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Inverse maximal overlap discrete wavelet packet transform - MATLAB imodwpt - MathWorks France
imodwpt
Perfect Reconstruction with the Inverse MODWPT
Inverse MODWPT Using Daubechies Extremal Phase Wavelet
Inverse MODWPT Using Scaling and Wavelet Filters
Inverse maximal overlap discrete wavelet packet transform
xrec = imodwpt(coefs)
xrec = imodwpt(coefs,wname)
xrec = imodwpt(coefs,lo,hi)
xrec = imodwpt(coefs) returns the inverse maximal overlap discrete wavelet packet transform (inverse MODWPT), in xrec. The inverse transform is for the terminal node coefficient matrix (coefs) obtained using modwpt with the default length 18 Fejér-Korovkin ('fk18') wavelet.
xrec = imodwpt(coefs,wname) returns the inverse MODWPT using the orthogonal filter specified by wname. This filter must be the same filter used in modwpt.
xrec = imodwpt(coefs,lo,hi) returns the inverse MODWPT using the orthogonal scaling filter, lo, and wavelet filter, hi.
Obtain the MODWPT of an ECG waveform and demonstrate perfect reconstruction using the inverse MODWPT.
xrec = imodwpt(wpt);
plot(wecg);
title('Original ECG Waveform');
plot(xrec);
title('Reconstructed ECG Waveform');
Find the largest absolute difference between the original signal and the reconstruction. The difference is on the order of
1{0}^{-11}
max(abs(wecg-xrec'))
Obtain the MODWPT of Southern Oscillation Index data using the Daubechies extremal phase wavelet with two vanishing moments ('db2'). Reconstruct the signal using the inverse MODWPT.
xrec = imodwpt(wsoi,'db2');
Obtain the MODWPT of Southern Oscillation Index data using specified scaling and wavelets filters with the Daubechies extremal phase wavelet with two vanishing moments ('db2').
[lo,hi] = wfilters('db2');
wpt = modwpt(soi,lo,hi);
xrec = imodwpt(wpt,lo,hi);
Plot the original SOI waveform and the reconstructed waveform.
plot(soi)
title('Original SOI Waveform');
title('Reconstructed SOI Waveform')
coefs — Terminal node coefficients
Terminal node coefficients of a wavelet packet tree, specified as a matrix. You must obtain the coefficient matrix from modwpt using the 'FullTree',false option. 'FullTree',false is the default value of modwpt.
wname — Synthesizing wavelet filter
fk18 (default) | character vector | string scalar
Synthesizing wavelet filter used to invert the MODWPT, specified as a character vector or string scalar. The specified wavelet must be the same wavelet as used in the analysis with modwpt.
Scaling filter, specified as an even-length real-valued vector. lo must be the same scaling filter as used in the analysis with modwpt. You cannot specify both a scaling-wavelet filter pair and a wname filter.
Wavelet filter, specified as an even-length real-valued vector. hi must be the same wavelet filter used in the analysis with modwpt. You cannot specify both a scaling-wavelet filter pair and a wname filter.
xrec — Inverse maximal overlap discrete wavelet packet transform
Inverse maximal overlap discrete wavelet packet transform, returned as a row vector. The inverse transform is the reconstructed version of the original signal based on the MODWPT terminal node coefficients. xrec has the same number of columns as the input coefs matrix.
modwpt | modwptdetails | dwpt
|
EUDML | On l-adic sheaves on Shimura varieties and their higher direct images in the Baily-Borel compactification. EuDML | On l-adic sheaves on Shimura varieties and their higher direct images in the Baily-Borel compactification.
On l-adic sheaves on Shimura varieties and their higher direct images in the Baily-Borel compactification.
Pink, Richard. "On l-adic sheaves on Shimura varieties and their higher direct images in the Baily-Borel compactification.." Mathematische Annalen 292.2 (1992): 197-240. <http://eudml.org/doc/164911>.
