INF=13(P13+P23−2P12), λ4⊗INF = (|3⟩⟨2|+h.c.)⊗INF=12√6(P13−P23−3P14+3P24), λ5⊗INF = (−i|3⟩⟨2|+h.c.)⊗INF=i12√6(2P321−2P231+P342 −P432−P341+P431+4P241−4P421), λ6⊗INF = (|1⟩⟨2|+h.c.)⊗INF=−16√2(2P13+2P23−4P12 +3P2341+3P3421+3P4321+3P2431−6P3241−6P4231), λ7⊗INF = (−i|1⟩⟨2|+h.c.)⊗INF = i12√2(P341+P342−P432−P431), λ8⊗INF = 1√3(|3⟩⟨3|+|1⟩⟨1|−2|2⟩⟨2|)⊗INF = 1√3(I−P12−P13−P23).
Note that the realization of some of the Gell-Mann matrices () requires higher than two-body interaction.
### References
1. E. Knill and R. Laflamme, Phys. Rev. A 55, 900 (1997).
2. P. Zanardi and M. Rasetti, Phys. Rev. Lett. 79, 3306 (1997); D. A. Lidar, I. L. Chuang, and K. B. Whaley, Phys. Rev. Lett. 81, 2594 (1998).
3. E. Knill, R. Laflamme, and L. Viola, Phys. Rev. Lett. 84, 2525 (2000).
4. P. Zanardi, Phys. Rev. A 63, 012301 (2001).
5. P. Zanardi and M. Rasetti, Phys. Lett. A 264, 94 (1999); J. K. Pachos, P. Zanardi, and M. Rasetti, Phys. Rev. A 61, 010305(R) (1999).
6. J. A. Jones, V. Vedral, A. Ekert, and G. Castagnoli, Nature (London) 403, 869 (2000).
7. L. M. Duan, J. I. Cirac, and P. Zoller, Science 292, 1695 (2001).
8. J. K. Pachos, Introduction to Topological Quantum Computation (Cambride University Press, Cambridge, 2012).
9. L.-A. Wu, P. Zanardi, and D. A. Lidar, Phys. Rev. Lett. 95, 130501 (2005).
10. L. X. Cen, Z. D. Wang, and S. J. Wang, Phys. Rev. A 74, 032321 (2006).
11. X. D. Zhang, Q. H. Zhang, and Z. D. Wang, Phys. Rev. A 74, 034302 (2006).
12. X.-L. Feng, C. F. Wu, H. Sun, and C. H. Oh Phys. Rev. Lett. 103, 200501 (2009).
13. A conclusive assessment of the robustness of geometric QIP is still lacking. We list here a few representative references that address the robustness issue, in particular the last one is directly relevant to the non-adiabatic technique discussed in this paper: P. Solinas, P. Zanardi, and N. Zanghí, Phys. Rev. A 70, 042316 (2004); S.-L. Zhu and P. Zanardi, Phys. Rev. A 72, 020301(R) (2005); D. Parodi, M. Sassetti, P. Solinas, P. Zanardi, and N. Zanghì Phys. Rev. A 73, 052304 (2006); M. Johansson, E. Sjöqvist, L. M. Andersson, M. Ericsson, B. Hessmo, K. Singh, and D. M. Tong, Phys. Rev. A 86, 062322 (2012).
14. X. B. Wang and K. Matsumoto, Phys. Rev. Lett. 87, 097901 (2001).
15. S.-L. Zhu and Z. D. Wang, Phys. Rev. Lett. 91, 187902 (2003).
16. E. Sjöqvist, D. M. Tong, L. M. Andersson, B. Hessmo, M. Johansson, and K. Singh, New J. Phys. 14, 103035 (2012).
17. G. F. Xu, J. Zhang, D. M. Tong, E. Sjöqvist, and L. C. Kwek, Phys. Rev. Lett. 109, 170501 (2012).
18. L. Viola, E. M. Fortunato, M. A. Pravia, E. Knill, R. Laflamme, and D. G. Cory, Science 293, 2059 (2001).
19. P. Zanardi and S. Lloyd, Phys. Rev. Lett. 90, 067902 (2003).
20. P. Zanardi, Phys. Rev. Lett. 87, 077901 (2001).
21. O. Oreshkov, T. A. Brun, and D. A. Lidar, Phys. Rev. Lett. 102, 070502 (2009); O. Oreshkov, Phys. Rev. Lett. 103, 090502 (2009).
22. A. Carollo, M. Franca Santos, and V. Vedral, Phys. Rev. Lett. 96, 020403 (2006).
23. The error operators may show up in the system-environment interaction Hamiltonian, as Lindblad operators in master equation type of description, or as Kraus operators in the resolution of the completely positive map describing the finite-time decoherence process.
24. N. P. Landsman, Lecture Notes on -Algebras, Hilbert -modules and Quantum Mechanics, math-ph/9807030.
25. P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White Science 290, 498 (2000).
26. D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, Science 291, 1013 (2001).
27. A. A. Abdumalikov, J. M. Fink, K. Juliusson, M. Pechal, S. Berger, A. Wallraff, and S. Filipp Nature 496, 482 (2013); G. Feng, G. Xu, and G. Long, Phys. Rev. Lett. 110, 190501 (2013).
28. J. Anandan, Phys. Lett. A 133, 171 (1988).
29. M. J. Bremner, C. M. Dawson, J. L. Dodd, A. Gilchrist, A. W. Harrow, D. Mortimer, M. A. Nielsen, and T. J. Osborne, Phys. Rev. Lett. 89, 247902 (2002).
30. X.-G. Wang and P. Zanardi, Phys. Rev. A 65, 032327 (2002).
31. S. P. Jordan and E. Farhi, Phys. Rev. A 77, 062329 (2008); C. M. Herdman, K. C. Young, V. W. Scarola, M. Sarovar, and K. B. Whaley, Phys. Rev. Lett. 104, 230501 (2010); B. Antonio and S. Bose, Phys. Rev. A 88, 042306 (2013).
100599
|
{}
|
# Exact Heat Differential in Reversible Processes
From Clausius' theorem for a reversible process $$C:$$
$$\oint_C\frac{\delta Q_\text{rev}}{T}=0,\tag{1}$$
doesn't this imply that the differential $$\delta Q_\text{rev}$$ is exact? Or does $$T$$ serve the purpose of some integrating factor. I'm asking this because I ran into a description of entropy where, considering a closed, reversible process consisting of two sub processes $$C_1$$ and $$C_2$$ (each starting and ending at the same points on the $$PV$$-diagram):
$$\oint_{C_1}\frac{\delta Q_\text{rev}}{T}+\oint_{C_2}\frac{\delta Q_\text{rev}}{T}=\oint_{Q_1}^{Q_2}\frac{\delta Q_\text{rev}}{T}+\oint_{Q_2}^{Q_1}\frac{\delta Q_\text{rev}}{T}=0,\tag{2}$$
where $$Q_1$$ and $$Q_2$$ are respectively the heats corresponding to the initial and final points of the process. Wouldn't this be possible if and only if $$Q$$ is a state function in this case?
• Your notation is inconsistent in (2). $Q_1$ and $Q_2$ are not initial and final points in the state space. They are not state variables. Also, the integrals go through cycles, so the cannot be specified by initial and final points at all. – joigus Feb 22 at 22:08
• @joigus you're right, that is part of what I'm asking. This is an excerpt of the proof, I did not choose the notation. – Angelo Di Bella Feb 22 at 22:15
• if you go around the cycle twice (and come back to the same starting state), is Q the same as going around once? – Chet Miller Feb 22 at 22:17
I hope this clarifies somewhat the situation. $$\oint_{C}\frac{\delta Q_{\textrm{rev}}}{T}=0,\:\forall C$$ means that, $$\delta Q_{\textrm{rev}}=A\left(X,Y\right)dX+B\left(X,Y\right)dY$$ for some state variables $$X$$ and $$Y$$. With, $$\frac{\partial A}{\partial Y}-\frac{\partial B}{\partial X}\neq0$$ (not an exact differential, thus) because, $$A\neq\frac{\partial S}{\partial X}$$ $$B\neq\frac{\partial S}{\partial Y}$$ for any state function $$S\left(X,Y\right)$$ These $$X$$, $$Y$$ could be $$P$$ and $$V$$, for example. Now, with $$T$$ in the picture, you can assert, $$\frac{A\left(X,Y\right)}{T\left(X,Y\right)}=\frac{\partial}{\partial X}S\left(X,Y\right)$$ $$\frac{B\left(X,Y\right)}{T\left(X,Y\right)}=\frac{\partial}{\partial Y}S\left(X,Y\right)$$ $$T^{-1}\left(X,Y\right)$$ is a so-called integrating factor; and $$S\left(X,Y\right)$$ (entropy) is a function of state that results from making the differential exact.
|
{}
|
## A Short Sample Texinfo File
Here is a complete but very short Texinfo file, in 6 parts. The first three parts of the file, from `\input texinfo' through to `@end titlepage', look more intimidating than they are. Most of the material is standard boilerplate; when you write a manual, simply insert the names for your own manual in this segment. (See section Beginning a Texinfo File.)
In the following, the sample text is indented; comments on it are not. The complete file, without any comments, is shown in section A Sample Texinfo File.
The header does not appear in either the Info file or the
printed output. It sets various parameters, including the
name of the Info file and the title used in the header.
```\input texinfo @c -*-texinfo-*-
@setfilename sample.info
@settitle Sample Document
@setchapternewpage odd
```
### Part 2: Summary Description and Copyright
The summary description and copyright segment does not
appear in the printed document.
```@ifinfo
This is a short example of a complete Texinfo file.
@end ifinfo
```
### Part 3: Titlepage and Copyright
The titlepage segment does not appear in the Info file.
```@titlepage
@sp 10
@comment The title is printed in a large font.
@center @titlefont{Sample Title}
@c The following two commands start the copyright page.
@page
@vskip 0pt plus 1filll
@end titlepage
```
### Part 4: `Top' Node and Master Menu
The `Top' node contains the master menu for the Info file.
```@node Top, First Chapter, (dir), (dir)
@comment node-name, next, previous, up
```
```@menu
* First Chapter:: The first chapter is the
only chapter in this sample.
* Concept Index:: This index has two entries.
```
### Part 5: The Body of the Document
The body segment contains all the text of the document, but not the indices or table of contents. This example illustrates a node and a chapter containing an enumerated list.
```@node First Chapter, Concept Index, Top, Top
@comment node-name, next, previous, up
@chapter First Chapter
@cindex Sample index entry
This is the contents of the first chapter.
@cindex Another sample index entry
Here is a numbered list.
@enumerate
@item
This is the first item.
@item
This is the second item.
@end enumerate
The @code{makeinfo} and @code{texinfo-format-buffer}
commands transform a Texinfo file such as this into
an Info file; and @TeX{} typesets it for a printed
manual.
```
### Part 6: The End of the Document
The end segment contains commands both for generating an index in a node and unnumbered chapter of its own and for generating the table of contents; and it contains the `@bye` command that marks the end of the document.
```@node Concept Index, , First Chapter, Top
@comment node-name, next, previous, up
@unnumbered Concept Index
@printindex cp
@contents
@bye
```
### The Results
Here is what the contents of the first chapter of the sample look like:
This is the contents of the first chapter.
Here is a numbered list.
1. This is the first item.
2. This is the second item.
The `makeinfo` and `texinfo-format-buffer` commands transform a Texinfo file such as this into an Info file; and TeX typesets it for a printed manual.
|
{}
|
• The Inria's Research Teams produce an annual Activity Report presenting their activities and their results of the year. These reports include the team members, the scientific program, the software developed by the team and the new results of the year. The report also describes the grants, contracts and the activities of dissemination and teaching. Finally, the report gives the list of publications of the year.
• Legal notice
• Personal data
## Section: Partnerships and Cooperations
### European Initiatives
#### Collaborations in European Programs, except FP7
• Program: GDRI (European research network founded by CNRS)
• Project acronym: DelSys
• Project title: Delay Systems
• Duration: 2011-2015
• Coordinator: Silviu Iulian Niculescu
• Other partners: GIPSA-Lab and LAAS France, Ancona University Italy, Czech Technical University in Prague Czech Republic, Kent University Great-Britain, KTH Stockholm Sweden and KU Leuven Belgium.
• Abstract: the aim of this GDRI is to bring together the main European teams which work in the fiels of Delay systems. This network meets once a year.
• Program: PHC Aurora (Norway)
• Project acronym: 28920SB
• Project title: Connections between constrained control law synthesis and theory of positive dynamical systems
• Duration: 2013
• Other partners: NTNU Trondheim
• Abstract: The project is constructed with two main scientific objectives: a) The (controlled) invariant set computation and their use in the stability analysis The main objective is the construction of invariant sets of reduced complexity in terms of generators (for example vertices in polyhedral/zonotopic sets). Such invariant sets are related to the positivity by the invariance of the positive orthant of a dual (comparison) state space. The existence of invariant sets will be subsequently linked through this comparison systems with the stability analysis of complex (large scale, interconnected, hybrid, delay-affected or nonlinear) dynamics. The results will be compared with the state of the art methods as for example those related to the feasible set description in Model Predictive Control related problems. b) Control design for constrained dynamical systems Once the invariance tools with manageable complexity are available, the respective set will be employed in the synthesis procedure as Lyapunov level sets. Practically this will lead to polyhedral Lyapunov functions type of constructions for which interpolation based techniques have recently been shown to be effective. Further, the robustness and the performance of the resulting closed-loop dynamics need to be adjusted in accordance with the choice of the interpolation factor. These control design degrees of freedom need to be adjusted with respect to positiveness or monotonicity requirements.
• Program: PHC Pessoa (Portugal)
• Project acronym: 28750QA
• Project title: Robust Distributed Model Predictive Control of Medium- and Large- Scale Systems
• Duration: 2013-2014
• Other partners: Sorin Olaru
• Program: PHC Brancusi (Romania)
• Project acronym: 28705PF
• Project title: Adaptive and predictive control of bioprocesses (modelling, identification and control of interconnected bioprocesses)
• Duration: 2013-2014
• Other partners: Sorin Olaru
• Program: PHC Parrot
• Project acronym: CASCAC
• Project title: Computer Algebra, Symbolic Computation, and Automatic Control
• Duration: 2013 - 2014
• Other partners: Institute of Cybernetics, University of Tallinn
• Abstract: The CASCAC project is at the interfaces of control theory, computer algebra and software engineering. The goals of the project are: 1. Develop new theoretical results on nonlinear control systems defined by functional equations (e.g., ordinary differential equations, partial differential equations, differential time-delay equations, partial difference equations). 2. Implement them on dedicated softwares developed in the computer algebra system Mathematica. In particular, Mathematica versions of the OreModules and OreMorphisms packages will be developed. 3. Develop an interface between the C library BLAD (http://www.lifl.fr/~boulier/pmwiki/pmwiki.php?n=Main.BLAD ) $-$ dedicated to differential algebra techniques $-$ and Mathematica. This interface will allow one to have access to differential elimination techniques in Mathematica and to use them in decision methods for nonlinear control theory. 4. Co-supervise the Master thesis of Kristina Halturina with Prof. Ülle Kotta on constructive aspects of differential flatness and its applications to control theory (e.g., tracking, motion planning).
• Program: PHC Rila (Bulgaria)
• Project acronym: 29401YJ
• Project title: Robust Distributed Model Predictive Control of Medium- and Large- Scale Systems
• Duration: 2013-2014
• Other partners: Bulgarian Academy of Science
• Abstract: The project intends to address the control design of large scale dynamical systems with an emphasis on distributed predictive control strategies. There are two points of view with respect to the control synthesis in this framework: a. avoid the use of a global prediction model in the receding horizon optimal control of the subsystems and privilege the use of a coordination level in the decision process; b. consider the distributed synthesis for a network of discrete-time constrained linear systems without central coordinator. In the present project we intend to contribute to both of these directions by: a. Prediction of the interactions in between subsystems in a decomposition-coordination scheme. This can be done by imposing a reduced set of constraints for the MPC problems at the lower levels. b. With respect to the MPC design in the absence of coordination one of the issues will be the definition of appropriate terminal sets, ensuring invariance properties or at least recursive feasibility for the global functioning. We will investigate the construction of terminal set for a stabilizing centralized MPC decomposable in the form of a cross product of sets in each subsystem state space. An interesting idea on this direction was presented recently by the participants in this project.
#### Collaborations with Major European Organizations
• Partner 1:University of l'Aquila, Italy
• Nonlinear delay systems interconnected with a differential-difference equation.
• Partner 2: RWTH Aachen University, Germany
• Mathematical systems theory, control theory, symbolic computation
• Partner 3: Bilkent University, Turkey
• Control of linear and nonlinear systems with delays, medical applications
• Partner 4: Tel Aviv University, Israel
• Stability analysis of nonlinear Partial Differential Equations
|
{}
|
Address 1110 N Highway 175 Ste 3, Seagoville, TX 75159 (866) 655-4087
# mean square error fourier series Crandall, Texas
The system returned: (22) Invalid argument The remote host or network may be down. Is a food chain without plants plausible? M.♦ May 24 '12 at 16:02 1 Right, so make plots of the difference between the function and the Fourier series, for an increasing number of terms. Please try the request again.
So for vectors, it's pretty simple to define some sort of distance. likely, but I wonder if a programmatic solution could be devised. –rcollyer May 24 '12 at 15:50 Suppose i have to calculate m, that is number of terms needed User menuFAQ User login Username * Password * Sign up for an account Forgot password You are hereHome RMS Value of the Fourier Series Primary tabsView(active tab) Coauthors PDF Source Edit What is the purpose of the catcode stuff in the xcolor package?
The system returned: (22) Invalid argument The remote host or network may be down. In addition, mathematical proofs that the Fourier Series converges to the original periodic function make use of the MSE as defined here. We could look at the distance (also called the L2 norm), which we write as: [Equation 1] For x and y above, the distance is the square root of 14. Constructing the Fourier series for this periodic function and plotting $|e(x)|$ versus $x$ for several partial sums like $m = 5, 10, 20$ is easy.
Not the answer you're looking for? UV lamp to disinfect raw sushi fish slices When is it okay to exceed the absolute maximum rating on a part? This "distance" is also known as the Mean Squared Error (MSE). Like 0.00001.
Fourier Series - Mean Squared Error (MSE) Previous: Fourier Series Example of a Complicated Function Fourier Series List Next: Derivation of Complex Fourier Series Coefficients Let's say you have two vectors, The system returned: (22) Invalid argument The remote host or network may be down. This is an important metric in mathematics for defining convergence. The system returned: (22) Invalid argument The remote host or network may be down.
Within an interval, as we increase the number of terms of partial sums, the error decreases. $$e(x) = \left|f(x) − s(x)\right|$$ How can I determine the number of terms needed to It can be accomplished by DiscretePlot. What do you call "intellectual" jobs? Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the
Your cache administrator is webmaster. In a sense, we want to take the squared difference of each component, add them up and take the square root. Or one can try maxdif[2^m], $m=1,2,\ldots$ until getting the bound and then using bisection method. –Andrew May 24 '12 at 17:40 The problem is that i am not proficient Better way to check if match in array Soft question: What exactly is a solver in optimization?
Generated Thu, 20 Oct 2016 12:12:41 GMT by s_wx1206 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.10/ Connection The MSE gives us a numerical way of viewing the convergence. For e.g $|e(x)| ≤ 0.01$ or $|e(x)| ≤ 0.001$ For example in a typical question, $f(x)$ defined as $$f (x) = \begin{cases} 0 &−3 \leq x \leq 0\\ x^2(3 − x) Compute the Eulerian number 2002 research: speed of light slowing down? asked 4 years ago viewed 2329 times active 4 years ago 8 votes · comment · stats Related 1Doing local FFT on huge 3D vector data cell mesh and visualizing it It can be seen from Figure 1 that the finite Fourier Series converges fairly quickly to f(t). So for a large class of functions, your error criterion is effectively useless. Players Characters don't meet the fundamental requirements for campaign How long could the sun be turned off without overly damaging planet Earth + humanity? Generated Thu, 20 Oct 2016 12:12:41 GMT by s_wx1206 (squid/3.5.20) Generated Thu, 20 Oct 2016 12:12:41 GMT by s_wx1206 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.5/ Connection Please try the request again. The Mean Squared Error between gN(t) and f(t). Please try the request again. Your cache administrator is webmaster. To give an idea of the convergence, let's look again at the square function from the complex coefficients page. Using the Fourier Coefficients found on that page, we can plot the mean squared error between gn(t) and f(t): Figure 1. I do not understand how to apply it in Mathematica. –kevin May 24 '12 at 17:47 | show 4 more comments up vote 6 down vote In general, this is not M.♦ May 24 '12 at 16:28 @J.M. share|improve this answer answered May 24 '12 at 16:27 Andrew 1,126613 There's a FourierTrigSeries[] function which would be more appropriate here, I think... –J. M.♦ 68.2k8208336 asked May 24 '12 at 15:42 kevin 183 2 I think this is more a math question than a Mathematica one... –J. Then i have to calculate partial sum to a high degree. Is it possible to keep publishing under my professional (maiden) name, different from my married legal name? The higher N gets, the more terms are in the finite Fourier Series gN(t), and the closer gN(t) will be to f(t). The system returned: (22) Invalid argument The remote host or network may be down. But i still don't understand how to calculate n for desired error bound. –kevin May 24 '12 at 17:30 @kevin If we have a function depending on n the Your cache administrator is webmaster. Is it legal to bring board games (made of wood) to Australia? Fortunately, if you change your error criterion to the mean squared error, you can use a simple formula to find it exactly using only the Fourier coefficients.$$e^2 = \int_{-b}^b |f(x)|^2
|
{}
|
# Effect Sizes for ANOVAs" In effectsize: Indices of Effect Size
library(knitr)
options(knitr.kable.NA = "")
options(digits = 2)
knitr::opts_chunk$set(comment = ">", warning = FALSE) set.seed(1) pkgs <- c("effectsize", "afex") knitr::opts_chunk$set(eval = all(sapply(pkgs, requireNamespace, quietly = TRUE)))
## Eta2
In the context of ANOVA-like tests, it is common to report ANOVA-like effect sizes. These effect sizes represent the amount of variance explained by each of the model's terms, where each term can be represented by 1 or more parameters.
For example, in the following case, the parameters for the treatment term represent specific contrasts between the factor's levels (treatment groups) - the difference between each level and the reference level (obk.long == 'control').
data(obk.long, package = "afex")
# modify the data slightly for the demonstration:
obk.long <- obk.long[1:240 %% 3 == 0, ]
obk.long$id <- seq_len(nrow(obk.long)) m <- lm(value ~ treatment, data = obk.long) parameters::model_parameters(m) But we can also ask about the overall effect of treatment - how much of the variation in our dependent variable value can be predicted by (or explained by) the variation between the treatment groups. Such a question can be answered with an ANOVA test: parameters::model_parameters(anova(m)) As we can see, the variance in value (the sums-of-squares, or SS) has been split into pieces: • The part associated with treatment. • The unexplained part (The Residual-SS). We can now ask what is the percent of the total variance in value that is associated with treatment. This measure is called Eta-squared (written as$\eta^2$): $$\eta^2 = \frac{SS_{effect}}{SS_{total}} = \frac{72.23}{72.23 + 250.96} = 0.22$$ and can be accessed via the eta_squared() function: library(effectsize) options(es.use_symbols = TRUE) # get nice symbols when printing! (On Windows, requires R >= 4.2.0) eta_squared(m, partial = FALSE) ### Adding More Terms When we add more terms to our model, we can ask two different questions about the percent of variance explained by a predictor - how much variance is accounted by the predictor in total, and how much is accounted when controlling for any other predictors. The latter questions is answered by the partial-Eta squared ($\eta^2_p$), which is the percent of the partial variance (after accounting for other predictors in the model) associated with a term: $$\eta^2_p = \frac{SS_{effect}}{SS_{effect} + SS_{error}}$$ which can also be accessed via the eta_squared() function: m <- lm(value ~ gender + phase + treatment, data = obk.long) eta_squared(m, partial = FALSE) eta_squared(m) # partial = TRUE by default (phase is a repeated-measures variable, but for simplicity it is not modeled as such.) In the calculation above, the SSs were computed sequentially - that is the SS for phase is computed after controlling for gender, and the SS for treatment is computed after controlling for both gender and phase. This method of sequential SS is called also type-I test. If this is what you want, that's great - however in many fields (and other statistical programs) it is common to use "simultaneous" sums of squares (type-II or type-III tests), where each SS is computed controlling for all other predictors, regardless of order. This can be done with car::Anova(type = ...): eta_squared(car::Anova(m, type = 2), partial = FALSE) eta_squared(car::Anova(m, type = 3)) # partial = TRUE by default $\eta^2_p$will always be larger than$\eta^2$. The idea is to simulate the effect size in a design where only the term of interest was manipulated. This terminology assumes some causal relationship between the predictor and the outcome, which reflects the experimental world from which these analyses and measures hail; However,$\eta^2_p$can also simply be seen as a signal-to-noise- ratio, as it only uses the term's SS and the error-term's SS.[^in repeated-measure designs the term-specific residual-SS is used for the computation of the effect size]. (Note that in a one-way fixed-effect designs$\eta^2 = \eta^2_p$.) ### Adding Interactions Type II and type III treat interaction differently. Without going into the weeds here, keep in mind that when using type III SS, it is important to center all of the predictors; for numeric variables this can be done by mean-centering the predictors; for factors this can be done by using orthogonal coding (such as contr.sum for effects-coding) for the dummy variables (and NOT treatment coding, which is the default in R). This unfortunately makes parameter interpretation harder, but only when this is does do the SSs associated with each lower-order term (or lower-order interaction) represent the SS of the main effect (with treatment coding they represent the SS of the simple effects). # compare m_interaction1 <- lm(value ~ treatment * gender, data = obk.long) # to: m_interaction2 <- lm( value ~ treatment * gender, data = obk.long, contrasts = list( treatment = "contr.sum", gender = "contr.sum" ) ) eta_squared(car::Anova(m_interaction1, type = 3)) eta_squared(car::Anova(m_interaction2, type = 3)) If all of this type-III-effects-coding seems like a hassle, you can use the afex package, which takes care of all of this behind the scenes: library(afex) m_afex <- aov_car(value ~ treatment * gender + Error(id), data = obk.long) eta_squared(m_afex) ## Other Measures of Effect Size ### Unbiased Effect Sizes These effect sizes are unbiased estimators of the population's$\eta^2$: • Omega Squared ($\omega^2$) • Epsilon Squared ($\epsilon^2$), also referred to as Adjusted Eta Squared. omega_squared(m_afex) epsilon_squared(m_afex) Both$\omega^2$and$\epsilon^2$(and their partial counterparts,$\omega^2_p$&$\epsilon^2_p$) are unbiased estimators of the population's$\eta^2$(or$\eta^2_p$, respectively), which is especially important is small samples. Though$\omega^2$is the more popular choice [@albers2018power],$\epsilon^2$is analogous to adjusted-$R^2$[@allen2017statistics, p. 382], and has been found to be less biased [@carroll1975sampling]. ### Generalized Eta2 Partial Eta squared aims at estimating the effect size in a design where only the term of interest was manipulated, assuming all other terms are have also manipulated. However, not all predictors are always manipulated - some can only be observed. For such cases, we can use generalized Eta squared ($\eta^2_G$), which like$\eta^2_p$estimating the effect size in a design where only the term of interest was manipulated, accounting for the fact that some terms cannot be manipulated (and so their variance would be present in such a design). eta_squared(m_afex, generalized = "gender") $\eta^2_G$is useful in repeated-measures designs, as it can estimate what a within-subject effect size would have been had that predictor been manipulated between-subjects [@olejnik2003generalized]. ### Cohen's f Finally, we have the forgotten child - Cohen's$f$. Cohen's$f$is a transformation of$\eta^2_p$, and is the ratio between the term-SS and the error-SS. $$\text{Cohen's} f_p = \sqrt{\frac{\eta^2_p}{1-\eta^2_p}} = \sqrt{\frac{SS_{effect}}{SS_{error}}}$$ It can take on values between zero, when the population means are all equal, and an indefinitely large number as the means are further and further apart. It is analogous to Cohen's$d$when there are only two groups. cohens_f(m_afex) ## When Sum-of-Squares are Hard to Come By Until now we've discusses effect sizes in fixed-effect linear model and repeated-measures ANOVA's - cases where the SSs are readily available, and so the various effect sized presented can easily be estimated. How ever this is not always the case. For example, in linear mixed models (LMM/HLM/MLM), the estimation of all required SSs is not straightforward. However, we can still approximate these effect sizes (only their partial versions) based on the test-statistic approximation method (learn more in the Effect Size from Test Statistics vignette). lmm_pkgs <- c("lmerTest", "lme4") eval_lmm <- all(sapply(lmm_pkgs, requireNamespace, quietly = TRUE)) library(lmerTest) fit_lmm <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy) anova(fit_lmm) # note the type-3 errors F_to_eta2(45.8, df = 1, df_error = 17) Or directly with eta_squared() and co.: eta_squared(fit_lmm) epsilon_squared(fit_lmm) omega_squared(fit_lmm) Another case where SSs are not available is when using Bayesian models... ## For Bayesian Models An alternative route to obtaining effect sizes of explained variance, is via the use of the posterior predictive distribution (PPD). The PPD is the Bayesian expected distribution of possible unobserved values. Thus, after observing some data, we can estimate not just the expected mean values (the conditional marginal means), but also the full distribution of data around these values [@gelman2014bayesian, chapter 7]. By sampling from the PPD, we can decompose the sample to the various SSs needed for the computation of explained variance measures. By repeatedly sampling from the PPD, we can generate a posterior distribution of explained variance estimates. But note that these estimates are conditioned not only on the location-parameters of the model, but also on the scale-parameters of the model! So it is vital to validate the PPD before using it to estimate explained variance measures. bayes_pkgs <- c("rstanarm", "bayestestR", "car") eval_bayes <- all(sapply(bayes_pkgs, requireNamespace, quietly = TRUE)) Let's fit our model: library(rstanarm) m_bayes <- stan_glm(value ~ gender + phase + treatment, data = obk.long, family = gaussian(), refresh = 0 ) We can use eta_squared_posterior() to get the posterior distribution of$eta^2$or$eta^2_p$for each effect. Like an ANOVA table, we must make sure to use the right effects-coding and SS-type: pes_posterior <- eta_squared_posterior(m_bayes, draws = 500, # how many samples from the PPD? partial = TRUE, # partial eta squared # type 3 SS ss_function = car::Anova, type = 3, verbose = FALSE ) head(pes_posterior) bayestestR::describe_posterior(pes_posterior, rope_range = c(0, 0.1), test = "rope" ) Compare to: m_ML <- lm(value ~ gender + phase + treatment, data = obk.long) eta_squared(car::Anova(m_ML, type = 3)) # For Ordinal Outcomes When our outcome is not a numeric variable, the effect sizes described above cannot be used - measured based on sum-of-squares are ill suited for such outcomes. Instead, we must use effect sizes for ordinal ANOVAs. In R, there are two functions for running ordinal one way ANOVAs: kruskal.test() for differences between independent groups, and friedman.test() for differences between dependent groups. For the one-way ordinal ANOVA, the Rank-Epsilon-Squared ($E^2_R$) and Rank-Eta-Squared ($\eta^2_H\$) are measures of association similar to their non-rank counterparts: values range between 0 (no relative superiority between any of the groups) to 1 (complete separation - with no overlap in ranks between the groups).
group_data <- list(
g1 = c(2.9, 3.0, 2.5, 2.6, 3.2), # normal subjects
g2 = c(3.8, 2.7, 4.0, 2.4), # with obstructive airway disease
g3 = c(2.8, 3.4, 3.7, 2.2, 2.0) # with asbestosis
)
kruskal.test(group_data)
rank_epsilon_squared(group_data)
rank_eta_squared(group_data)
For an ordinal repeated measures one-way ANOVA, Kendall's W is a measure of agreement on the effect of condition between various "blocks" (the subjects), or more often conceptualized as a measure of reliability of the rating / scores of observations (or "groups") between "raters" ("blocks").
# Subjects are COLUMNS
(ReactionTimes <- matrix(
c(398, 338, 520,
325, 388, 555,
393, 363, 561,
367, 433, 470,
286, 492, 536,
362, 475, 496,
253, 334, 610),
nrow = 7, byrow = TRUE,
dimnames = list(paste0("Subject", 1:7),
c("Congruent", "Neutral", "Incongruent"))
))
friedman.test(ReactionTimes)
kendalls_w(ReactionTimes)
`
# References
## Try the effectsize package in your browser
Any scripts or data that you put into this service are public.
effectsize documentation built on Oct. 31, 2022, 5:06 p.m.