@article{Pink1992,
keywords = {canonical model of a Shimura variety; Baily-Borel compactification; -adic sheaf},
title = {On l-adic sheaves on Shimura varieties and their higher direct images in the Baily-Borel compactification.},
AU - Pink, Richard
TI - On l-adic sheaves on Shimura varieties and their higher direct images in the Baily-Borel compactification.
KW - canonical model of a Shimura variety; Baily-Borel compactification; -adic sheaf
Benoît Stroh, Sur une conjecture de Kottwitz au bord
José I. Burgos, Jörg Wildeshaus, Hodge modules on Shimura varieties and their higher direct images in the Baily–Borel compactification
Mladen Dimitrov, Galois representations modulo p and cohomology of Hilbert modular varieties
canonical model of a Shimura variety, Baily-Borel compactification,
\ell
p
Articles by Richard Pink
|
(d) 420, 3 VIEW SOLUTION
The value of x for which 2x, (x + 10) and (3x + 2) are the three consecutive terms of an AP, is
-
-
18 VIEW SOLUTION
The value of k for which the system of equations x + y – 4 = 0 and 2x + ky = 3, has no solution, is
-2
\ne
The first term of an AP is p and the common difference is q, then its 10th term is
(a) q + 9p
(b) p – 9p
(d) 2p + 9q VIEW SOLUTION
The quadratic polynomial, the sum of whose zeroes is –5 and their product is 6, is
(d) –x2 + 5x + 6 VIEW SOLUTION
The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ – b cos θ), is
{a}^{2}+{b}^{2}
{a}^{2}-{b}^{2}
\sqrt{{a}^{2}+{b}^{2}}
\sqrt{{a}^{2}-{b}^{2}}
If the point P(k, 0) divides the line segment joining the points A(2, –2) and B(–7, 4) in the ratio 1 : 2, then the value of k is
The value of p, for which the points A(3, 1), B(5, p) and C(7, –5) are collinear, is
If one of the zeroes of the quadratic polynomial x2 + 3x + k is 2, then the value of k is
ABC is an equilateral triangle of side 2a, then length of one of its altitude is ____________. VIEW SOLUTION
In the given figure ∆ABC is circumscribing a circle, the length of BC is _____ cm.
\left({\mathrm{sin}}^{2}\mathrm{\theta }+\frac{1}{1+{\mathrm{tan}}^{2} \mathrm{\theta }}\right)
= ____________.
The value of (1 + tan2 θ) (1 – sin θ) (1 + sin θ) = _____________. VIEW SOLUTION
{\left(\frac{\mathrm{sin} 35°}{\mathrm{cos} 55°}\right)}^{2}+{\left(\frac{\mathrm{cos} 43°}{\mathrm{sin} 47°}\right)}^{2}-2 \mathrm{cos} 60°=_______.
ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is _________. VIEW SOLUTION
If the probability of winning a game is 0.07, what is the probability of losing it? VIEW SOLUTION
If the mean of the first n natural number is 15, then find n. VIEW SOLUTION
Two cones have their heights in the ratio 1 : 3 and radii in the ratio 3 : 1. What is the ratio of their volumes? VIEW SOLUTION
The ratio of the length of a vertical rod and the length of its shadow is
1:\sqrt{3}.
Find the angle of elevation of the sun at that moment? VIEW SOLUTION
A die is thrown once. What is the probability of getting an even prime number? VIEW SOLUTION
In the given Figure, DE || AC and DC || AP. Prove that
\frac{\mathrm{BE}}{\mathrm{EC}}=\frac{\mathrm{BC}}{\mathrm{CP}}
In the given Figure, two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2 ∠OPQ.
The rod AC of a TV disc antenna is fixed at right angles to the wall AB and a rod CD is supporting the disc as shown in the given figure. If AC = 1.5 m long and CD = 3 m, find (i) tanθ (ii) secθ + cosecθ
If a number x is chosen at random from the numbers –3, –2, –1, 0, 1, 2, 3. What is probability that x2 ≤ 4? VIEW SOLUTION
Class: 3 – 5 5 – 7 7 – 9 9 – 11 11 – 13
Frequency: 5 10 10 7 8
Class: 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 100 – 120 120 – 140
Find the sum of first 20 terms of the following AP:
1, 4, 7, 10, _________ VIEW SOLUTION
The perimeter of a sector a circle of radius 5.2 cm is 16.4 cm. Find the area of the sector. VIEW SOLUTION
A cone of base radius 4 cm is divided into two parts by drawing a plane through the mid-points of its height and parallel to its base. Compare the volume of the two parts. VIEW SOLUTION
In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then prove that the angle opposite to the first side is a right angle. VIEW SOLUTION
Find the area of triangle PQR formed by the points P(–5, 7), Q(–4, –5) and R (4, 5).
If the point C(–1, 2) divides internally the line segment joining A(2, 5) and B(x, y) in the ratio 3 : 4, find the coordinates of B. VIEW SOLUTION
Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial f(x) = ax2 + bx + c, a ≠ 0, c ≠ 0.
Divide the polynomial f(x) = 3x2 – x3 – 3x + 5 by the polynomial g(x) = x – 1 – x2 and verify the division algorithm. VIEW SOLUTION
Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are given by 2y – x = 8, 5y – x = 14 and y – 2x = 1.
If 4 is a zero of the cubic polynomial x3 – 3x2 – 10x + 24, find its other two zeroes. VIEW SOLUTION
A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. Find the original speed of the train. VIEW SOLUTION
Prove that the parallelogram circumscribing a circle is a rhombus. VIEW SOLUTION
Prove that: 2(sin6θ + cos6θ) – 3 (sin4θ + cos4θ) + 1 = 0. VIEW SOLUTION
The following table gives production yield per hectare (in quintals) of wheat of 100 farms of a village :
Production yield/hect. 40 – 45 45 – 50 50 – 55 55 – 60 60 – 65 65 – 70
Change the distribution to 'a more than' type distribution and draw its ogive.
The median of the following data is 525. Find the values of x and y, if total frequency is 100:
Class : Frequency:
A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 6 m. At a point on the plane, the angle of elevation of the bottom and top of the flag-staff are 30° and 45° respectively. Find the height of the tower.
\left(\mathrm{Take} \sqrt{3}=1.73\right)
Show that the square of any positive integer cannot be of the form (5q + 2) or (5q + 3) for any integer q.
Prove that one of every three consecutive positive integers is divisible by 3. VIEW SOLUTION
The sum of four consecutive numbers in AP is 32 and the ratio of the product of the first and last terms to the product of two middle terms is 7 : 15. Find the numbers.
Solve : 1 + 4 + 7 + 10 + ... + x = 287 VIEW SOLUTION
A bucket is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper circular ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the bucket, at the rate of ₹ 40 per litre. (Use π = 3.14) VIEW SOLUTION
Construct a triangle with sides 4 cm, 5 cm and 6 cm. Then construct another triangle whose sides are
\frac{2}{3}
times the corresponding sides of the first triangle. VIEW SOLUTION
|
Alternating Current, Popular Questions: CBSE Class 12-science SCIENCE, Science - Meritnation
Rithika Laxmi asked a question
If current I1= 3A sin wt and I2= 4A cos wt, then I3 is: ..Experts in the solution given below why we are multiplying and dividing particularly with 5
8. \mathrm{If} \mathrm{current} {\mathrm{I}}_{3}=3\mathrm{A} \mathrm{sin} \mathrm{\omega t} \mathrm{and} {\mathrm{I}}_{2}=4\mathrm{A} \mathrm{cos} \mathrm{\omega t}, \mathrm{then} {\mathrm{I}}_{3} \mathrm{is} :\phantom{\rule{0ex}{0ex}}\left(1\right) 5\mathrm{A} \mathrm{sin} \left(\mathrm{\omega t}+53°\right) \left(2\right) 5\mathrm{A} \mathrm{sin} \left(\mathrm{\omega t}+37°\right)\phantom{\rule{0ex}{0ex}}\left(3\right) 5\mathrm{A} \mathrm{sin} \left(\mathrm{\omega t}+45°\right) \left(4\right) 5\mathrm{A} \mathrm{sin} \left(\mathrm{\omega t}+30°\right)
Amrutha Kannan asked a question
Calculate the reading which will be given by a hot wire voltmeter if it isconnected across the terminals of a generator whose voltage waveform is represented by
V= 200sin ωt + 100sin 3ωt + 50sin5ωt
E=
{E}_{0}
\left(\mathrm{\pi t}-\frac{\mathrm{\pi }}{2\mathrm{a}}\mathrm{x}\right)
\mathrm{\pi }
\frac{1}{2}
What is power loss in an ac circuit containing pure inductor?