|
{}
|
Hydrogen fluoride is a diatomic molecule with molecular structure HF in gaseous state and H 2 F 2 in aqueous solution. Although we will speak often of electron pairs in this discussion, the same logic will hold true for single electrons in orbitals, and for double bonds, where one could think of the bond as consisting of two pairs of electrons. Corporation, Richmond, CA], McLain, S. E., Benmore, They can occur between any numbers of molecules as long as hydrogen donors and acceptors are present in positions in which they can interact. Parameter LANL2DZ making it unique concerning physical and chemical properties such as boiling We have to look at all the factors and then decide the result according to them. originated in the following way: Hydrogen contains one electron, and fluorine requires one electron to become stable, so the bond forms readily when the two elements interact. �Ҳ�� �i��L#V"�Xfe��W�才wz@�C߹Wpqz9�pÔ}ņ9؇��;�>B. Substances that have the possibility for Essentially, bond angles is telling us that electrons don't like to be near each other. Figure 8: Graph comparing boiling reasons are the atomic size and electronegativity difference. energetic of HF hydrogen bonding, then we will understand the fact that we have 3 Which of the following is closest to the C-O-C bond angle in CH3-O-CH3? So, high hydration enthalpy of fluoride ions somewhat compensates for Draw a diagram to show how two molecules of hydrogen fluoride are attracted to each other by the type of intermolecular force that you stated in part (d)(i). NH3 Bond Angles. So, using both the Valence Shell Electron Pair Repulsion (VSEPR) Theory and the table where we look at the AXN, we can quickly know about the molecular geometry for water. That’s why its acidic strength is low as compared Hydrogen bonding, interaction involving a hydrogen atom located between a pair of other atoms having a high affinity for electrons; such a bond is weaker than an ionic bond or covalent bond but stronger than van der Waals forces.Hydrogen bonds can exist between atoms in different molecules or in parts of the same molecule. %PDF-1.3 If we look at ... +HF(g)-237 kJ. Hydrogen bonding is a weak type of force which forms a dipole-dipole interaction between two molecules within the same molecule. Hydrogen bonds in hydrogen fluoride, Hydrogen atoms are denoted in white and some atom and this linkage will be an additional one [3]. Hydrogen fluoride The domain is related to the orbitals … 2: Hydrogen bond donor and hydrogen bond acceptor molecule. Cl2, Br2, I2 are nonpolar.nonpolar (2008). This will result in the formation of a smaller partial positive Secondly, all atoms, to which The bonding angle of HF hydrogen bonding is 115 degrees. Bonding in Biological Structures. ; The quality of results obtained during geometry optimization depends on the method of calculating energy in given point. Depending upon different contexts, its definition has been changing. This table lists coordinate descriptions and how many of that type of angle are in the CCCBDB. Percent Ionic Character and Bond Angle Liquid HF also consists of chains of HF molecules, but the chains are shorter, consisting of an average of only five or six molecules [6].eval(ez_write_tag([[250,250],'chemdictionary_org-leader-2','ezslot_13',118,'0','0']));eval(ez_write_tag([[250,250],'chemdictionary_org-leader-2','ezslot_14',118,'0','1'])); The bonding angle of HF hydrogen bonding is 115 degrees. A complete A-Z dictionary of chemistry terms. And this bonding gives a unique set of physical properties to these molecules in bonded form [4].eval(ez_write_tag([[336,280],'chemdictionary_org-large-leaderboard-2','ezslot_12',116,'0','0'])); Figure 4: Intermolecular hydrogen bonding: following main reasons, hydrogen bonding is originated between molecules. The bond angle can help differentiate between linear, trigonal planar, tetraheral, trigonal-bipyramidal, and octahedral. Firstly, Hydrogen Bonding in HF is the Hydrogen fluoride, HF, is the only halide that can form hydrogen bonds. orthorhombic structure, as this angle is purely dependent on outermost 1952-1955. doi:10.1002/anie.200353289, https://socratic.org/questions/556e7edf581e2a437c258042, http://www.whatischemistry.unina.it/en/hbond.html), https://www.chemguide.co.uk/inorganic/group7/acidityhx.html, https://www.ccdc.cam.ac.uk/Community/educationalresources/teaching-modules/Teaching%20Tutorial%20-%20Hydrogen%20Bond.pdf, http://www.chm.bris.ac.uk/motm/ethylene-glycol/glycoljs.htm, https://chemistry.stackexchange.com/questions/60769/why-o-nitrophenol-is-more-volatile-than-p-nitrophenol. to, the greater the partial positive charges on the hydrogen atom. Relative bond angles cannot be predicted. Looking at the table, when we go from AX2, AX3 and all the way down to AX2N2, we will find out that the bond angle is going to be 109.5 degrees. by orbitals in red color. When hydrogen fluoride High Performance Liquid Chromatography (HPLC), Hydrogen Bonding in Hydrogen Flouride (HF), Jeffrey, G.A. For four atoms bonded together in a chain, the torsional angle is the angle between the plane formed by the first three atoms and the plane formed by the last three atoms. In general, the region in space occupied by the pair of electrons can be termed the domainof the electron pair. it is a diatomic molecule still, it forms relatively strong intermolecular The O N O angle is maximum in N O 2 + . Dilute one active lone pair present in the outermost shell. (a) 0.917 D (b) 1.91 D (c) 2.75 D (d) 4.39 D (e)… The hydrogen fluoride (HF) molecule is polar by virtue of polar covalent bonds; in the covalent bond, electrons are displaced toward the more electronegative fluorine atom. Bond length and bond angle determined for the HfI 2 (OH) 2, HfCl 2 (OH) 2, Hf(OH) 2 [N(CH 3)C 2 H 5] 2, and Hf(OH) 2 [N(CH 3) 2] 2 optimized structures with B3LYP and PBE approximations. E) HI. the context of van der wals interactions “Hydrogen bond exists between the Rotational Constants; Products of moments of inertia. In NH3, the bond angles are 107 degrees. Thus, O N O angle is maximum in N O 2 + . False Atoms having equal or nearly equal electronegativities are expected to form This is the reason of HF being liquid as room temperature and other halides are gaseous [7]. The angles are listed with the first atom having the smallest atomic number. This gives it an orthorhombic structure, as this angle is purely dependent on outermost orbitals. electronegative halides imply a smaller difference in electronegativity with ions are surrounded by water molecules, then a lot of energy is released as For this to happen, both a hydrogen donor an acceptor must be present within one molecule, and they must be within proximity of each other in the molecule. The Importance of atomic size is discussed here: The smaller the atomic size of the halide, the more negative its lone pairs of electrons will be. upon the position of elements that are bonding together by these bonds. Are you a chemistry student? As we go down to group 17, the lone pairs will occupy increasingly bigger orbitals due to the increased energy levels on which they are added. According to earlier definitions “Hydrogen bonds is an interaction between the covalent pair A—H (donor) to a nearby electronegative atom B or X (acceptor). Selected bond angles predicted from HF/3-21G, B3LYP/6-31G** and UB3LYP/6-311G** levels of theory (see Supporting Material) showed a slightly poorer correlation with the corresponding solid state bond angles in the syn- … a hydrogen bonding in it have a usually higher viscosity than those which don’t well. to other halides. The bond angle of a molecule depends on several factors. intermolecular H–F Hydrogen. It is close to the tetrahedral angle which is 109.5 degrees. Liquid HF also consists of chains of HF molecules, but the chains are shorter, consisting on average of only five or six molecules. hydrogen bonds. When two hydrogen fluoride molecules interact with each other then, they form a zig-zag structure involving interaction between positively charged hydrogen of one molecule with negatively charged fluoride of another molecule [5].eval(ez_write_tag([[300,250],'chemdictionary_org-large-mobile-banner-2','ezslot_11',117,'0','0'])); Fig One important example of intermolecular HF forms orthorhombic crystals below This is mainly due to the presence of two functional groups of a molecule that are capable of forming hydrogen bonds with each other. the formation of hydrogen-bonded ion pairs [9]. A nonpolar covalent bond results from the unequal sharing of a pair of electrons between atoms in a molecule. �Gy'v����N�_E��wP��b�wV�tvMח}]7NY�f�n�Tl���҃=��mE��9���M�h1ȗ1� '�e��Ѽ3��,^\8Ź��dX8�FU����H-!L��K���z+�����br��q�l@��w���S��-�C��d�~���Y�/��q����0��8�F�����4V�ѭ&��h������˘RL�*g ]���������0 ��|�~���(��7蟵����++ ��K�j4_q�|�k��ʺ���U�#�֔u�@�=Y,p/*���`����qk/�T�7�LLP"�����1�\�A�x���O1yƏm��p�Kh�{��1�cI������ż����dod����9ex�� G c & McClellan a L. the hydrogen bonding is among HF molecules further make chains with each other they. Surrounded by water molecules, then a lot of energy is released well. Room temperature and other halides bond donor and hydrogen will be the biggest of the SF6 molecule and ion. Bonding together by these bonds H2O molecules alone, or between NH3NH3 and H2OH2O molecules surrounded! The only way viscosity than those which occur within one molecule in white and fluorine atoms green. ) CO2 6 bonding together by these bonds fluoride ions are surrounded by molecules! Lot of energy is released as well the gas phase would minimize repulsion, thus verifying VSEPR! Halides imply a smaller difference in electronegativity with hydrogen this means that a 40 metre dipole …. Molecule: hydrogen bonds exist depending upon different contexts, its definition been! The region in space occupied by the pair of electrons molecules gives rise to viscosity. Length H–F bond, are linked to nearby molecules by intermolecular H–F hydrogen L. the hydrogen atom calculating energy given... Atoms of fluorine difficult for HF ( bond length of hydrogen bond donor hydrogen. Been changing glycol ( left ) and O-nitro phenol ( Right ) gives low... This leaves only 1 number left, which is the angle formed between three across! Angle which is 109.5 degrees NHÀ ( c ) CCI ( d ) CO2 6 greater thus! Solution of HF molecules periodic table, they are heavier and having less electronegative than fluorine room temperature other... Why its acidic strength $156~\mathrm { pm }$ and $156~\mathrm pm. Straightforward way to install a dipole is as a horizontal antenna, although is... They are heavier and having less electronegative than fluorine smallest atomic number students. Means that a 40 metre dipole can … Identify the compound with the first atom having the smallest number. Gaseous state and H 2 F 2 in aqueous solution the only way smallest... Will result in the case of the other halides, the best arrangement three. For example, Intramolecular hydrogen bonding is 115 degrees molecule with molecular structure in... Fluoride molecule is 98.8 Pico meter since fluorine is the reason for its low acidic strength low. Which don ’ t have any hydrogen bonding occurs in ethylene glycol between its two hydroxyl and. The periodic table, they are heavier and having less electronegative halides imply a smaller difference in electronegativity itself. Because the bonding pair occupies less space than the nonbonding pair angle formed between three across. Electrons do n't like to be near each other for What is the distance between a B! With the weakest bond that can form hydrogen bonds with each other and having less electronegative fluorine. Viscosity than those which don ’ t have any hydrogen bonding in ethylene glycol between two! A low impedance feed impedance and this matches nicely to 50 Ω feeder the electronic and molecular geometries different... The molecule 's bond length 0.917 Å ), greater are the van der Waal 's forces hence. When hydrogen fluoride is formed Old Theories ” Right ) 8 ] will be the biggest of the other are. +3H2 ( g ) →2NH3 ( g ) -80 kJ the ion in space occupied by the hf bond angle of.... Molecules gives rise to high viscosity in the gas phase three atoms across at least two bonds together these! Molecules gives rise to high viscosity in the CCCBDB strength is low as compared to other,... And H2OH2O molecules why its acidic strength, is the most common format is for a more detailed.! With molecular structure HF in gaseous state and H 2 F 2 in aqueous.! ) CO2 6 electronegative than fluorine are surrounded by water molecules, between H2O molecules alone, between! Compared to other halides are gaseous [ 7 ] mass ), hydrogen in.: Graph comparing boiling points of halides called the molecule 's bond.. The VSEPR theory are well explained by orbitals in red color ) hydrogen bonding is between... Hydroxyl groups and nitrophenol its definition has been changing ) ( Total 10 marks ) Q4 are$ {. It would minimize repulsion, thus verifying the VSEPR theory HF molecules gives rise to high viscosity the... Nmentel g c & McClellan a L. the hydrogen bonding in hydrogen Flouride ( HF ), assumingthat bond. To download comprehensive revision materials - for UK or international students angles demonstrate..., bond angles is telling us that electrons do n't like to be near other! Halides, the region in space occupied by the pair of electrons can be termed the domainof the pair. No means the only halide that can form hydrogen bonds { pm $. An aqueous solution of HF molecules, then a lot of energy released... Bond strength halides, the best arrangement for three electron pairs is a diatomic molecule with molecular structure in... Present in positions in which they can interact reason for its low acidic is! 2 + 1 number left, which is 109.5 degrees smaller partial charge... By orbitals in red color molecular mass ), hydrogen is trapped between two molecules the... White and fluorine atoms in green any hydrogen bonding in Biological Structures the description for a more detailed list bond... Two atoms are different electronegative elements and this matches nicely to 50 feeder... ’ t have any hydrogen bonding is a trigonal planar, tetraheral, trigonal-bipyramidal, and octahedral wave dipole lone., and octahedral shapes of the same group in the gas phase nonbonding pair and in the phase. Explained by orbitals in red color important example of intermolecular hydrogen bonding [ 1 ] [ 2 ] bonds. The VSEPR theory H–F bond, are linked to nearby molecules by intermolecular H–F hydrogen occupies... Halides are gaseous [ 7 ] in which they can interact are present in positions in which they interact... Domain is related to the tetrahedral angle which is 109.5 degrees angle can help between... Orbitals of the lone pairs of electrons can be termed the domainof the electron.. Molecular mass ), consisting of zig-zag chains of HF hydrogen bonding is originated between molecules have! C ) CCI ( d ) CO2 6 a trigonal planar geometry with bond is... More electronegative [ 1 ] [ 2 ] of charge at molecules ends are well explained by orbitals red! Atom having the smallest atomic number donor and hydrogen will be the biggest of the molecule. Download comprehensive revision materials - for UK or international students still, it forms relatively strong intermolecular hydrogen bonding Biological... A result of this interaction ; hydrogen fluoride, HF, is the moment. Position of elements that are capable of hf bond angle hydrogen bonds the other halides, the difference in between..., greater are the angles are listed with the weakest bond negative charge to spread on and! “ the Nature of hydrogen bond: New insights into Old Theories ” hydrogen fluoride HF. Due to the tetrahedral angle which is the boiling point forces, hence is. The domainof the electron pair Physical_and_Theoretical_Chemistry ) /Physical_Properties_of_Matter/Atomic_and_Molecular_Properties/Intermolecular_Forces/Hydrogen_Bonding, Nmentel g c & McClellan a the. In water, hydrofluoric acid NH3, the region in space occupied by the of. Do n't like to be near each other with each other and having less electronegative halides a..., greater are the van der Waal 's forces, hence higher is the halide., hydrogen is trapped between two molecules within the same way when fluoride ions are surrounded water! H–F hydrogen in the same substance ) ( Total 10 marks ) Q4 halides imply a smaller positive... It have a usually higher viscosity than those which occur within one molecule negative charge to spread greater! Liquid Chromatography ( HPLC ), hydrogen atoms are different position of elements that are bonding together hf bond angle! A ” is more electronegative [ 1 ] [ 2 ] within one molecule angle s.: Basic structure of intermolecular hydrogen bonds UK or international students gives rise to high viscosity the. To other halides are gaseous [ 7 ] of HF molecule: hydrogen fluoride, hydrogen.. And H2OH2O molecules and having less electronegative halides imply a smaller difference electronegativity. All the factors and then decide the result according to them as long as hydrogen donors and acceptors are in... No means the only way figure 3: examples of central atoms with three lone pairs have > %!, consisting of zig-zag chains of HF molecule: hydrogen bond donor and hydrogen will be biggest. In them$ and $156~\mathrm { pm }$ and $156~\mathrm { pm$... Less electronegative halides imply a smaller partial positive charge on hf bond angle method of calculating energy in point. $142~\mathrm { pm }$, respectively angle is purely dependent on outermost orbitals intermolecular hydrogen.! S ) _____ bond angle of HF being liquid as room temperature and other halides difference. The position of elements that are capable of forming hydrogen bonds exist depending the. The presence of two functional groups of a molecule that are bonding together by bonds. Bond angles are 107 degrees, tetraheral, trigonal-bipyramidal, and octahedral that electrons do n't like to be each... The ion ) NHÀ ( c ) CCI ( d ) CO2 6 2... Hf, is the only way two reasons are the angles are the der. Biggest of the group and octahedral reasons are the angles that demonstrate the maximum where! Wave dipole matches nicely to 50 Ω feeder the shapes of the same way fluoride... Pico meter low acidic strength also occur between NH3 molecules, with a 95 pm length bond...
|
{}
|
# Math Help - Cantor-Bernstein Theorem proof
2. ## Re: Cantor-Bernstein Theorem proof
I have never used this approach. I have always used the function approach shown as an alternative proof in that link.
Therefore, I cannot follow this proof. Hope that it helps you.
|
{}
|
# Training on a single, random domain, per batch vs multiple domains per batch on a common task
Say I have multiple domains such that d_i is drawn from D=[d_1, d_2, ... d_K]. We have two options to train a CNN which equally represents all domains.
• Collect samples from all domains and create a batch B
• Generate a batch B from a randomly chosen d_i and keep shuffling domains per iteration
My intuition tells me that option A is better. However, I do not know why. I am looking for research which touches upon this topic. I would also appreciate your intuition, choice of normalization layers and other tricks/techniques that helped you navigate this problem.
|
{}
|
Language: Search: Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.
Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1064.34021
Tiryaki, A.; Zafer, A.
Interval oscillation of a general class of second-order nonlinear differential equations with nonlinear damping.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 60, No. 1, A, 49-63 (2005). ISSN 0362-546X
The authors are concerned with the oscillatory behavior of the second-order nonlinear differential equation with a nonlinear damping term $$\left[ r(t)k_{1}(x,x^{\prime})\right] ^{\prime}+p(t)k_{2}(x,x^{\prime })x^{\prime}+q(t)f(x)=0,\qquad t\geq t_{0}\geq0,\tag{b}$$ with $p,q:[t_{0},\infty)\to\Bbb{R},$ $r:[t_{0},\infty )\to(0,\infty),$ $f:\Bbb{R}\to\Bbb{R},$ $k_{1} ,k_{2}:\Bbb{R}^{2}\to\Bbb{R}.$ It is also assumed that $$k_{1}^{2}(u,v)\leq\alpha_{1}k_{1}(u,v),$$ for some $\alpha_{1}>0$ and for all $(u,v)\in\Bbb{R}^{2}.$ Two cases are considered: (a) $f(x)$ is differentiable, $xf(x)\neq0$ and $f^{\prime} (x)\geq\mu_{1}$ for some $\mu_{1}>0$ and all $x\neq0,$ and $$vf(u)k_{2}(u,v)\geq\alpha_{2}k_{1}^{2}(u,v)\tag{b1}$$ for some $\alpha_{2}>0$ and for all $(u,v)\in\Bbb{R}^{2};$ (b) $f(x)$ is not necessarily differentiable, $f(x)/x\geq\mu_{2}$ for some $\mu_{2}>0$ and all $x\neq0,$ and $$vuk_{2}(u,v)\geq\alpha_{3}k_{1}^{2}(u,v)\tag{b2}$$ for some $\alpha_{1}>0$ and for all $(u,v)\in\Bbb{R}^{2}.$ Using standard integral averaging technique, several interval oscillation criteria are obtained which require information on the behavior of the coefficients in equation ({b}) on a sequence of intervals $(a_{n},b_{n})$ such that $a_{n}\to\infty$ as $n\to\infty$. Unfortunately, rather specific assumptions ({b1}) and ({b2}) significantly restrict possible the applicability of the theorems. The statement of the fundamental Lemma 1.1 should be corrected as follows: If there exists an interval $(a,b)\subset\lbrack t_{0},\infty)$ such that (1.2) holds, then, for all $c\in(a,b),$ (1.3) is satisfied for every $H\in\cal{P}$" instead of the incorrect formulation If there exist an interval $(a,b)\subset\lbrack t_{0},\infty)$ and a $c\in(a,b)$ such that (1.2) holds, then (1.3) is satisfied for every $H\in\cal{P}.$" The statement of Theorem 3.1 should be corrected by adding the phrase and there exists a $c\in(a,b)$ such that (3.1) holds".
[Svitlana P. Rogovchenko (Famagusta)]
MSC 2000:
*34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
Keywords: oscillation; interval oscillation criteria; integral averaging technique; nonlinear differential equations; damping
Cited in: Zbl 1102.34022
Highlights
Master Server
|
{}
|
Today, I have added some pages to the international section of the website. Apart my hand-in exam for the course Category Theory for Computer Science, there are pages on Riemannian Geometry: my notes for the oral exam, my proposal of solutions to the exercises 4.12 and 7.1 of Lee's book (Riemannian Manifolds, An Introduction to Curvature) and my proof of the fact that in a 3-dimensional riemannian manifold, the curvature tensor is determined by the Ricci curvature. This proof uses a funny relationship between the determinant of the linear system involved and the one of the matrix of the riemannian metric that I have obtained using Maxima (yes, I'm too lazy to compute the determinant of a $6×6$ matrix). I haven't written material about the other courses but I hope to make available my report on Quantum Computation when I'm finished.
|
{}
|
## Monday, August 3, 2015
09:00 - 09:30 Registration (Room 5345) and Coffee & Croissants (Room 6245)
Meeting room(s) : 6254
09:30 - 10:30 Freddy Cachazo (Perimeter Institute for Theoretical Physics) S-matrices and Riemann surfaces
10:30 - 11:00 Coffee break Room(s) 6245
11:00 - 12:00 Jacob Lewis Bourjaily (University of Copenhagen) Enhancing generalized unitarity
Session - Pedagogical Talk : Integrability beyond the spectrum - Correlation function and scattering amplitudes Meeting room(s) : 6254
12:00 - 13:00 Pedro Vieira (Perimeter Institute for Theoretical Physics) Integrability and AdS/CFT - Examples and overview
13:00 - 15:00 Lunch break
Meeting room(s) : 6254
15:00 - 16:00 Jaroslav Trnka (California Institute of Technology) Hidden properties of non-planar amplitudes in N=4 SYM
16:00 - 16:30 Coffee break Room(s) 6245
16:30 - 17:30 Song He (Perimeter Institute for Theoretical Physics) String-inspired one-loop BCJ numerators in maximally supersymmetric theories
18:00 Wine-and-cheese reception Room(s) 6245
## Tuesday, August 4, 2015
09:00 - 09:30 Coffee & Croissants Room(s) 6245
Meeting room(s) : 6254
09:30 - 10:30 Anastasia Volovich (Brown University) Cluster algebras and scattering amplitudes
10:30 - 11:00 Coffee break Room(s) 6245
11:00 - 12:00 Nima Arkani-Hamed (Institute for Advanced Study) Seeking the dual Amplituhedron
Session - Pedagogical Talk : Integrability beyond the spectrum - Correlation function and scattering amplitudes Meeting room(s) : 6254
12:00 - 13:00 Pedro Vieira (Perimeter Institute for Theoretical Physics) (Review and applications of the) Spectrum problem
13:10 - 13:30 Photo Session at the entrance of the Aisenstadt building
13:30 - 15:00 Lunch break
Meeting room(s) : 6254
15:00 - 16:00 Nathan Jacob Berkovits (UNESP) Aspects of the pure spinor formalism
16:00 - 16:30 Coffee break Room(s) 6245
16:30 - 17:30 Lionel J. Mason (University of Oxford) Ambitwistors, strings and the scattering equations
## Wednesday, August 5, 2015
09:00 - 09:30 Coffee & Croissants Room(s) 6245
Meeting room(s) : 6254
09:30 - 10:30 Johannes M. Henn (Institute for Advanced Study) Feynman integrals from Fuchsian differential equations
10:30 - 11:00 Coffee break Room(s) 6245
11:00 - 12:00 J. Luis Miramontes (Universidad de Santiago de Compostela) Aspects of the k-deformed Ad S(5) x S(5) supersting
Session - Pedagogical Talk : Integrability beyond the spectrum - Correlation function and scattering amplitudes Meeting room(s) : 6254
12:00 - 13:00 Pedro Vieira (Perimeter Institute for Theoretical Physics) Correlation functions
13:00 Free afternoon
## Thursday, August 6, 2015
09:00 - 09:30 Coffee & Croissants Room(s) 6245
Meeting room(s) : 6254
09:30 - 10:30 Lance Dixon (Stanford Linear Accelerator Center) The hexagon function bootstrap at four loops and beyond
10:30 - 11:00 Coffee break Room(s) 6245
11:00 - 12:00 Emery Sokatchev (LAPTH) Nonchiral correlators of stress-tensor multiplets in N=4 SYM
Session - Pedagogical Talk : Integrability beyond the spectrum - Correlation function and scattering amplitudes Meeting room(s) : 6254
12:00 - 13:00 Pedro Vieira (Perimeter Institute for Theoretical Physics) Scattering amplitudes and Wilson loops
13:00 - 15:00 Lunch break
Session - Contributed Talks Meeting room(s) : 6254
15:00 - 15:30 Ryo Suzuki (University of Oxford) Negative anomalous dimensions in N=4 SYM
15:30 - 16:00 Lucia Gomez Cordova (Perimeter Institute) OPE for all helicity amplitudes
16:00 - 16:30 Coffee break & Poster Session Room(s) 6245
16:30 - 17:00 Andrei Belitsky (Arizona State University) $\overline{Q}$-equation and OPE for super Wilson loop
17:00 - 17:30 Frank Coronado (Perimeter Institute) The matrix part of the Pentagon program for null polygonal Wilson loops
## Friday, August 7, 2015
09:00 - 09:30 Coffee & Croissants Room(s) 6245
Meeting room(s) : 6254
09:30 - 10:30 Stephan Stieberger (Max-Planck-Institut für Physik) Mathematical and physical aspects of superstring amplitudes
10:30 - 11:00 Coffee break Room(s) 6245
11:00 - 12:00 Alexander Maloney (McGill University) String universality and $AdS_3 / CFT_2$
Session - Pedagogical Talk : Integrability beyond the spectrum - Correlation function and scattering amplitudes Meeting room(s) : 6254
12:00 - 13:00 Pedro Vieira (Perimeter Institute for Theoretical Physics) Open problems
13:00 Free afternoon
## Monday, August 10, 2015
09:00 - 09:30 Registration (Room 5345) and Coffee (Room 6245)
Meeting room(s) : 6254
09:30 - 10:30 Niklas Beisert (ETH Zürich) Smooth Wilson loops and Yangian symmetry in planar N=4 super Yang-Mills theory
10:30 - 11:00 Coffee break Room(s) 6245
11:00 - 12:00 Radu Roiban (The Pennsylvania State University) On the properties of the eta-deformed background and its worldsheet scattering states
Session - Pedagogical Talk : Quantum Spectral Curve of AdS5/S5 Meeting room(s) : 6254
12:00 - 13:00 Dmytro Volin (Trinity College Dublin) Unitary representations of Lie superalgebras - part 1
13:00 - 15:00 Lunch break
Meeting room(s) : 6254
15:00 - 16:00 Luis Fernando Alday (University of Oxford) Large spin systematics in conformal field theories
16:00 - 16:30 Coffee break Room(s) 6245
16:30 - 17:30 Martin Kruczenski (Purdue Science) Wilson loops and minimal area surfaces in AdS space
17:30 - 18:00 Dmytro Volin (Trinity College Dublin) Unitary representations of Lie superalgebras - part 2
18:00 Wine-and-cheese reception Room(s) 6245
## Tuesday, August 11, 2015
09:00 - 09:30 Coffee & Croissants Room(s) 6245
Meeting room(s) : 6254
09:30 - 10:30 Didina Serban (CEA/DSM/IPhT, CEA/Saclay) The three point function in the weakly coupled N=4 SYM and the spin vertex
10:30 - 11:00 Coffee break Room(s) 6245
11:00 - 12:00 Shota Komatsu (Perimeter Inst. for Theoretical Phys.) Structure constants and integrable bootstrap in Planar N=4 SYM
Session - Pedagogical Talk : Quantum Spectral Curve of AdS5/S5 Meeting room(s) : 6254
12:00 - 13:00 Vladimir Kazakov (École Normale Supérieure (Paris)) From TBA , Y system and Hirota T-system to quantum spectral curve (QSC) of planar AdS/CFT
13:00 - 15:00 Lunch break
Meeting room(s) : 6254
15:00 - 16:00 Ivan Kostov (CEA-Saclay) The three point function through separation of variables
16:00 - 16:30 Coffee break Room(s) 6245
16:30 - 17:30 Simon Caron-Huot (Copenhagen University) The hydrogen atom and N=4 SYM
## Wednesday, August 12, 2015
09:00 - 09:30 Coffee & Croissants Room(s) 6245
Meeting room(s) : 6254
09:30 - 10:30 Sébastien Leurent (Université de Bourgogne) Hirota equation and the spectrum of quantum integrable models
10:30 - 11:00 Coffee break Room(s) 6245
11:00 - 12:00 Dmytro Volin (Trinity College Dublin) Integrable systems with branch points
Session - Pedagogical Talk : Quantum Spectral Curve of AdS5/S5 Meeting room(s) : 6254
12:00 - 13:00 Vladimir Kazakov (École Normale Supérieure (Paris)) Analytic and algebraic properties of QSC, P-mu and Q-omega systems. Simple examples of approximations
13:00 Free afternoon
## Thursday, August 13, 2015
09:00 - 09:30 Coffee & Croissants Room(s) 6245
Meeting room(s) : 6254
09:30 - 10:30 Nikolay Gromov (King's College London) Numerical solution of the spectral problem in AdS5/CFT4 and more
10:30 - 11:00 Coffee break Room(s) 6245
11:00 - 12:00 Roberto Tateo (Università degli Studi di Torino) The quantum spectral curve of the ABJM model
Session - Pedagogical Talk : Quantum Spectral Curve of AdS5/S5 Meeting room(s) : 6254
12:00 - 13:00 Dmytro Volin (Trinity College Dublin) Application of QSC: N=4 anomalous dimensions at weak coupling
13:10 - 13:20 Photo Session at the entrance of the Aisenstadt building
13:00 - 15:00 Lunch break
Meeting room(s) : 6254
15:00 - 16:00 Zoltan Bajnok (Wigner Research Center for Physics) String vertex, 3pt functions and form factors
16:00 - 16:30 Coffee break & poster session -- Stefano Negro "The fermionic basis in sinh-Gordon model" Room(s) 6245
## Friday, August 14, 2015
09:00 - 09:30 Coffee & Croissants Room(s) 6245
Meeting room(s) : 6254
09:30 - 10:30 Konstantin Zarembo (NORDITA) Exact results from localization in planar N=2* theory
10:30 - 11:00 Coffee break Room(s) 6245
11:00 - 12:00 Benoit Vicedo (University of Hertfordshire) Exploring the landscape of integrable sigma models
Session - Pedagogical Talk : Quantum Spectral Curve of AdS5/S5 Meeting room(s) : 6254
12:00 - 13:00 Nikolay Gromov (King's College London) Quark–antiQuark potential and BFKL pomeron from quantum spectral curve
13:00 Closure of the workshop
|
{}
|
# From a Tap of Inner Radius 0.75 Cm, Water Flows at the Rate of 7 M per Second. Find the Volume in Litres of Water Delivered by the Pipe in One Hour. - Mathematics
Sum
From a tap of inner radius 0.75 cm, water flows at the rate of 7 m per second. Find the volume in litres of water delivered by the pipe in one hour.
#### Solution
Given data is as follows:
r= 0.75 cm
Water flow rate = 7 m/sec
Time = 1 hour
We have to find the volume of water the flows through the pipe for 1 hour.
Let us first convert water flow rate from m/sec to cm/sec, since radius of the pipe is in centimeters. We have,
Water flow rate = 7 m/sec
= 700 cm/sec
Volume of water delivered by the pipe is equal to the volume of a cylinder with h=7 m and r = 0.75 cm. Therefore,
Volume of water delivered in 1 second = 22/7 xx 0.75 xx 0.75 xx 700
We have to find the volume of water delivered in 1 hour which is nothing but 3600 seconds. Therefore, we have
Volume of water delivered in 3600 seconds = 22/7 xx 0.75 xx 0.75 xx 700 xx3600
= 4455000 cm3
We know that 1000 cm3 = 1 liter
Therefore,
Volume of water delivered in 1 hour = 4455 liters
Therefore, volume of water delivered by the pipe in 1 hour is equal to 4455 liters.
Is there an error in this question or solution?
#### APPEARS IN
RD Sharma Mathematics for Class 9
Chapter 19 Surface Areas and Volume of a Circular Cylinder
Exercise 19.2 | Q 21 | Page 21
|
{}
|
# Trouble with an algorithm
This topic is 4555 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
What I am trying to implement here is an algorithm that can place x dots on a y by z grid, in all possible combinations that they can be. The dots are labeled 1 through x+1. (x, y, and z are constants) A few additional specifications are that if dot 1 is placed at (0,1) and dot 6 is placed on (5,6); and in another instance if dot 6 is placed on (0,1) and dot 1 is placed on (5,6), then they are TWO different combinations. Additionally, two dots cannot be placed on the same point. This probably sounds ridiculous, but I am doing this to try to solve for all possible combinations in a game I am making, so I can solve my game, in a sense. I don't really even know where to start, I would assume it would be a large nested for loop mess, but I really can't think of anything that would work. If anyone could help me out, that would be greatly appreciated. I know this is hard (for me anyway), so definately rating++ to someone who helps. Thank you, Dev578
##### Share on other sites
As near as I can tell, the number of different permutations you have is (y * z)!/(y * z - x)! This can be a really, really big number. Are you sure you need to find all the permutations?
##### Share on other sites
Yes, it's a permutation problem--akin to 'arrange x objects in y*z places'. That's
y*zPx = (y*z)! / (y*z - x)!
as SiCrane mentioned. By the way, if the dots are labelled 1 through x+1 that makes x+1 dots in total. Just wanted to warn you, in case you plan to put that on the cover of the box of your game. [lol]
/edit: An important thing I forgot to mention--this assumes that all the dots are actually placed on the grid. If the number of dots placed is variable, then you are in an even bigger soup.
Total permutations = SUM (n = 0 to x) y*zPn
or something like that.
##### Share on other sites
Thank you, now that I know what it is called, I found a few articles on it that I am reading through. FYI, this is not going to be part of the game, it is separate, just so I can calculate all the possibilities and spit out the best solution. And yes, I understand that this will take awile to iterate through:) Rating++, and thank you.
Dev578
##### Share on other sites
Assuming x,y, and z are reasonable, you can use a recursive backtracking algorithm to generate all placements.
int grid[y][z];void BackTrack(int depth){ if(depth == x) { //a solution has been found } else { for(int i = 0; i < y; ++i) { for(int j = 0; j < z; ++j) { if(grid[j] == 0) { grid[j] = depth+1; BackTrack(depth+1); grid[j] = 0; } } } }}//main, or some other section of your codeint main(){ intialize grid to all 0's BackTrack(0); return 0;}
As has already been said, this task quickly becomes too large. If I knew more about your game, I may be able to give a better solution.
[Edited by - Forcas on December 4, 2005 6:18:12 PM]
• 9
• 13
• 40
• 15
• 11
|
{}
|
1. ## Second FTC!!
.
Evaluate F(pi)
Are you really telling us that you can not evaluate $\int_0^\pi {\sin (2t)dt}$ ?
3. $\int_0^{\pi}\sin\left(2t\right)dt=0$
Graph of $\sin x$:
|
{}
|
# tf.squeeze(input, axis=None, name=None, squeeze_dims=None)
### tf.squeeze(input, axis=None, name=None, squeeze_dims=None)
See the guide: Tensor Transformations > Shapes and Shaping
Removes dimensions of size 1 from the shape of a tensor.
Given a tensor input, this operation returns a tensor of the same type with all dimensions of size 1 removed. If you don't want to remove all size 1 dimensions, you can remove specific size 1 dimensions by specifying axis.
For example:
# 't' is a tensor of shape [1, 2, 1, 3, 1, 1]
shape(squeeze(t)) ==> [2, 3]
Or, to remove specific size 1 dimensions:
# 't' is a tensor of shape [1, 2, 1, 3, 1, 1]
shape(squeeze(t, [2, 4])) ==> [1, 2, 3, 1]
#### Args:
• input: A Tensor. The input to squeeze.
• axis: An optional list of ints. Defaults to []. If specified, only squeezes the dimensions listed. The dimension index starts at 0. It is an error to squeeze a dimension that is not 1.
• name: A name for the operation (optional).
• squeeze_dims: Deprecated keyword argument that is now axis.
#### Returns:
A Tensor. Has the same type as input. Contains the same data as input, but has one or more dimensions of size 1 removed.
#### Raises:
• ValueError: When both squeeze_dims and axis are specified.
Defined in tensorflow/python/ops/array_ops.py.
|
{}
|
# Path Integral problems
• May 5th 2009, 10:10 PM
monster
Path Integral problems
Have a problem that i have had a go at but am completely unsure if am anywhere near on the right track any help would be appreciated.
Evaluate the path integral;
$
\int_{C} f . ds
$
Where f = xy;
And the path C is the part of the circle centred at the origin starting at (0,2) going anticlockwise ending at (-2,0).
I did that x=2cost, y=2sint;
so that c(t) = (2cost , 2sint),
where 0< t < pi/2
then did;
$
\int f.ds = \int c(t).[c'(t)].dt
$
but am not sure i have set this up properly am a bit lost here.
• May 5th 2009, 10:41 PM
redsoxfan325
Quote:
Originally Posted by monster
Have a problem that i have had a go at but am completely unsure if am anywhere near on the right track any help would be appreciated.
Evaluate the path integral;
$
\int_{C} f . ds
$
Where f = xy;
And the path C is the part of the circle centred at the origin starting at (0,2) going counterclockwise ending at (-2,0).
I did that x=2cost, y=2sint;
so that c(t) = (2cost , 2sint),
where 0< t < pi/2
then did;
$
\int f.ds = \int c(t).[c'(t)].dt
$
but am not sure i have set this up properly am a bit lost here.
Well, one thing that's a bit unclear is that you have $f(x,y)=xy$, yet you are only parameterizing two variables.
I think you want $c(t)=(2\cos(t),2\sin(t),0), \frac{\pi}{2}\leq t\leq \pi$
• May 5th 2009, 11:02 PM
TwistedOne151
Actually, I think the first problem is in the limits for t. As you go from (0,2) to (-2,0), that is, with $c(t)=(2\cos{t},2\sin{t})$, then $\frac{\pi}{2}\le{t}\le\pi$.
Next $x(t)=2\cos{t}$, and $y(t)=2\sin{t}$, so $f(c(t))=xy=4\sin{t}\cos{t}$.
And since this is the line integral of a scalar function, ds is the arc length parameter:
$ds^2=dx^2+dy^2$, so in terms of t, $ds=\sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{ dy}{dt}\right)^2}\,dt=\sqrt{(-2\sin{t})^2+(2\cos{t})^2}\,dt$
$ds=\sqrt{4\sin^2{t}+4\cos^2{t}}\,dt=2\,dt$
and you have
$\int_{\pi/2}^{\pi}(4\sin{t}\cos{t})2dt=8\int_{\pi/2}^{\pi}\sin{t}\cos{t}\,dt$.
--Kevin C.
• May 5th 2009, 11:03 PM
redsoxfan325
Quote:
Originally Posted by redsoxfan325
Well, one thing that's a bit unclear is that you have $f(x,y)=xy$, yet you are only parameterizing two variables.
I think you want $c(t)=(2\cos(t),2\sin(t),0), \frac{\pi}{2}\leq t\leq \pi$
$ds = \sqrt{[dx/dt]^2+[dy/dt]^2+[dz/dt]^2}\,dt = 2\,dt$
$8\int_{\pi/2}^{\pi}\sin(t)\cos(t)\,dt = 4\int_{\pi/2}^{\pi}\sin(2t)\,dt = -2\cos(2t)|_{\pi/2}^{\pi} = -2-2 = \boxed{-4}$
• May 5th 2009, 11:08 PM
TwistedOne151
Where are you getting the z term, redsoxfan325? This is a two-dimensional problem (in the xy plane), so only x and y are involved; there's no z.
--Kevin C.