10°C
\left(A\right) {10}^{-15}C\phantom{\rule{0ex}{0ex}}\left(B\right) {10}^{-6}C\phantom{\rule{0ex}{0ex}}\left(C\right) {10}^{-10}C\phantom{\rule{0ex}{0ex}}\left(D\right) {10}^{-8}C
1/\mathrm{\pi \mu F}
An inductor 200 mH, capacitor 500 mF, resistor 10W are connected in series with a 100 V, variable frequency a.c. source. Calculate the(i) frequency at which the power factor of the circuit is unity.(ii) current amplitude at this frequency.(iii) Q-factor.
in a series RC circuit of r= 30 ohms and c=0.25 micro farad , f=50 Hz ,find the current for AC voltage of 100 v. Also calculate the magnitude of voltage across the resistor and capacitor. are they in phase with one another? is the algebric sum of these voltages more or less or equal to the source voltage?
draw a labelled diagram of an ac generator. obtain the expression for the end induced in the rotating coil of N turns each of cross-sectional area A ,in the presence of a magnetic field B .
Tahera Sadaf asked a question
show that a pure inductor does not consume electric power when connected across an a.c source
Experts in this question why we take peak time as T/4
Why does an indicator not allow alternating current through it?
An ac generator consists of a coil of 100 turns and cross sectional area of 3m² rotating at a constant angular speed of 60 rad/sec in a uniform magnetic field of 0.04T. The resistance of this coil is 500 ohm. Calculate i) Maximum current drawn from the generator and ii) Maximum power dissipated in the coil.
how can improve the quality factor of a series resonance circuit
Question) Calculate the RMS value of alternating current shown in the figure.
Ninad Alurkar asked a question
In the given AC circuit, which of the following is correct:
(a) voltage across resistance is lagging by 90° than the voltage across capacitor.
(b) voltage across capacitor is lagging by 180° than voltage across inductor.
(c) voltage across inductor is leading by 90° than voltage across resistance.
(d) Resistance of the circuit is equal to magnitude of impedance of circuit.
a 100 mH inductor , a 20 uF capacitor and a 10 ohm resistor are connected in series to a 100 V , 50 Hz ac source . calculate (i) impedance of the circuit at resonance (ii) current at resonance (iii) resonant frequency
1. Show that the relation between Ac current and AC voltage in case of AC applied to a resistor is similar to that in the DC applied to it.
Explain the fig of magnetisation and demagnetisation in NCERT page240?
Rishita R Varghese asked a question
define the virtual current in the a.c circuit
Write condition for resonance of series LCR circuit
Define the term impedance of a series LCR circuit. Derive a mathematical expression for it using phasor diagram.
Obtain resonance frequency of a series LCR circuit with L=2.0 H, C=32µF and R=10 Ω
|
Thermodynamics - Live Session - NEET 2020Contact Number: 9667591930 / 8527521718
Which among the following state functions is an extensive property of the system?
Which among the following is not a state function?