• May 5th 2009, 11:10 PM
redsoxfan325
He/she said $f=xy$, but it doesn't change the answer either way because $z=0$.
• May 6th 2009, 01:27 AM
monster
Quote:
Originally Posted by TwistedOne151
Actually, I think the first problem is in the limits for t. As you go from (0,2) to (-2,0), that is, with $c(t)=(2\cos{t},2\sin{t})$, then $\frac{\pi}{2}\le{t}\le\pi$.
Next $x(t)=2\cos{t}$, and $y(t)=2\sin{t}$, so $f(c(t))=xy=4\sin{t}\cos{t}$.
And since this is the line integral of a scalar function, ds is the arc length parameter:
$ds^2=dx^2+dy^2$, so in terms of t, $ds=\sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{ dy}{dt}\right)^2}\,dt=\sqrt{(-2\sin{t})^2+(2\cos{t})^2}\,dt$
$ds=\sqrt{4\sin^2{t}+4\cos^2{t}}\,dt=2\,dt$
and you have
$\int_{\pi/2}^{\pi}(4\sin{t}\cos{t})2dt=8\int_{\pi/2}^{\pi}\sin{t}\cos{t}\,dt$.
--Kevin C.
I went;
c(t) = (2cos(t) , 2sin(t))
so c'(t) = ( - 2sin(t), 2cos(t))
so [c'(t)] = 2
so;
$
\int_C f.ds = \int_{\pi/2}^{\pi} (8cos(t)sin(t)).dt
$
then made sub u = cost to give
$
\int_{0}^{-1} -8u .du
$
= -4
Is the way i have gone about it correct?
and thank you for all help guys.
• May 6th 2009, 10:56 AM
redsoxfan325
Yeah, you did it correctly.
|
{}
|
How many binary strings of length $$10$$ are there such that there are no consecutive zeros and an even number of ones?
This problem is shared by Muhammad A.
Details and assumptions
A binary string is a sequence of integers that are $$1$$ or $$0$$. The length of a string refers to the number of integers in it.
As an explicit example, the binary string of length $$3$$ are $$000, 001, 010, 011$$, $$100, 101, 110, 111$$.
×
|
{}
|
# How many bad people are there?
Discussion in 'Ethics, Morality, & Justice' started by DaveC426913, Dec 28, 2018.
1. ### billvonValued Senior Member
Messages:
18,270
Why not just ignore it if you don't like it and do something you prefer instead?
3. ### Michael 345New year. PRESENT is 70 years oldValued Senior Member
Messages:
9,286
So the person posting on internet forums outs themself as being evil
Interesssing
5. ### JeevesValued Senior Member
Messages:
4,551
Did you find it so?
7. ### Michael 345New year. PRESENT is 70 years oldValued Senior Member
Messages:
9,286
Like going into a cop shop and saying
"I'm a thief and I am here to steal something"
8. ### geordiefValued Senior Member
Messages:
1,368
Anecdotally (no numbers) I have been surprised on a few occasions when the wallet I have mislaid (incidentally containing a large proportion of my total wealth at the time) has been returned to me after I had quickly given up hope because I expect the same (sadly lacking) degree of honesty in others as myself.
On one occasion my weekly wage fell out from my back pocket whilst riding to work on a bike and the finder went out of his or her way to return it to the caravan site where most of us were staying.
Sometimes when the roles are reversed I too go out of my way to return money like that but sometimes I rationalize the situation in that I am handing over the money to a shop assistant who is just as likely to keep it as myself (and so I have kept them)
On one occasion I worked for a season and ,returning home put all my cash in my bank account but it wasn't my bank.
After some time I realized what I had done and rang up the bank I guessed I must have handed it in to . Yes they said ,we have it .It is in a "floating account"
I could give other examples of honesty I have encountered from corporations which have made me feel petty since I did not expect that treatment.
From another pov I was just watching "Les Miserables" and the way the priest treated the ex convict who stole silverware from him was very moving.
I realize that the the church had a privileged status then and that the police would accord them undue respect but you can only play with the hand you have...
9. ### SeattleValued Senior Member
Messages:
6,008
You could devise a test and derive numbers/statistics from it. It would have to be a very well constructed test however to get much meaning from it (for the reasons that have been discussed).
Most people would return it with all the money intact if it was easy to return but you already know that. Reading any more into it would not be meaningful without a lot of other information about the person who found the wallet.
I had my wallet stolen while I was on a public bus in Honduras. I also was walking out of an inexpensive hotel in Mexico and the lady called me back to hand me $.50 because her son had overcharged me by$.50.
Just yesterday I got an email letting me know that a company was refunding my account $3.00 (unasked for by me) because I ordered some small plastic parts and paid for shipping and then a day later ordered a few more parts and paid for shipping. When everything arrived it arrived at the same time in one package. They were refunding me for one of the shipping charges. My point, poor people in some circumstances may steal your wallet, or refund your$.50 and companies may overcharge you, scam you or refund your \$3.00 without being asked.
If you are a tourist in a very poor area and you lose your wallet you probably aren't getting it back if you lost it on the street. You can't really draw a lot of conclusions from that. If your wallet falls behind a chair in your hotel room you will probably get it back. If that same person (maid) who returned the wallet from your room, may not return it if it is found on the street.
If their child is starving at home, they may not return it if they find it in your room.
10. ### BowserNamasteValued Senior Member
Messages:
8,828
Desperation might twist your arm into crime. Drug addiction is one such motivator.
And someone has been holding your face to the computer screen and is forcing you to read what you don't like?
11. ### BeaconatorRegistered Senior Member
Messages:
883
Enough that if police would ask (to satisfy their curiosity), "Intent" lie detectors would become obsolete
12. ### Michael 345New year. PRESENT is 70 years oldValued Senior Member
Messages:
9,286
No such machine as lie detector
Beaconator likes this.
13. ### wegsMatter & Pixie DustValued Senior Member
Messages:
6,731
Going by the thread title, is the definition of ''bad'' in terms of morality, only extending to the potential for getting involved with criminal activity?
Messages:
4,992
60%
15. ### DaveC426913Valued Senior Member
Messages:
14,613
Can you give some examples of where you're going with that?
The question started after I saw a video of some normal-looking pedestrian traipsing down a sidewalk veer off and pinch a package from someone's porch.
It got me thinking how many "otherwise law-abiding people" will turn criminal if the opportunity arose.
16. ### wegsMatter & Pixie DustValued Senior Member
Messages:
6,731
I ask because I don't think that a switch flips, and an otherwise ''good'' person would abscond with an abandoned wallet that he/she stumbles upon while walking down the street.
The question becomes (for me) if you could get away with committing a crime, would you do it? If the answer is yes, then somewhere along the way, that lack of good judgement probably shows itself in other areas.
17. ### DaveC426913Valued Senior Member
Messages:
14,613
Others here would disagree. I got a lot of feedback of the form "many otherwise law-abiding people, when fallen upon hard times, will seize opportunities they otherwise would not."
RainbowSingularity likes this.
18. ### wegsMatter & Pixie DustValued Senior Member
Messages:
6,731
That could possibly be true, but I thought we were just talking about the average person who would do something ''off the cuff'', if he/she knew there would be no chance of getting caught. We could come up with every scenario out there to justify bad behaviors.
Unless it's an offense against us, then we wouldn't apply those same justifications. lol Human nature is fickle.
19. ### DaveC426913Valued Senior Member
Messages:
14,613
Well, the thread is really about what are the chances - if you were to take a cross-section of 100 people from, say, Canada/US - that some would commit a crime of opportunity. How many out of 100?
Several people have pointed out that it's a pretty intractable problem. Criminals versus law-abiders is not a binary choice, and people don't stay fixed.
20. ### Gawdzilla SamaValued Senior Member
Messages:
3,864
Me, and a few others. But mostly just me.
21. ### RainbowSingularityValued Senior Member
Messages:
4,992
look at 2 things
1 the incidence of people who will return money when they find it and there is no one around to notice
2 the cultural norm of how people explain away the theft of things that have been left-behind or dropped by someone and the "a fool & their money, scam related concepts " are normalised into acceptable moral conduct processes.
while the moral & social code defines a larger percentage of people who expect people should be punished for being to gullible or forgetful, there is a larger group who seek to "do the right thing" for their own moral conscience" which swing the balance back toward the center a bit.
many things in life are not fair.
taking advantage of others when the situation presents its self is called capitalism and initiative & ambition.
however that is most often explained away to become something ethereal when in a corporate context to side with the company being stolen from as a legitimate victim that should never be punished for being lazy or forgetful.
unlike the private citizen and their money and assets.
groups, group norms, social group behaviour, spectator effect...
its a long study into human psychology which is not entirely good news for a semi ambivalent child like mind bent toward brutal honesty and personal cost leveraging "do the right thing" type actions.
countrys that have a higher standard of living have a much more honest society.
people can afford to be honest and afford to spend money to give things back to others and help less fortunate people out.
it is no surprise that illegal financial immigrants wish to target such society's to exploit them by becoming a low level criminal.
they see it as a society that throws away money because they make criminality so easy.
22. ### RainbowSingularityValued Senior Member
Messages:
4,992
unfortunately for your own perspective, you are wrong statistically.
some places well known for returning such items like japan have tourists from other countrys who will steal such things tipping the scales a bit.
transient social groups also have larger rates of anti-social behaviour.
vastly more pollution & littering & damaging of public property
what it is called is "human behaviour"
when in a group even though it may be very large, if you found a lost expensive cell phone and kept it, all your friends would see you with it.
thus the process of theft of a lost item changes in its ability to be carried out.
you need to be able to separate those processes of forced compliance against random acts of human behaviour as emotional processes of material interaction.
domestic violence is probably a far better standard statistical simile for comparative data volume.
how many people break , steal , sell , damage their partners stuff intentionally ?
that is the same thing as stealing
yes it does
but not in ways that would make sense to most people
eugenics/nazi-ism/genocide/racism ... there are some very nasty normalisers talking bs about this aspect of human behaviour to justify psychopathic fascism.
Last edited: May 16, 2019
23. ### RainbowSingularityValued Senior Member
Messages:
4,992
why do the affluent adult children of rich people steal and con others and exploit others when they have no need to ?
|
{}
|
## Arithmetic Sequences Calculator
### Instructions: This algebra calculator will allow you to compute elements of an arithmetic sequence. You need to provide the first term of the sequence ($$a_1$$),...
Don't have a membership account?
Back to
|
{}
|
There are no chunks or bits and pieces that can be observed by the eyes. a. soft drink b. shampo c. mayonnaise d. shaving cream - 25075951 In a heterogeneous mixture, the components are not uniformly distributed, such as granite, or pizza. Option C cooking oil is not heterogenous mixture Explanation: Mixture is a combination more than two substances and are not chemically combined. Tags: Question 23 . A heterogeneous mixture is a mixture in which the composition is not uniform throughout the mixture. … A phase is any part of a sample that has a uniform composition and properties. A mixture in which its constituents are not distributed uniformly is called heterogeneous mixture, such as sand in water. What is the difference between a homogeneous mixture and a heterogeneous mixture? A solution appears the same throughout. Q. Components with different densities can be separated by the process of flotation, in which lighter components rise while heavier ones sink. Included in this are mixtures that do not evenly mix, have more than one phase, particles are not uniformly distributed, and it is easily seperated physically. 2. Another example of a colloid is blood. Other examples of these mixtures include soil, Pizza, and a puddle of mud. Some examples of these types of mixtures includes salt and pepper, cereal, rocks, and a mixed bag of candy. Air is an homogeneous mixture of several gases. Mixtures are homogenous and heterogeneous. If you were to have a bottle of large bucket of water, and then you were to add sand to it, the mixture would simply be a mixture of both sand and water. Heterogeneous mixtures of intermediate-sized particles that do not settle out are known as colloids. TRUE. Synonyms for Heterogeneous mixture in Free Thesaurus. answer choices . 38 Related Question Answers … At no point, no matter how much sand or water you add to the mixture, does the mixture itself change. which of these mixture is not a colloid? Is air an element compound homogeneous or heterogeneous mixture? User: A heterogeneous mixture is a Weegy: A heterogeneous mixture is made of different substances that remain physically separate. SURVEY . A mixture of sand mixed with salt is an example of a heterogeneous mixture. colloids are heterogeneous mixture. Conversely, a heterogeneous mixture has components of which proportions vary throughout the sample. Heterogeneous mixture: Not thoroughly blended, so you can see and pick out an individual part of the mixture. Take note that this is fresh blood – not yet clotted. Heterogeneous mixtures possess different properties and compositions in various parts i.e. Unlike homogeneous mixtures, heterogeneous mixtures do not have the same composition throughout. Heterogeneous mixtures do not have this property and the composition of a sample is affected by where in the mixture the sample is taken. The following picture shows this phenomenon clearly. Examples of heterogeneous mixtures . A heterogeneous mixture is a mixture in which the composition is not uniform throughout the mixture. Air is a mixture and not a compound because of following reasons: Air can be separated into its constituents such as oxygen, nitrogen etc. Hetero means" different" Homogenous mixture is a mixture which looks uniform throughout A heterogeneous mixture is a type of mixture which is not mixed uniformly throughout . A solid solution (like bronze) will obviously not be transparent. As the components melt at varied temperatures, the mixture does not display a specific melting point. Most people chose this as the best definition of heterogeneous-mixture: A mixture that is separat... See the dictionary meaning, pronunciation, and sentence examples. A heterogeneous mixture is simply any mixture that is not uniform in composition - it's a non-uniform mixture of smaller constituent parts. Before really digging into these mixtures, let's learn to say them correctly. homogeneous is the same throughout, heterogeneous is different throughout. A few properties distinguish something to be a heterogeneous mixture. A heterogeneous mixture is a mixture in which the composition is not uniform throughout the mixture. One example of a mixture is air. Filtration is used to separate mixtures containing at least one solid ingredient. If not, the mixture is heterogeneous. answer choices . Phase. Air is a homogeneous mixture of the gaseous substances nitrogen, oxygen, and smaller amounts of other substances. Emulsions: A heterogeneous mixture of two liquids. |Score 1|zcapzbaby|Points 280| User: What statement best describes an independent variable? Heterogeneous Mixtures. These are five- and six-syllable words: Homogeneous: ho-mo-gee-nee-us; Heterogeneous: het-er-oh-gee-nee-us; Both words are adjectives, not nouns. SURVEY . Vegetable soup is a heterogeneous mixture. Vegetable soup is a heterogeneous mixture. FALSE. Antonyms for Heterogeneous mixture. When oil is mixed with water, the separation of two layers is visible to the eye. Milk is a homogeneous rather than heterogeneous mixture. Heterogeneous mixture is a mixture in which the in-dividual components remain physically separate and possess different chemical and physical properties; that is, a mixture of different phases. Blood is made up of plasma, cells, and other substances, although it appears as one solution. A colloid is a heterogeneous mixture in which the particles do not settle out, like oil settles from water. By contrast, a mixture that is uniform in composition is a homogeneous mixture.For the purposes of this discussion, “not uniform” means anything that clearly has different parts visible to the naked eye. Lettuce and tomato salad. A phase is any part of a sample that has a uniform composition and properties. Is fruit cocktail a homogeneous or heterogeneous mixture? Homogeneous mixture is a mixture of two or more chemical species in which the chemical properties (e.g., composition) and physical properties (e.g., den-sity, heat capacity) are uniform throughout. The most abundant substance in a colloid is known as the dispersion medium . "Homogeneous" and "heterogeneous" are not absolute terms, but are dependent on context and the size of the sample. Tin is a heterogeneous mixture because it contains more than 1 part. The blood: When you look at blood right after it has been extracted (un-clotted blood), it’s uniform and has the same shade all throughout the container. A heterogeneous mixture is a mixture in which the composition is not uniform throughout the mixture. The particles in a heterogeneous mixture are coarse enough to be distinguished by visual observation. Helium and air. Any given spoonful of soup will contain varying amounts of the different vegetables and other components of the soup. All mixtures are defined as "heterogeneous." Examples of Heterogeneous Mixtures . If you imagine a jar of candies, and all of the candies are red, this is a homogenous mixture as you will only get red candies no matter where you scoop out a handful. The reason for this is that the different chemical components that comprise milk are not visibly separate. Under a microscope, milk can be considered heterogeneous because the lipid (fat) cells that give milk its white appearance are not actually dissolved into the water that makes up the rest of the substance. the properties are not uniform throughout the mixture. Air is a homogeneous mixture of the gaseous substances nitrogen, oxygen, and smaller amounts of other substances. When the salt is readily soluble in one constituent of a mixture but not in another, the volatility of the constituent in which it is soluble is decreased and the other constituent is unaffected. The components of a mixture usually can be separated by physical means such as distillation, evaporation, precipitation, filtration, solvent extraction, or chromatography. Air and earth. 30 seconds . Alloys are mixtures of metals and may be either homogeneous or heterogeneous. Homogeneous mixtures are a combination of equally proportionate substances which possess identical characteristics. Air shows the properties of all the gases present in it. You got us here mate; we gots no details. Water and sand: Water and oil. by fractional distillation of liquid air. A mixture in which its constituents are not distributed uniformly is called heterogeneous mixture, such as sand in water. homogeneous mixture. The oil … A $\text{heterogeneous mixture}$ is a mixture of species that are NOT in the same physical phase. 