Which of the following is correct for isothermal expansion of an ideal gas -
1. Wrev = Wirr
2. Wrev + Wirr = 0
3. Wrev > Wirr
4. qrev = qirr
The heat of combustion of solid benzoic acid at constant volume is -321.30 kJ at 27o C. The heat of combustion at constant pressure will be
1. -321.30 - 300 R
2. -321.30 + 300R
4. -321.30 + 900 R
The hypothetical reaction,
\mathrm{A}\to 2\mathrm{B}
, proceed through following sequence of steps
\mathrm{A}\to \mathrm{C}; ∆\mathrm{H}={\mathrm{q}}_{1}\phantom{\rule{0ex}{0ex}}\mathrm{C}\to \mathrm{D}; ∆\mathrm{H}={\mathrm{q}}_{2}\phantom{\rule{0ex}{0ex}}\left(1/2\right)\mathrm{D}\to \mathrm{B}; ∆\mathrm{H}={\mathrm{q}}_{3}
The heat of reaction will be
{\mathrm{q}}_{1}-{\mathrm{q}}_{2}+2{\mathrm{q}}_{3}
{\mathrm{q}}_{1}+{\mathrm{q}}_{2}-2{\mathrm{q}}_{3}
{\mathrm{q}}_{1}+{\mathrm{q}}_{2}+2{\mathrm{q}}_{3}
{\mathrm{q}}_{1}+2{\mathrm{q}}_{2}-2{\mathrm{q}}_{3}
A solution of 200 mL of 1 M KOH is added to 200 mL of 1 M HCl and the mixture is well shaken. The rise in temperature T1 is noted. The experiment is repeated by using 100 mL of each solution and increase in temperature T2 is again noted. Which of the following is correct?
1. T1 = T2
2. T2 is twice as large as T1
4. T1 is four times as large as T2
{\mathrm{CH}}_{4}\left(\mathrm{g}\right)+360 \mathrm{kJ}\to \mathrm{C}\left(\mathrm{g}\right)+4\mathrm{H}\left(\mathrm{g}\right)\phantom{\rule{0ex}{0ex}}{\mathrm{C}}_{2}{\mathrm{H}}_{6}\left(\mathrm{g}\right)+620 \mathrm{kJ}\to 2\mathrm{C}\left(\mathrm{g}\right)+6\mathrm{H}\left(\mathrm{g}\right)
The value of C-C bond energy is
1. 260 kJ mol-1
The work done on the system when one mole of an ideal gas at 500 K is compressed isothermally and reversibly to 1/10th of its original volume (R = 2 cal)
2. 1.51 kcal
3. -23.30 kcal
4. 2.303 kcal
\mathrm{C}\left(\mathrm{s}\right)+{\mathrm{O}}_{2}\left(\mathrm{g}\right)\to {\mathrm{CO}}_{2};∆\mathrm{H}=-395 \mathrm{kJ}\phantom{\rule{0ex}{0ex}}\mathrm{S}\left(\mathrm{s}\right)+{\mathrm{O}}_{2}\left(\mathrm{g}\right)\to {\mathrm{SO}}_{2}\left(\mathrm{g}\right); ∆\mathrm{H}=-295 \mathrm{kJ}\phantom{\rule{0ex}{0ex}}{\mathrm{CS}}_{2}\left(\mathrm{l}\right)+3{\mathrm{O}}_{2}\left(\mathrm{g}\right)\to {\mathrm{CO}}_{2}\left(\mathrm{g}\right)+2{\mathrm{SO}}_{2}; ∆\mathrm{H}=-1110 \mathrm{kJ}
The heat of formation of CS2(l) is
3. 25.6 kJ mol-1
Which of the following process has negative value of
∆
S ?