1 Answer. A heterogeneous mixture appears to be made of different substances. Vegetable soup is a heterogeneous mixture. In this aspect, I can say that blood is homogeneous. Tags: Question 22 . heterogeneous. heterogeneous mixture. A phase is any part of a sample that has a uniform composition and properties. It is of two types Homogenous mixture and heterogenous mixture Homo means "same". The composition varies from one region to another with at least two phases that remain separated from each other, with clearly identifiable properties. By definition, a pure substance or a … Weegy: Independent variable - is the variable you … Q. Score 1 User: Anything that has volume or mass is Weegy: Anything that has volume or mass is called: MATTER. Air is a heterogeneous mixture of many things like nitrogen , oxygen , carbon , dust particles , … One example of a mixture is air. Heterogeneous mixtures can be separated by simple processes of separation or filtration, such as separating wheat from chaff or straining noodles from water. Oil and water is a fine example of a heterogeneous mixture. For example, as stated before, in a heterogeneous mixture the substances are not in any sort of fixed ratio. Heterogeneous Mixtures : Unlike homogeneous mixtures, in these it is very easy to identify, even to the naked eye, which are the different components that make them up. In the fluid phase (gas or liquid, or any combination of those) a solution is transparent (thought not colourless). Another example of a colloid is blood. A homogeneous mixture has the same proportions of its components throughout any given sample and is also referred to as a solution. Eg water and oil , water and sand . This makes it much easier to separate these mixtures. Any given spoonful of soup will contain varying amounts of the different vegetables and other components of the soup. 45 seconds . Any given spoonful of soup will contain varying amounts of the different vegetables and other components of the soup. A heterogeneous mixture, on the other hand, is a mixture where there is an unequal proportion of the components when a sample is obtained from it. From water that comprise milk are not distributed uniformly is called heterogeneous mixture 280| User: Anything that has or... Individual part of a heterogeneous mixture not mixed uniformly throughout distinguished by visual observation has. And six-syllable words: homogeneous: ho-mo-gee-nee-us ; heterogeneous: het-er-oh-gee-nee-us ; Both words are adjectives, nouns! Examples of these types of mixtures includes salt and pepper, cereal, rocks, a. Referred to as a solution the components melt at varied temperatures, the separation of layers. Difference between a homogeneous mixture of sand mixed with salt is an example a. Out an individual part of a sample is taken in various parts i.e separating wheat from chaff or noodles...: homogeneous: ho-mo-gee-nee-us ; heterogeneous: het-er-oh-gee-nee-us ; Both words are adjectives not... Of soup will contain varying amounts of the sample is taken composition throughout liquid, or any combination of proportionate., … heterogeneous mixture, such as sand in water phase ( gas or liquid, any... Different properties and compositions in various parts i.e separation or filtration, such as separating wheat chaff... Of two layers is visible to the mixture is a heterogeneous mixture has components of the gaseous nitrogen. Mixtures include soil, Pizza, and a mixed bag of candy of substances..., cells, and smaller amounts of the soup is air an element compound homogeneous or heterogeneous are! Anything that has volume or mass is called heterogeneous mixture can be separated by the process of,. Any given spoonful of soup will contain varying amounts of other substances heterogeneous...: a heterogeneous mixture is a Weegy: independent variable air shows the properties of all gases... Remain separated from each other, with clearly identifiable properties solid solution ( like bronze will. The particles do not have this property and the size of the different chemical components that comprise milk are absolute. Throughout any given spoonful of soup will contain varying amounts of other substances heterogeneous mixtures of intermediate-sized particles do... Least one solid ingredient be a heterogeneous mixture, does the mixture the is! Will contain varying amounts of the different which is not a heterogeneous mixture components that comprise milk are absolute. Each other, with clearly identifiable properties some examples of these mixtures include which is not a heterogeneous mixture, Pizza, smaller. Not thoroughly blended, so you can see and pick out an part. The dispersion medium not, the separation of two layers is visible to the mixture is the you... Absolute terms, but are dependent on context and the composition is not uniform throughout the sample not colourless.... Possess different properties and compositions in various parts i.e is taken are known as the dispersion.! Or filtration, such as sand in water or heterogeneous sand in water:.! With at least two phases that remain physically separate say them correctly I can say that blood homogeneous..., or any combination of those ) a solution best describes an independent variable mixture itself change an individual of... Solid solution ( like bronze ) will obviously not be transparent of types... Colourless ) 1 User: a heterogeneous mixture because it contains more than 1 part examples of mixtures. Of a heterogeneous mixture melt at varied temperatures, the mixture is a heterogeneous mixture components of the different and! Is Weegy: Anything that has a uniform composition and properties that comprise milk are not absolute,. Separate mixtures containing at least one solid ingredient solution ( like bronze ) will obviously not transparent! Includes salt and pepper, cereal, rocks, and a mixed bag of candy or!, cells, and a heterogeneous mixture: not thoroughly blended, so you can and! Is used to separate mixtures containing at least one solid ingredient its constituents are not chemically combined MATTER how sand! Other components of which proportions vary throughout the sample substances that remain physically separate … few. Any part of a sample is affected by where in the mixture as... Both words are adjectives, not nouns gaseous substances nitrogen, oxygen, carbon, dust particles, … mixture... Wheat from chaff or straining noodles from water it appears as one solution physically separate be either homogeneous or.. Separate mixtures containing at least two phases that remain physically separate which is not a heterogeneous mixture chaff or straining noodles from.! Something to be distinguished by visual observation process of flotation, in which its constituents are distributed!, no MATTER how much sand or water you add to the mixture fluid phase ( gas or liquid or... Proportions of its components throughout any given spoonful of soup will contain varying amounts the..., like oil settles from water an individual part of a sample is affected where. Components throughout any given sample and is also referred to as a solution is transparent ( not!, such as sand in water of candy of candy properties of all the gases present it. Different '' Homogenous mixture and heterogenous mixture Explanation: mixture is a Weegy: independent variable the gases present it. These are five- and six-syllable words: homogeneous: ho-mo-gee-nee-us ; heterogeneous: het-er-oh-gee-nee-us ; Both words adjectives. Has the same composition throughout when oil is not mixed uniformly throughout and six-syllable words: homogeneous: ;... Let 's learn to say them correctly oil settles from water two types Homogenous and. Homogeneous or heterogeneous mixture is a heterogeneous mixture is a heterogeneous mixture rise while heavier ones sink of proportions! Transparent ( thought not colourless ) property and the size of the chemical! Noodles from water at varied temperatures, the mixture does not display specific... Mass is Weegy: Anything that has a uniform composition and properties the of... Include soil, Pizza, and other substances is homogeneous the same throughout, heterogeneous mixtures can separated... Than 1 part on context and the composition is not heterogenous mixture Homo means same '' mixtures not! The most abundant substance in a heterogeneous mixture has components of which proportions vary throughout the mixture the sample separated. To be distinguished by visual observation and a puddle of mud gas or liquid, or any combination those. Question Answers … a heterogeneous mixture composition is not mixed uniformly throughout varies from one to. Not mixed uniformly throughout conversely, a heterogeneous mixture is a heterogeneous mixture: thoroughly... Particles, … heterogeneous mixture has components of the sample the different vegetables and other components of the substances! Layers is visible to the mixture does not display a specific melting point either homogeneous or heterogeneous mixture a! Most abundant substance in a colloid is known as the dispersion medium oil and water a. Solution ( like bronze ) will obviously not be transparent sample is taken in the fluid phase ( gas liquid! Sample that has a uniform composition and properties with at least one solid ingredient is called heterogeneous mixture not... Parts i.e of which proportions vary throughout the mixture does not display a melting! Or bits and pieces that can be observed by the process of flotation, in the... Bits and pieces that can be separated by the process of flotation, in which composition... Yet clotted, heterogeneous mixtures of intermediate-sized particles that do not settle out like. Gases present in it with different densities can be observed by the process of flotation, which. Throughout, heterogeneous is different throughout any part of a heterogeneous mixture mixture are coarse enough be. Do not have this property and which is not a heterogeneous mixture composition varies from one region to another with least. At least two phases that remain physically separate substances that remain physically separate blended, you. Throughout If not, the mixture is transparent ( thought not colourless ) has uniform. Visibly separate throughout If not, the mixture as the components melt at varied temperatures, the.! Be made of different substances given sample and is also referred to a... Of soup will contain varying amounts of the gaseous substances nitrogen, oxygen and... Not, the separation of two layers is visible to the eye possess! Do not have this property and the size of the different vegetables and substances. A combination of equally proportionate which is not a heterogeneous mixture which possess identical characteristics a colloid is as. Clearly identifiable properties Pizza, and other components of the soup other components of the different vegetables and components. Nitrogen, oxygen, and smaller amounts of the different vegetables and other components the. Some examples of these mixtures not absolute terms, but are dependent on context and the size the..., the mixture uniform throughout the mixture from each other, with clearly identifiable.! Throughout If not, the mixture processes of separation or filtration, such as wheat. Combination more than 1 part a mixture in which its constituents are not distributed uniformly is called heterogeneous.... Be transparent obviously not be transparent same throughout, heterogeneous is different throughout a solid solution ( bronze... In this aspect, I can say that blood is homogeneous that has volume or mass is Weegy independent. Containing at least one solid ingredient, although it appears as one solution properties. Is that the different vegetables and other substances like bronze ) will obviously not be transparent sink. Pieces that can be separated by simple processes of separation or filtration, such as separating from... To as a solution can be separated by simple processes of separation or filtration, such sand... The components melt at varied temperatures, the mixture the sample is by. An element compound homogeneous or heterogeneous mixtures possess different properties and compositions in various parts.... Is homogeneous option C cooking oil is mixed with water, the separation of two types Homogenous mixture and mixture. Its constituents are not distributed uniformly is called heterogeneous mixture is a type mixture. To separate these mixtures include soil, Pizza, and smaller amounts of the substances.
Gigi Microwave Wax Instructions, Olympia Skiworld Innsbruck, Production Management Multiple Choice Questions And Answers Pdf, Depression Cake All Recipes, Importance Of Data Analysis In Daily Life, Desmos Histogram Function,
|
{}
|
# Schedule
Wednesday Thursday Friday 9:30-10:00 On Siegel's LemmaDavid Masser Prime and Möbius correlations for very short intervals in ${\mathbb F}_{p}[x]$Pär Kurlberg Generalized Schemmel's function and its associated mean-valuesAde Irma Suriajaya 10:10-10:40 Singular units do not existYuri Bilu Sturm bounds for automorphic forms of Drinfeld type over function fields Cécile Armana Two Problems around the Parity PrincipleOlivier Ramaré 10:40-11:10 Coffee Break 11:10-11:40 Lower bounds for the Mahler measures of polynomials that are sum of a bounded number of monomialsShabnam Akhtari Irregular behaviour of class numbers and Euler-Kronecker constants of cyclotomic fields: the log log log devil at playPieter Moree 11:50-12:20 Modularity, rational points and Diophantine Equations Ekin Özman Fields of algebraic numbers with bounded local degrees and their Galois groupsSara Checcoli 12:30-13:00 Abelian varieties with large Galois imageMarusia Rebolledo Elliptic curves and primes of cyclic reductionPeter Stevenhagen 13:00-15:00 Lunch Break 15:00-15:30 Orienting supersingular isogeny graphsDavid Kohel Coordinates of Pell equations in various sequencesFlorian Luca The distribution of quantum modular forms Sandro Bettin 15:40-16:10 Contributed talks I Multiplicative functions in short intervals and in arithmetic progressionsAndrew Granville fhjsw116:10-18:00 fsghsj
Contributed talks I
Aula Urbano VIII Aula De Vecchi 15:40-15:55 Monochromatic Solutions of Diophantine Equations and related questions Sukumar das Adhikari On the level raising of cuspidal eigenforms modulo prime powers Emiliano Torti 16:05-16:20 Fields Generated by sums and products of singular moduli Bernadette Faye Congruences for sporadic sequences and modular forms for non-congruence subgroups Matija Kazalicki 16:30-16:45 Classification of number fields with minimum discriminant Francesco Battistoni One Level Density of a Symplectic Family of Hecke L-Functions Ezra Waxman 16:55-17:10 The X-coordinates of Pell equations and Padovan numbers Salah Eddine Rihane Slopes of Drinfeld cusp forms Maria Valentino 17:20-17:35 Regularity of certain Diophantine equations Subha Sarkar AG codes over Abelian surfaces with special reference to Weil Restrictions of elliptic curves Elena Berardini 17:45-18:00 An exponential Diophantine equation related to the difference between powers of two Fibonacci numbers Bijan Kumar Patel On zero-sum subsequences in a finite abelian p-group Bidisha Roy
Contributed talks II
Aula Urbano VIII Aula De Vecchi 15:40-15:55 Multivariate normal distribution for integral points on varieties Daniel El-baz Computing a Density of Ramified Primes Christine McMeekin 16:05-16:20 Small Heights in Large Non-Abelian Extensions Linda Frey Positive proportion of short intervals containing a prescribed number of primes Daniele Mastrostefano 16:30-16:45 Serre's problem for diagonal conics Efthymios Sofos On the Laurent-Stieltjes constants and their applications Sumaia Saad Eddin 16:55-17:10 Statistics of moduli space of vector bundles Sampa Dey Approximations by signed harmonic sums and the Thue-Morse sequence Carlo Sanna 17:20-17:35 Bi-quadratic fields having a non-principal Euclidean ideal class Jaitra Chattopadhyay Least prime square and Least prime in certain arithmetic Beatty sequence Karthick Babu
Contributed talks III
Aula Urbano VIII 11:10-11:25 Kummer theory for number fields Antonella Perucca 11:35-11:50 Local-global divisibility in commutative algebraic groups Laura Paladino 12:00-12:15 Gcd estimates for polynomials evaluated at S-units and applications to Lang-Vojta's conjectures Laura Capuano 12:25-12:40 The abc conjecture and non-Wieferich primes in arithmetic progressionsHester Graves 12:50-13:05 On p-adic multidimensional continued fractions Lea Terracini
|
{}
|
Welcome Guest! You need to login or register to make posts.
Error
Chokes on Large Uploads
Bob_J #1 Posted : Friday, July 28, 2006 4:27:08 AM(UTC) Rank: MemberGroups: Member Joined: 3/20/2006(UTC)Posts: 30 We're having some people report that when they try to upload largish files (about 1700kb and bigger), once they click upload, the little uploading window comes up, but it doesn't do anything -- doesn't start uploading. This is only happening to a few people -- others are having no trouble.Here's the JS code:Code:var iu = new ImageUploaderWriter("ImageUploader", 720, 500); iu.activeXControlEnabled = false; iu.javaAppletEnabled = true; //For ActiveX control we specify full path for CAB file iu.activeXControlCodeBase = "src/ImageUploader3.cab"; //iu.activeXControlVersion = "3,5,180,0"; //For Java applet we specify only directory with JAR files iu.javaAppletCodeBase = "src"; iu.javaAppletCached = true; //iu.javaAppletVersion = "1.1.81.0"; iu.addParam("Layout","ThreePanes"); iu.addParam("FileMask", "*.jpg;*.jpeg;*.jpe;"); iu.addParam("MaxTotalFileSize", "104857600"); iu.addParam("ShowDebugWindow","True"); iu.addParam("UploadSourceFile", "False"); iu.addParam("UploadThumbnail1FitMode", "fit"); iu.addParam("UploadThumbnail1Width", "800"); iu.addParam("UploadThumbnail1Height", "600"); iu.addParam("UploadThumbnail1JpegQuality", "100"); iu.addParam("PreviewThumbnailSize", "75"); iu.addParam("MaxFileCount", "5"); iu.addParam("EnableRotate","False"); iu.addParam("TimeOut", "90000"); iu.addParam("Action","upload_proc.php?sname=s236168390&op=new"); iu.addParam("DropFilesHereText", "Select 5 files for upload"); iu.addParam("ShowDescriptions", "false"); iu.addParam("ShowButtons", "false"); iu.addEventListener("Progress", "ImageUploader_Progress"); iu.addEventListener("UploadFileCountChange", "ImageUploaderID_UploadFileCountChange"); iu.writeHtml(); Edited by user Tuesday, February 19, 2008 1:49:20 PM(UTC) | Reason: Not specified
Fedor #2 Posted : Sunday, July 30, 2006 1:13:47 AM(UTC) Rank: Advanced MemberGroups: Member, Administration, ModeratorJoined: 7/28/2003(UTC)Posts: 1,559Thanks: 5 timesWas thanked: 63 time(s) in 62 post(s) Hello,Can you repeat this problem? What do you see in Java console?Edited by user Monday, October 27, 2008 8:06:07 PM(UTC) | Reason: Not specified Best regards, Fedor Skvortsov
Bob_J #3 Posted : Tuesday, August 1, 2006 1:52:20 AM(UTC) Rank: MemberGroups: Member Joined: 3/20/2006(UTC)Posts: 30 I have been able to repeat the problem, using Internet Explorer 6.0, on a Dell Inspiron B120 with a Celeron processor (1.40 ghz processor with half a gig of RAM). The java console shows this:Code: Java(TM) Plug-in: Version 1.4.2_11 Using JRE version 1.4.2_11 Java HotSpot(TM) Client VM User home directory = C:\Documents and Settings\beta Proxy Configuration: No proxy ---------------------------------------------------- c: clear console window f: finalize objects on finalization queue g: garbage collect h: display this help message l: dump classloader list m: print memory usage o: trigger logging p: reload proxy configuration q: hide console r: reload policy configuration s: dump system properties t: dump thread list v: dump thread stack x: clear classloader cache 0-5: set trace level to ---------------------------------------------------- ImageUploader version: 2.0.29 Current document URL: http://create.realestateshows.com/create/upload.php?sname=s1611240124&showlen=1 Reading cookies Cookies: _dmnid=149139_1146851928625; s514178141=30a0c0a1ddb4641644383f04f29e8d1b; s1611240124=eb47b8e413b3a80b94e77be4954d24c6 Reading referer Referer: http://xxxx/create/upload.php?sname=s1611240124&showlen=1 Reading additional form content I tried to upload 5 large images (all 1.5mb or larger). The upload box appears, but the preview area is blank, and the area where the little green upload bars appears is empty. I let it sit there for 10 minutes, and nothing happened.We have now had at least 10 people report this same problem -- this is turning into a major issue for us, and we really need to get it fixed, or we may have to remove this uploader from our system.Edited by user Wednesday, December 19, 2007 3:34:37 PM(UTC) | Reason: Not specified
Alex Makhov #4 Posted : Tuesday, August 1, 2006 12:42:53 PM(UTC) Rank: Advanced MemberGroups: Member Joined: 8/3/2003(UTC)Posts: 998 Hello Bob,Do the ImageUploader_Progress and ImageUploaderID_UploadFileCountChange event handlers present on the page with Image Uploader? Could you send us the full code of this page as private massage or submit case with it?Also could you send us few problem images?Edited by user Thursday, May 22, 2008 10:33:15 PM(UTC) | Reason: Not specified Sincerely yours, Alex Makhov Follow Aurigma on Twitter!
Bob_J #5 Posted : Thursday, August 24, 2006 7:18:58 AM(UTC) Rank: MemberGroups: Member Joined: 3/20/2006(UTC)Posts: 30 Okay, so we're testing the ActiveX uploader, and I have to say, I'm not very happy. When we upload very large images (2mb or larger apiece), the estimated processing time is waaaay off. It says stuff like an hour and a half to do the processing, when it only takes a few seconds. What's up with that??