1. Dissolution of sugar in water
2. Stretching of rubber band
3. Decomposition of lime stone
A particular reaction at 27oC for which
∆\mathrm{H}>0
∆\mathrm{S}>0
is found to be non-spontaneous. The reaction may proceed spontaneously
1. The temperature is decreased
2. The temperature is increased
3. The temperature is kept constant
4. It is carried in an open vessel at 27oC
For the reaction between CO2 and graphite
{\mathrm{CO}}_{2}\left(\mathrm{g}\right)+\mathrm{C}\left(\mathrm{s}\right)\to \to 2\mathrm{CO}\left(\mathrm{g}\right)
∆\mathrm{H}=+170.0 \mathrm{kJ}
∆\mathrm{S}=+170 {\mathrm{JK}}^{-1}
. The reaction spontaneous at -
Entropy of vaporisation of water 100oC, if molar heat of vaporisation is 9710 cal mol-1 will be
1. 20 cal mol-1 K-1
{\mathrm{NH}}_{3}\left(\mathrm{g}\right)+\mathrm{HCl}\left(\mathrm{g}\right) \to {\mathrm{NH}}_{4}\mathrm{Cl}\left(\mathrm{s}\right)
1. Both
∆\mathrm{H}
∆\mathrm{S}
are +ve
∆\mathrm{H}
is -ve and
∆\mathrm{S}
is +ve
∆\mathrm{H}
is +ve and
∆\mathrm{S}
is -ve
∆\mathrm{H}
∆\mathrm{S}
are -ve
One mole of perfect gas expands isothermally to ten times its original volume. The change in entropy
2. 2.303 R
3. 10.0 R
4. 100.0 R
|
EUDML | A combinatorial approach to hyperharmonic numbers. EuDML | A combinatorial approach to hyperharmonic numbers.
Benjamin, Arthur T.; Gaebler, David; Gaebler, Robert
Benjamin, Arthur T., Gaebler, David, and Gaebler, Robert. "A combinatorial approach to hyperharmonic numbers.." Integers 3 (2003): Paper A15, 3 p., electronic only-Paper A15, 3 p., electronic only. <http://eudml.org/doc/128235>.
@article{Benjamin2003,
author = {Benjamin, Arthur T., Gaebler, David, Gaebler, Robert},
keywords = {hyperharmonic numbers; harmonic numbers; Stirling numbers of the first kind; -Stirling numbers; -Stirling numbers},
title = {A combinatorial approach to hyperharmonic numbers.},
AU - Benjamin, Arthur T.
AU - Gaebler, David
AU - Gaebler, Robert
TI - A combinatorial approach to hyperharmonic numbers.
KW - hyperharmonic numbers; harmonic numbers; Stirling numbers of the first kind; -Stirling numbers; -Stirling numbers
István Mező, Ayhan Dil, Euler-Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence
István Mező, Exponential generating function of hyperharmonic numbers indexed by arithmetic progressions
hyperharmonic numbers, harmonic numbers, Stirling numbers of the first kind,
r
-Stirling numbers,
r
-Stirling numbers
Bell and Stirling numbers
Articles by Gaebler
|
EUDML | On the distinguishing features of the Dobrakov integral. EuDML | On the distinguishing features of the Dobrakov integral.
On the distinguishing features of the Dobrakov integral.
Panchapagesan, T.V.
Panchapagesan, T.V.. "On the distinguishing features of the Dobrakov integral.." Divulgaciones Matemáticas 3.1 (1995): 79-114. <http://eudml.org/doc/47824>.
@article{Panchapagesan1995,
author = {Panchapagesan, T.V.},
keywords = {semivariation; -simple function; -measurable function; Dobrakov integration theory; operator-valued measure; Lebesgue integral; Bochner integral; Pettis integral; Bartle-Dunford-Schwartz integral; Dinculeanu integral; Fubini theorem; Radon-Nikodým theorem; -simple function; -measurable function},
title = {On the distinguishing features of the Dobrakov integral.},
AU - Panchapagesan, T.V.
TI - On the distinguishing features of the Dobrakov integral.