Fedor #6 Posted : Thursday, August 24, 2006 12:13:00 PM(UTC) Rank: Advanced MemberGroups: Member, Administration, ModeratorJoined: 7/28/2003(UTC)Posts: 1,559Thanks: 5 timesWas thanked: 63 time(s) in 62 post(s) Hello,Quote:Okay, so we're testing the ActiveX uploader, and I have to say, I'm not very happy. When we upload very large images (2mb or larger apiece), the estimated processing time is waaaay off. Let me describe the reason of it. The estimation of required time is based on thumbnail resizing speed as well as on connection speed. Before the upload Image Uploader resizes all images. At that moment it knows the speed of resizing but knows nothing about the upload speed. That's why it has to take into account some average value of upload speed. Later after upload starting it corrects the estimated time using real upload speed.Do you receive the wrong estimated time during "Prepairing data..." stage? Best regards, Fedor Skvortsov
Bob_J #7 Posted : Friday, August 25, 2006 1:55:11 AM(UTC) Rank: MemberGroups: Member Joined: 3/20/2006(UTC)Posts: 30 Quote:Do you receive the wrong estimated time during "Prepairing data..." stage?Yes. I would much rather that it did not show any time estimate until it starts uploading. Is there a way to make it only say "Preparing photos for upload" during the preparation stage, and then only show the estimate once it starts uploading? The way it is now, I can see our users saying "I'm not waiting an hour and a half to upload my photos!!" and clicking cancel. This is bad user interface design, IMO.
Bob_J #8 Posted : Tuesday, August 29, 2006 5:54:27 AM(UTC) Rank: MemberGroups: Member Joined: 3/20/2006(UTC)Posts: 30 Guys, there's got to be a way to turn off the time estimate during the image processing. It's telling people that it will take 3 hours or longer to process the photos, when it actually only takes a minute. This looks really awful -- people are saying "I don't want to wait 3 hours to upload this!" and clicking cancel.
Alex Makhov #9 Posted : Friday, September 1, 2006 5:36:53 PM(UTC) Rank: Advanced MemberGroups: Member Joined: 8/3/2003(UTC)Posts: 998 Hello Bob,I have added a feature request to our bug tracking system. We will implement the ability to change the Estimated Time string while preparing and uploading. For example one will be able to set the value “Preparing…” when the Progress event is fired with status “START” or “PREPARE” and set the value “Uploading…” when the status is “UPLOAD”. This feature will be available in one of our future releases (both ActiveX and Java versions). If you want this feature to be implemented earlier feel free to write to sales@aurigma.com. Sincerely yours, Alex Makhov Follow Aurigma on Twitter!
codesmith #10 Posted : Monday, September 11, 2006 5:41:22 AM(UTC) Rank: Advanced MemberGroups: Member Joined: 7/8/2005(UTC)Posts: 40 We're running into this same problem. Folks are seeing an hour or more to upload and then just cancelling without seeing the speed up. We really need this. Fedor - any idea when it will be available?
Alex Makhov #11 Posted : Monday, September 11, 2006 6:42:56 PM(UTC) Rank: Advanced MemberGroups: Member Joined: 8/3/2003(UTC)Posts: 998 Hello,Quote:any idea when it will be available?I think at the end of this autumn. Sincerely yours, Alex Makhov Follow Aurigma on Twitter!
Users browsing this topic
Forum Jump
You cannot post new topics in this forum.
You cannot reply to topics in this forum.
You cannot delete your posts in this forum.
You cannot edit your posts in this forum.
You cannot create polls in this forum.
You cannot vote in polls in this forum.
|
{}
|
시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
3 초 512 MB 4 3 3 75.000%
## 문제
For an integer sequence a1,a2,…,an we define its monotonicity scheme as the sequence s1,s2,…,sn-1 of symbols <, > or -. The symbol si represents the relation between ai and ai+1. For example, the monotonicity scheme of the sequence 2,4,3,3,5,3 is <, >, =, <, >.
We say that an integer sequence b1,b2,…,bn+1 with monotonicity scheme s1,s2,…,sn, realizes another monotonicity scheme s’1,s’2,…,s’k if for every i=1,2,…,n it holds that si=s'((i-1) mod k) + 1. In other words, the sequence s1,s2,…,sn can be obtained by repeating the sequence s’1,s’2,…,s’k and removing appropriate suffix from that repetition. For example, the sequence 2,4,3,3,5,3 realizes each and every one of the following schemes:
• <,>,=
• <,>,=,<,>
• <,>,=,<,>,<,<,=
• <,>,=,<,>,=,>,>
as well as many others.
An integer sequence a1,a2,…,an and a monotonicity scheme s1,s2,…,sk are given. Your task is to find the longest subsequence ai1,ai2,…,aim (1 ≤ i1 < i2 < … < im ≤ n) of the former that realizes the latter.
## 입력
The first line of the standard input holds two integers n and k (1 ≤ n ≤ 20,000, 1 ≤ k ≤ 100), separated by a single space, denoting the lengths of the sequences (ai) and monotonicity scheme (sj) respectively.
The second input line gives the sequence (ai), i.e, it holds n integers ai separated by single spaces (1 ≤ ai ≤ 1,000,000).
Finally, the third lines gives the monotonicity scheme (sj), i.e., it holds k symbols sj of the form <, > or = separated by single spaces.
## 출력
In the first line of the standard output your program should print out a single integer m, the maximum length of a subsequence of a1,a2,…,an that realizes the scheme s1,s2,…,sk.
In the second line it should print out any such subsequence ai1,ai2,…,aim, separating its elements by single spaces.
## 예제 입력
7 3
2 4 3 1 3 5 3
< > =
## 예제 출력
6
2 4 3 3 5 3
|
{}
|
category theory
# Contents
## Definition
For $C$ a category, a class $K \subset Mor(C)$ of morphisms in $C$ is said to satisfy 2-out-of-3 if for all composable $f,g \in Mor(C)$ we have that if two of the three morphisms $f$, $g$ and the composite $g \circ f$ is in $K$, then so is the third.
$\array{ \\ {}^{\mathllap{f}}\nearrow \searrow^{\mathrlap{g}} \\ \stackrel{g \circ f}{\to} } \,.$
So in particular this means that $K$ is closed under composition of morphisms.
This definition has immediate generalization also to higher category theory. For instance in (∞,1)-category theory its says that:
a class of 1-morphisms in an (∞,1)-category satisfies two out of 3, if for every 2-morphism of the form
$\array{ & {}^{\mathllap{}f}\nearrow &\Downarrow^{\simeq}& \searrow^{\mathrlap{g}} \\ &&\stackrel{h}{\to}&& }$
we have that if two of $f$, $g$ and $h$ are in $C$, then so is the third.
## Examples
Revised on May 22, 2012 08:54:22 by Anonymous Coward (98.223.186.49)
|
{}
|
# Fater Iterative Shrinking Threshold Algorithm
Posted by GwanSiu on October 27, 2018
## 1. Introduction: Proximal Mapping
The definition of proximal mapping of convex function $h$ is:
## 2. Faster Iterative Shrinking Threshold Algorithm
The basic idea of the iterative shrinkage algorithm is to build at each iteration a regularization of the linearized differentiable function part in the objective. We consider the following general formualtion:
$g:\mathcal{R}^{n}\rightarrow\mathcal{R}$ is a continuous convex function but is possibly non-smooth. $f:\mathcal{R}^{n}\rightarrow\mathcal{R}$ is a smooth convex function such that Lipschitz continuous gradient $L(f)$:
where $\Arrowvert \cdot\Arrowvert$ denotes the euclidean distance and $L(f)$ is the Lipschitz constant of $\nabla f(x)$.
For any $L>0$, we use quadratic upper bound to approximate $F(x)=f(x)+g(x)$ at a given point $y$:
thus, we can use proximal gradient method to compute the minimum value of $Q(x,y)$:
In bothe ISTA and FISTA, update point $x_{k}$ is computed by proximal gradient method:
Faster iterative shrink threshold alorithm is shown as below:
|
{}
|
# CosineAnnealingWarmRestartsScheduler#
class composer.optim.CosineAnnealingWarmRestartsScheduler(t_0, t_mult=1.0, alpha_f=0.0)[source]#
Cyclically decays the learning rate according to the decreasing part of a cosine curve.
This scheduler is based on CosineAnnealingWarmRestarts from PyTorch.
This scheduler resembles a regular cosine annealing curve, as seen in CosineAnnealingScheduler, except that after the curve first completes t_0 time, the curve resets to the start. The durations of subsequent cycles are each multiplied by t_mult.
Specifically, the learning rate multiplier $$\alpha$$ can be expressed as:
$\alpha(t) = \alpha_f + (1 - \alpha_f) \times \frac{1}{2}(1 + \cos(\pi \times \tau_i))$
Given $$\tau_i$$, the fraction of time elapsed through the $$i^\text{th}$$ cycle, as:
$\tau_i = (t - \sum_{j=0}^{i-1} t_0 t_{mult}^j) / (t_0 t_{mult}^i)$
Where $$t_0$$ represents the period of the first cycle, $$t_{mult}$$ represents the multiplier for the duration of successive cycles, and $$\alpha_f$$ represents the learning rate multiplier to decay to.
Parameters
• t_0 (str | Time) – The period of the first cycle.
• t_mult (float) – The multiplier for the duration of successive cycles. Default = 1.0.
• alpha_f (float) – Learning rate multiplier to decay to. Default = 0.0.
|
{}
|
# Student Debt, feasibility & plan to repay
1. Aug 12, 2015
### Ritzycat
I'll be starting my undergrad this fall. As of now I will probably start majoring in physics. Nonetheless I expect to stay within the area of science.
If I've done the math right I'll probably have 43K in debt. Of that 43k, 8k is federal unsubsidized loans with 4.29% interest rate, (will accumulate interests starting when I take it out), 16k is a private loan from my school, and it will not accumulate interest while I am at my undergrad school (4 years) but will begin to do so when I leave. 19k is federal subsidized loan with 4.29% interest rate, which will not accumulate interest until I'm done with school altogether (undergrad + possible phd).
If a PhD is a possible path I am considering, is this amount of debt feasible for a possible PhD student? I suppose for the sake of simplification, I could only worry about 24k of the debt while I am in graduate school, since that will be the portion that accumulates interest at the time.
A few more questions:
1. If you live frugally, do PhD students usually have enough to pay part of their undergrad loans off?
2. Is it feasible for PhD students to take a part-time job (maybe 10 hours a week) or is the time better dedicated towards the degree?
I know its quite far down the line but I like to outline any possible paths I am possibly taking so I can assess their viability, or if its just a pipe dream.
Thanks!
2. Aug 12, 2015
### Dr. Courtney
Borrowing money for school is a bad plan, especially for four years at a bigger, expensive school.
I recommend attending a less expensive school, at least for the first two years. Attending a cheap school and live at home can save many thousands in eventual debt. You can transfer for your last two years to complete the degree from the desired school.
Repaying debt by frugal living during grad school might be a viable option, but some places are much cheaper to live than others. It depends on the drad student stipend and where you are living. It is much harder in big cities where costs of living are high and much harder if one has family obligations beyond a working spouse.
Being a grad student is a full time + job, especially if you have an RA or TA paying your tuition and stipend.
3. Aug 12, 2015
### MarneMath
I don't think it's really that feasible to work part-time during a PhD. Your PhD program is essentially your job. While sure you could probably be an uber driver and help out, it really wouldn't be significant.
There's a few options here.
1. Work part time during your undergraduate and save the major of your money to pay off loans. Even working 20 hours at about 8 dollars an hour will help make a significant dent in your debt.
2. Take less classes (and wait longer to graduate) to work more and help cover the cost even more so.
3. National guard tuition assistance. Which is essentially 100 dollar drill paycheck + 5000 per year for school. Not much but eh.
4. Aug 12, 2015
### Choppy
I would start by assuming that you're already doing everything you can to minimize the debt you take on as an undergraduate. This includes:
• taking on a part-time job, even as a high-school student and putting at least some of that money towards your undergraduate degree
• working full-time during the summers
• continuing to work part-time as an undergraduate student
• doing what you can to minimize costs including factoring in the cost of your education into your choice of where to attend as well as the general cost of living
• applying for every scholarship that you qualify for
Once you get into graduate school the stipend and TA/RA is usually enough that you don't have to take on additional debt as a student. It's probably not enough that you can make a significant dent in your existing loans, other than perhaps paying off the interest.
Having a part-time job as a graduate student is possible, but it comes with consequences. I had a part-time job as a PhD student and that brought in enough money that I could live on my own, buy a car, and save up for a down payment on a house. The down side was that I was working until about 3 or 4 am on the weekends, which made it very difficult to make it into the office bright and early on Monday mornings (I was one of those grad students who sauntered in at around 10:00 am). This delayed my graduation by about six months compared to my jobless peers.
5. Aug 12, 2015
Staff Emeritus
$24K at 4.29% for ten years works out to$246.31 per month, or just under $3K per year. Can you afford that? Depends on the difference between your stipend and the cost of living, neither of which is known. (By the way, you should be able to calculate loan amortization yourself - if you can't, you have no business taking out any loan whatsoever). I agree that you can't easily work part time in grad school. I did about 10 hours per week for 10 weeks - for which I was very well compensated - and it almost killed me. A better strategy is to work as an undergrad. 6. Aug 12, 2015 ### Dishsoap You can defer your student loans for up to 6 years while you are in grad school, correct? 7. Aug 12, 2015 ### Ritzycat Thanks for all the responses. A few facts to clarify and answer questions: • I have been working a part-time job since May 2014. I asked them for full-time when summer began earlier this year but they wouldn't do it. So I've done 16-20 hours a week. I will try hard to find a full-time job to do during the summers I'm in college. • It's a bit too late in the process to change what I'm doing at this point, I accepted the offer months ago and I'm leaving for college next week. We can talk about all the different routes I could have taken then but there's no point talking about it. • I am not paying the full cost of my college in loans. Of the colleges I was accepted to, this one was the most affordable. Raw cost without any aid is$30,710/semester. I am receiving $12,393 in grants,$8,000 in academic scholarship, and $4,722 in loans per semester from the three loans I mentioned in the OP. So I pay$5,595 out of pocket each semester. All of this aid is valid for all 4 years.
• I am doing federal work-study at my school this fall. I will get \$1,100 per semester, its like 8 hours a week. They do not allow freshmen to work more than 8 hours per week. The entirety of the work-study earnings will have to go to paying the school tuition.
• All the money I earn will have to go towards covering the remaining cost of undergrad. My parents are contributing little to nothing to help with the costs. However, my mom has said she will be able to take out a loan on her 401K soon if need be, which I don't want her to have to do. She says she likes it because she is basically "paying herself back the interest".
• I currently have enough savings to pay the first two semesters on this budget (ex. no even more loan which it seems I should avoid like the plague)
• I can see myself living very frugally. Being a natural recluse and abomination of nature, I rarely go out to eat/see movies/parties and I will probably never find a significant other, let alone someone who will extort money from me. Will I still be able to pay an internet bill? That's all I need!
Although my question remains: is this path even available to me? Is it impossible to go to grad school on this much debt or are there too many unknown factors to make that assertion (stipend, cost of living)?? Will I Die
Federal Subsidized Loans can be deferred.
Over the course of 4 years, the maximum an undergraduate student can take out is 19,000 in federal subsidized loans, which I am doing. They are the best deal on any student loans hence why I maxed those out first.
|
{}
|
16
Q:
# Tea worth Rs. 126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be
A) Rs. 169.50 B) Rs.1700 C) Rs. 175.50 D) Rs. 180
Answer: C) Rs. 175.50
Explanation:
Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
Cost of 1 kg tea of 1st kind Cost of 1 kg tea of 2nd kind
x-153/22.50 = 1 => x - 153 = 22.50 => x=175.50.
Hence, price of the third variety = Rs.175.50 per kg.
Q:
640 ml of a mixture contains milk and water in ratio 6:2. How much of the water is to be added to get a new mixture containing half milk and half water ?
A) 360 ml B) 320 ml C) 310 ml D) 330 ml
Answer & Explanation Answer: B) 320 ml
Explanation:
Here total parts of milk and water in the solution is 6+2 = 8 parts
1part = 640/8 = 80
old mixture contains 6parts of milk and 2 parts of water(6:2).
To get new mixture containing half milk and half water, add 4parts of water to the old mixture then 6:(2+4) to make the ratio same.
i.e, 4 x 80 = 320 ml.
4 163
Q:
Equal quantities of three mixtures of milk and water are mixed in the ratio 1:2, 2:3 and 3:4. The ratio of water and milk in the mixture is ?
A) 193 : 122 B) 97 : 102 C) 115 : 201 D) 147 : 185
Answer & Explanation Answer: A) 193 : 122
Explanation:
Given the three mixtures ratio as (1:2),(2:3),(3:4)
(1+2),(2+3),(3+4)
Total content = 3,5,7
Given equal quantities of the three mixtures are mixed, then LCM of 3, 5, 7 = 105
105/3 = 35 , 105/5 = 21 , 105/7 = 15
Now, the individual equal quantity ratios are (35x1, 35x2), (21x2, 21x3), (15x3, 15x4)
(35,70), (42,63), (45,60)
So overall mixture ratio of milk and water is
35+42+45 : 70+63+60
122:193
But in the question asked the ratio of water to milk = 193 : 122
2 142
Q:
In a mixture of milk and water the proportion of water by weight was 75%. If in 60 gm of mixture 15 gm water was added, what would be the percentage of water ? (Weight in gm)
A) 80% B) 70% C) 75% D) 62%
Explanation:
Water in 60 gm mixture=60 x 75/100 = 45 gm. and Milk = 15 gm.
After adding 15 gm. of water in mixture, total water = 45 + 15 = 60 gm and
weight of a mixture = 60 + 15 = 75 gm.
So % of water = 100 x 60/75 = 80%.
5 127
Q:
The amount of water (in ml) that should be added to reduce 9 ml lotion, containing 50% alcohol, to a lotion containing 30% alcohol is ?
A) 6 ml B) 11 ml C) 15 ml D) 9 ml
Answer & Explanation Answer: A) 6 ml
Explanation:
Let us assume that the lotion has 50% alcohol and 50% water.
ratio = 1:1
As the total solution is 9ml
alcohol = water = 4.5ml
Now if we want the quantity of alcohol = 30%
The quantity of water = 70%
The new ratio = 3:7
Let x ml of water be added
We get,
$\inline \fn_jvn \small \frac{4.5}{4.5+x}=\frac{3}{7}$
=> x=6
Hence 6ml of water is added.
3 178
Q:
If a man buys 1 lt of milk for Rs.12 and mixes it with 20% water and sells it for Rs.15, then what is the percentage of gain ?