KW - semivariation; -simple function; -measurable function; Dobrakov integration theory; operator-valued measure; Lebesgue integral; Bochner integral; Pettis integral; Bartle-Dunford-Schwartz integral; Dinculeanu integral; Fubini theorem; Radon-Nikodým theorem; -simple function; -measurable function
N.U. Ahmed, Vector and operator valued measures as controls for infinite dimensional systems: optimal control
José Rodríguez, On integration of vector functions with respect to vector measures
semivariation,
𝒫
-simple function,
𝒫
-measurable function, Dobrakov integration theory, operator-valued measure, Lebesgue integral, Bochner integral, Pettis integral, Bartle-Dunford-Schwartz integral, Dinculeanu integral, Fubini theorem, Radon-Nikodým theorem,
𝒫
𝒫
Articles by Panchapagesan
|
Mechanism - Collar Finance
Using Collar for Borrowing
Collar is a lending protocol for pegged cryptoassets.
As an illustration, throughout this article we will only consider the example of borrowing USDT using USDC.
An example of depositing USDC to borrow USDT using Collar
On a market for borrowing USDT using USDC, users can deposit n USDC into a Collar vault as collateral and get back two types of tokens: n CALL tokens and n COLL tokens, both minted with an expiry that specifies the duration of the loan. These tokens have the following properties:
Before expiry anyone can:
Redeem 1 CALL and 1 USDT for 1 USDC
Redeem 1 CALL and 1 COLL for 1 USDC
After expiry anyone can:
Reedem 1 COLL for x USDT and y USDC, where
x+y = 1
x = \cfrac{\mathrm{total\thinspace USDT}}{\mathrm{total\thinspace (USDT + USDC)}}
This just means the lender receives a mix of USDT and USDC that is in proportion to the amounts repaid and defaulted (respectively) by all the borrowers.
Essentially, when a borrower deposits USDC into the vault, a covered call option and a protective put option are minted. The covered call acts as the borrower's deposit proof and is kept by the borrower. The protective put option is sold to a lender for his USDT. The price difference between the put option and the USDT acts as the loan interest.
TLDR Each loan in Collar involves 4 types of tokens: the asset deposited by a borrower as collateral (BOND token), one that represents the borrower's right to repay the loan (CALL token), the right to the debt (COLL token), and the asset borrowed (WANT token). Borrowers sell their COLL tokens to lenders for their WANT tokens. For more details, please see Collar Tokens.
Borrowing In-Depth
When a borrower wants to borrow USDT using USDC, they deposit USDC into a Collar vault as collateral and receive calUSDC tokens proving their deposit and colUSDC tokens representing their debt, and then they sell the colUSDC for USDT on a Uniswap-like AMM that is incentivized through COLLAR governance token emissions. When they want to repay the loan they have 2 options. The first is to repay the USDT to the vault and burn their calUSDC to unlock their USDC. The second is to sell their USDT back for colUSDC and burn their calUSDC to unlock their USDC. Using the second option ensures the borrower pays interest only on the duration of the loan (the first option is provided to borrowers to be used in cases of lack of colUSDC liquidity).
Importantly, the loan interest is determined by the USDT/colUSDC price. There are several market forces controlling this price:
at expiry, USDT ~= colUSDC, since colUSDC will be redeemable for USDT/USDC
the price of 1 colUSDC will always be less than 1 USDT, as otherwise someone can arbitrage by minting colUSDC, selling it for USDT, and then repaying the loan with USDT
the price of colUSDC should rise as expiry approaches since the opportunity cost gets lower (assets will be unlocked in less time)
Furthermore, If colUSDC << USDT:
buy pressure on colUSDC will increase both from lenders and from those who have borrowed USDT at an earlier time because they will sell it back for colUSDC and retrieve their USDC, arbitraging the system.
Therefore, the price should follow a pattern similar to this:
colUSDC/USDT price
A borrower who borrows on one month and repays the loan in the next month will only have to pay the difference in price between these two times as the interest for their loan. Buy pressure on colUSDC comes from lenders who want to pocket the premium (buy colUSDC for $0.95 and wait 6 months to get $1 back).