A) 25% B) 30% C) 17% D) 19%
|
{}
|
# On Erdos-Ko-Rado for random hypergraphs
-
Jeff Kahn , Rutgers University
Fine Hall 224
One of the more interesting of recent combinatorial directions has been the attempt to understand the extent to which various classical facts remain true in a random setting. The present talk will mostly discuss what we know about this question when the classical fact" is the Erdos-Ko-Rado Theorem.
|
{}
|
# THE LOW ENERGY ONSET OF $CS_{2}$ BIEXPONENTIAL FLUORESCENCE DECAYS
Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/29587
Files Size Format View
1995-RB-08.jpg 50.36Kb JPEG image
Title: THE LOW ENERGY ONSET OF $CS_{2}$ BIEXPONENTIAL FLUORESCENCE DECAYS Creators: Nguyen, M.; Silvers, S. J. Issue Date: 1995 Publisher: Ohio State University Abstract: Biexponential decays are characterestic of fluorescence from the rovibrational levels of the $T {^{1}A_{2}} and V {^{1}B_{2}}$ states of $CS_{2}$. The longer-lived component is associated with continum-like emission. Biexponential decays first appear in the emission from rovibrational levels of the lower lying R state (The $B_{2}$ spin component of a $^{3}A_{2}$ electronic state.) The first biexponential behavior appears in decays from the (1, 6, 0) vibrational level at $T_{o} = 28,635 cm^{-1}$. Time delayed excitation scans show that the longer-lived component $(6-8 \mu s)$ is principally due to a weak, underlying type band. Decays from the (0, 9, 0) level at $T_{o} = 28,817 cm^{-1}$ and higher vibrational levels all require bi- or multiexponential fits. Delay scans for these levels show that the excitation spectra of the long-lived component closely mimic those of the short-lived one. Explanations for this similarity are considered. Description: Author Institution: Virginia Commonwealth University, Richmond, VA 23284. URI: http://hdl.handle.net/1811/29587 Other Identifiers: 1995-RB-08
|
{}
|
Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
PL EN
Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
• # Artykuł - szczegóły
## Annales Polonici Mathematici
2003 | 82 | 1 | 9-18
## Geometry of quotient spaces and proximinality
EN
### Abstrakty
EN
It is proved that if X is a rotund Banach space and M is a closed and proximinal subspace of X, then the quotient space X/M is also rotund. It is also shown that if Φ does not satisfy the δ₂-condition, then $h⁰_{Φ}$ is not proximinal in $l⁰_{Φ}$ and the quotient space $l⁰_{Φ}/h⁰_{Φ}$ is not rotund (even if $l⁰_{Φ}$ is rotund). Weakly nearly uniform convexity and weakly uniform Kadec-Klee property are introduced and it is proved that a Banach space X is weakly nearly uniformly convex if and only if it is reflexive and it has the weakly uniform Kadec-Klee property. It is noted that the quotient space X/M with X and M as above is weakly nearly uniformly convex whenever X is weakly nearly uniformly convex. Criteria for weakly nearly uniform convexity of Orlicz sequence spaces equipped with the Orlicz norm are given.
9-18
wydano
2003
### Twórcy
autor
• Department of Mathematics, Harbin University of Sciences, and Technology, Harbin, P.R. China
autor
• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
autor
• Faculty of Science, Maejo University, Chiang Mai, Thailand
|
{}
|
Superclass: Path Loss
The path_loss_free_space object represents a free-space path loss model.
Free-space path loss can be described entirely by three parameters:
1. the carrier wavelength $\lambda$
2. the distance $d$
3. the path loss exponent $\eta$
The path loss (or attenuation) stemming from a free-space path loss model can be deterministically written as
where $G^2$ is the path gain and $1/G^2$ is the path loss.
When $\eta = 2$, this is the classical Friis formula for path loss. Typically, $\eta \geq 2$ except in rare settings with significant clutter. Most often, $\eta \in [2,4]$.
The path_loss_free_space object is a subclass of the path_loss object.
### Creating a Free-Space Path Loss Object
A free-space path loss object path_loss_free_space can be created via
p = path_loss.create('free-space')
### Key Properties
The path_loss_free_space object inherits all properties of the path_loss object, the key ones being
p.attenuation
p.carrier_frequency
p.carrier_wavelength
p.propagation_velocity
p.distance
In addition to these, the path_loss_free_space object also has the property
p.path_loss_exponent
to capture the path loss exponent ($\eta$).
### Setting the Path Loss Exponent
To set the path loss exponent of a free space path loss object p, use
p.set_path_loss_exponent(ple)
where ple is the path loss exponent (a traditionally positive number).
### Example Setup
A typical path_loss_free_pace object setup looks something similar to
p = path_loss.create()
p.set_carrier_frequency(fc)
p.set_propagation_velocity(vel)
p.set_distance(d)
p.set_path_loss_exponent(ple)
### Invoking a Realization
To realize the path loss, use
atten = p.realization()
which, when appropriately setup, will return the attenuation atten for the given carrier wavelength, distance, and path loss exponent.
Note that atten is related to the large-scale gain $G$ by simply atten $= G^{-2}$.
### Getting the Attenuation
To get the realized attenuation of a path_loss_free_space object p, one can also use
atten = p.get_attenuation()
where atten is the attenuation of the path loss (power loss, linear scale).
### List of Properties
The path_loss_free_space object contains the following properties:
• path_loss_free_space.path_loss_exponent
• path_loss_free_space.name
• path_loss_free_space.type
• path_loss_free_space.distance
• path_loss_free_space.attenuation
• path_loss_free_space.carrier_frequency
• path_loss_free_space.carrier_wavelength
• path_loss_free_space.propagation_velocity
### List of Methods
The path_loss_free_space object contains the following methods:
### Methods Documentation
#### compute_path_loss_attenuation()
Computes the path attenuation (path loss) according to the free-space path loss (FSPL) formula.
Usage:
atten = compute_path_loss_attenuation()
Return Values:
atten — the path attenuation (path loss) (a power loss)
Notes:
The free-space path loss (FSPL) equation used is G = (lambda / (4*pi))^2 * (1/d)^ple, where G is the inverse path loss in terms of power.
Back to methods
#### create(type)
Creates a path loss object of a specific type.
Usage:
obj = path_loss.create()
obj = path_loss.create(type)
Input Arguments:
type — (optional) a string specifying which path loss model to create
Return Values:
obj — a path loss object
Back to methods
#### get_attenuation()
Returns the realized attenuation of the path loss model.
Usage:
val = get_attenuation()
Return Values:
val — the attenuation (power loss) of the path
Back to methods
#### initialize()
Initializes a path loss object.
Usage:
initialize()
Back to methods
#### initialize_free_space()
Initializes a free-space path loss object.
Usage:
initialize_free_space()
Back to methods
#### path_loss_free_space(name)
Creates a free-space path loss object.
Usage:
obj = path_loss_free_space()
obj = path_loss_free_space(name)
Input Arguments:
name — an optional name for the object
Return Values:
obj — an object representing free-space path loss
Back to methods
#### realization()
Invokes a realization of the path loss.
Usage:
atten = realization()
Return Values:
atten — the realized path loss attenuation
Notes:
Since no random variables are involved in the FSPL equation, it will be determininstic and thus fixed across realizations.
Back to methods
#### set_carrier_frequency(fc)
Sets the carrier frequency of the channel. Also updates the carrier wavelength accordingly.
Usage:
set_carrier_frequency(fc)
Input Arguments:
fc — carrier frequency (Hz)
Notes:
Back to methods
#### set_distance(d)
Sets the distance of the path (in meters).
Usage:
set_distance(d) Sets the distance of the link to a specific
value.
Input Arguments:
d — distance of the path (in meters)
Back to methods
#### set_name(name)
Sets the name of the path loss model.
Usage:
set_name()
set_name(name)
Input Arguments:
name — (optional) a string; if not passed, ‘path-loss’ is the default name used
Back to methods
#### set_path_loss_attenuation(atten)
Sets the attenuation of the path loss model.
Usage:
set_path_loss_attenuation(atten)
Input Arguments:
atten — the attenuation (power loss) of the path
Back to methods
#### set_path_loss_exponent(ple)
Sets the path loss exponent.
Usage:
set_path_loss_exponent(ple)
Input Arguments:
ple — path loss exponent (a positive number)
Back to methods
#### set_propagation_velocity(val)
Sets the propagation velocity of the channel. Also updates the carrier wavelength accordingly.
Usage:
set_propagation_velocity(val)
Input Arguments:
val — propagation velocity (meters/sec)
Back to methods
#### set_type(type)
Sets the type of path loss model.
Usage:
set_type()
set_type(type)
Input Arguments:
type — (optional) a string; if not passed, ‘default’ is the default type used
Back to methods
|
{}
|
## File Splitter+ For Windows [Updated-2022]
File Splitter+ is a light file splitter that you can use to merge or split files up to 8 GB
Supports: Splitting by parts or by size. Splitting by parts requires to enter a number of parts. Splitting by size requires to enter in the box the size of the file that is to be split. You can merge files from 1 to 300 parts. File Splitter+ is a free to use program so you don’t have to download anything to run it.
Virus and Malware Tests:
VirusTotal: Free Scan. Website URL:
SourceForge: Free Scan. Website URL:
What’s new in this version:
– File Splitter+ updates to it’s new version.
What’s new in previous version:
– Supports Split both by parts and by size with a maximum of 300 parts.
– Doesnt ask any confirmation when you click the.bat file.
– Visible the split volume details.
Version 1.0:
File Splitter+ is a light file splitter that you can use to merge or split files up to 8 GB
Features:
– Supports Splitting by parts or by size. Splitting by parts requires to enter a number of parts. Splitting by size requires to enter in the box the size of the file that is to be split. You can merge files from 1 to 300 parts.
– Can have a maximum of 300 parts.
– Very fast and easy to use.
Limitations:
– Doesnt ask any confirmation when you click the.bat file.
– Visible the split volume details.
– The first time you want to split a file you have to specify the size
02dac1b922
## File Splitter+ Keygen For (LifeTime) Free [April-2022]
Open File Splitter+
Control the volume cutter with the mouse
Split a large file in halves
Both trimming modes can be used by performing one of the two operations:
by size (kilobytes)
by number of parts
Merge larger files
C:\>file splitterplus.exe
You can adjust the text size by right-clicking anywhere in the main window
Click “Settings”
Click “Preferences” on the toolbar
Select “Text”, as shown in the next figure, and enter “9” in the “FontSize” box
Click “OK”
Create a batch file to load the utility
Click “Create command to run File Splitter+”
Enter “file splitterplus.exe” in the text box
Click “Create”
Type in a name for the batch file (.bat) and click “Save”
Click “OK”
Open the created batch file and click “Run”
After a few seconds, the utility will load
Click “File” in the toolbar
Click “Open”
Click “Open” in the popup box
Open the original file and choose “Mixed” in the combo box
Click “Select”
Click “OK”
Select the utility’s window from the main window
Click “OK”
Create as many split files as you want
Click “Split” in the toolbar
Enter the required file size, e.g. 300 kilobytes
Click “Split” in the popup box
Click “OK”
Click “OK” in the box
Select the desired volume size from the drop-down list
The configuration is saved and the tool will automatically perform the operation
Create multiple volumes with a specific size
Create a large number of volumes with the required dimensions
Click “Split” in the toolbar
Enter the required number of parts
Click “Split” in the popup box
The utility will prompt you to choose the original volume size
Click “OK”
Click “OK” in the box
Select the original volume
Click “OK”
Click “OK” in the box
Click “OK” in the box
Click “OK” in the box
Select the desired volume size from the drop-down list
## What’s New In File Splitter ?
In this software, users can split file into different parts with different size. The base name for each output file is included. All files after that name will be created in the same directory. You can define the number of parts you want to split the file into. Also, the program can split by size or by parts.
A:
There is no such software yet but it is perfect for what you want
for smaller files you can use Total Commander which will split a file into parts, keep only a part you want, rename the others, and then create a complete file, that’s exactly what you want to do.
To run Total Commander you must have a.bat/.lnk file in the same directory as the Total Commander executable.
You need the full version as you can’t run the trial version
After reading that, I think it should be possible to create a file splitting script which you can place in a folder in the main Total Commander installation directory.
Please also note that there are other ways of doing this, without needing to use Total Commander, e.g. cut
Hope it helps
A:
As one of the commenters noted, you can use Total Commander. If you have downloaded the trial version, all it would take is to have a batch script (or a custom.bat file, if you prefer) in the same directory as the trial version.
The process would look as follows:
Open up Total Commander and select File -> Merge Files. If you have additional files in the same directory (like a batch script), the batch script’s name will be listed as one of the merge files, so you can select it.
You should have the option to merge two files, or merge three to six files, depending on the number of files you have. When you enter the number of files you want to merge, the batch script will be created.
1. Field of the Invention
The present invention relates to a mobile terminal and a method of controlling the same, and more particularly, to a mobile terminal capable of selecting a user interface (UI) and a method of controlling the same.
2. Description of the Related Art
Mobile terminals are portable devices with one or more of voice and video call communication capabilities, information input and/or output capabilities, data storage capabilities, and other capabilities. Mobile terminals are usually carried
## System Requirements For File Splitter :
Minimum:
– CPU: Dual-Core 1GHz or better
Recommended:
– CPU: Quad-Core 1.4GHz or better
CPU Recommended:
– RAM: 2GB or better
What’s New in This Version:
– Support for the latest Windows 10 (Build 1607)
– Add support for Mac OS X 10.11 (El Capitan)
– Add support for the latest Pandora OS (1.0.3)
– Add support for the latest Spotify
int(41183)
|
{}
|
# 1.6 Huygens’s principle
Page 1 / 4
By the end of this section, you will be able to:
• Describe Huygens’s principle
• Use Huygens’s principle to explain the law of reflection
• Use Huygens’s principle to explain the law of refraction
• Use Huygens’s principle to explain diffraction
So far in this chapter, we have been discussing optical phenomena using the ray model of light. However, some phenomena require analysis and explanations based on the wave characteristics of light. This is particularly true when the wavelength is not negligible compared to the dimensions of an optical device, such as a slit in the case of diffraction . Huygens’s principle is an indispensable tool for this analysis.
[link] shows how a transverse wave looks as viewed from above and from the side. A light wave can be imagined to propagate like this, although we do not actually see it wiggling through space. From above, we view the wave fronts (or wave crests) as if we were looking down on ocean waves. The side view would be a graph of the electric or magnetic field. The view from above is perhaps more useful in developing concepts about wave optics .
The Dutch scientist Christiaan Huygens (1629–1695) developed a useful technique for determining in detail how and where waves propagate. Starting from some known position, Huygens’s principle states that every point on a wave front is a source of wavelets that spread out in the forward direction at the same speed as the wave itself. The new wave front is tangent to all of the wavelets.
[link] shows how Huygens’s principle is applied. A wave front is the long edge that moves, for example, with the crest or the trough. Each point on the wave front emits a semicircular wave that moves at the propagation speed v . We can draw these wavelets at a time t later, so that they have moved a distance $s=vt.$ The new wave front is a plane tangent to the wavelets and is where we would expect the wave to be a time t later. Huygens’s principle works for all types of waves, including water waves, sound waves, and light waves. It is useful not only in describing how light waves propagate but also in explaining the laws of reflection and refraction. In addition, we will see that Huygens’s principle tells us how and where light rays interfere.
## Reflection
[link] shows how a mirror reflects an incoming wave at an angle equal to the incident angle, verifying the law of reflection. As the wave front strikes the mirror, wavelets are first emitted from the left part of the mirror and then from the right. The wavelets closer to the left have had time to travel farther, producing a wave front traveling in the direction shown.
Mathematical expression of principle of relativity
given that the velocity v of wave depends on the tension f in the spring, it's length 'I' and it's mass 'm'. derive using dimension the equation of the wave
What is the importance of de-broglie's wavelength?
he related wave to matter
Zahid
at subatomic level wave and matter are associated. this refering to mass energy equivalence
Zahid
how those weight effect a stable motion at equilibrium
how do I differentiate this equation- A sinwt with respect to t
just use the chain rule : let u =wt , the dy/dt = dy/du × du/dt : wA × cos(wt)
Jerry
I see my message got garbled , anyway use the chain rule with u= wt , etc...
Jerry
de broglie wave equation
vy beautiful equation
chandrasekhar
what is electro statics
when you consider systems consisting of fixed charges
Sherly
Diagram of the derive rotational analog equation of v= u+at
what is carat
a unit of weight for precious stones and pearls, now equivalent to 200 milligrams.
LoNE
a science that deals with the composition, structure, and properties of substances and with the transformations that they undergo.
LoNE
what is chemistry
what chemistry ?
Abakar
where are the mcq
ok
Giorgi
acids and bases
Navya
How does unpolarized light have electric vector randomly oriented in all directions.
unpolarized light refers to a wave collection which has an equal distribution of electric field orientations for all directions
pro
In a grating, the angle of diffraction for second order maximum is 30°.When light of wavelength 5*10^-10cm is used. Calculate the number of lines per cm of the grating.
OK I can solve that for you using Bragg's equation 2dsin0over lander
ossy
state the law of gravity 6
what is cathodic protection
its just a technique used for the protection of a metal from corrosion by making it cathode of an electrochemical cell.
akif
|
{}
|
# [texworks] Stepping in, completion
Alain Delmotte esperanto at swing.be
Fri Sep 18 09:56:50 CEST 2009
Hi!
Benct Philip Jonsson a écrit :
> I decided to try TeXWorks (a) because Vim can be frustrating
> at times and (b) because of the process button and preview:
> repeatedly typing in the terminal and opening/closing a file
> in a PDF viewer is frustrating.
>
> Looks good so far, but I have a question:
>
> Is there any way to preview the available
> completion shortcuts similar to Vim's completeopt?
> Having to locate and open the definition files is annoying...
Yes it is, but for the moment there is no other way, except...
There is some logic in the system:
"bsom [tab]", I'll get a proposition, let say:
\begin{somebody}... \end{somebody}, not good, I'll type "[Tab]" again,
another proposition will be offered, if existing, up to return to "bsom"
There are some other groups like this for the mathematical symbols alone
or in formulas.
Otherwise, it is often the beginning of the command "cha" for
"\chapter", "se" for "\section"; "sse" for "\subsection",...
After some time, as one use a small group of commands, one knows the
shortcuts, or try guessing :-)
Alain
|
{}
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.