Parallels with Traditional Finance
calUSDC is effectively a call option on USDC, allowing its holder to buy USDC with USDT for a set price up until expiry, hence it's name.
On the other hand, colUSDC is a claim on the loan collateral that can only be exercised after expiry, so we chose to prefix it with col (for collateral).
This construction is similar to a collar, an option strategy from traditional finance used to limit both downside and upside. It is based on buying a put option and financing that by selling a call option on the same asset, and that's where our protocol gets its name.
Protection Against De-Pegs
Borrowing assets using Collar gives you protection against de-pegs of both the asset you borrow and the one you deposit as collateral (although not both at the same time). These are the possible scenarios for borrowers of USDT using USDC as an example:
USDC De-Pegs
Borrowers keep the USDT and never repay the loans.
The vault contains USDC, so, at expiry, the lenders redeem their colUSDC for USDC.
USDT De-Pegs
Borrowers repay the USDT and burn their calUSDC to unlock the USDC.
The vault contains USDT, so, at expiry, the lenders redeem their colUSDC for USDT.
USDC and USDT Stay Pegged
Borrowers either keep the USDT, repay the USDT and burn their calUSDC to unlock the USDC, or buy back colUSDC and burn it and their calUSDC to unlock the USDC.
The vault contains both USDT and USDC depending on the choices made by the borrowers, so, at expiry, the lenders redeem their colUSDC for a mix of USDT and USDC.
Minimizing Pairs
With the mechanism described so far, we'd need to establish a new AMM pool for each BOND/WANT token pair. This would heavily split liquidity across pools, as you'd need
O(n^2)
pairs to cover all possibilities.
Instead, in the cases of DAI, USDC, and USDT as BOND tokens, we plan to only have a single pool in which all 3 are paired against Curve's 3Crv LP token, as that will allow us to get liquidity against DAI, USDC and USDT with a single pair. From the user's side this just adds an extra step to the flow, as the borrower will need to withdraw the asset they want from the 3Pool after borrowing 3Crv from Collar. Please see CIP 1.
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Zariski Density of Points with Maximal Arithmetic Degree
2022 Zariski Density of Points with Maximal Arithmetic Degree
Kaoru Sano, Takahiro Shibata
Given a dominant rational self-map on a projective variety over a number field, we can define the arithmetic degree at a rational point. It is known that the arithmetic degree at any point is less than or equal to the first dynamical degree. In this paper, we show that there are densely many
\stackrel{‾}{\mathbb{Q}}
-rational points with maximal arithmetic degree (i.e., whose arithmetic degree is equal to the first dynamical degree) for self-morphisms on projective varieties. For unirational varieties and Abelian varieties, we show that there are densely many rational points with maximal arithmetic degree over a sufficiently large number field. We also give a generalization of a result of Kawaguchi and Silverman in the Appendix.
Kaoru Sano. Takahiro Shibata. "Zariski Density of Points with Maximal Arithmetic Degree." Michigan Math. J. Advance Publication 1 - 20, 2022. https://doi.org/10.1307/mmj/20205960
Received: 3 August 2020; Revised: 6 December 2020; Published: 2022
Kaoru Sano, Takahiro Shibata "Zariski Density of Points with Maximal Arithmetic Degree," Michigan Mathematical Journal, Michigan Math. J. Advance Publication, 1-20, (2022)
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Research:Onboarding new Wikipedians/OB6 - Meta
The purpose of this experiment is to compare the current onboarding experience (very similar to R:OB5) to a new test version, which presents calls to action after redirecting the user back to the page they were on prior to registration. Learn more about the test user experience.
2.1 Metrics (quantitative)
3.2 Newcomer productivity
RQ: How does OB6 affect newcomers' editing activities?
OB6 represents a substantial improvement to the user experience. Rather than directing users to a Special page after they register an account, this change to the onboarding experience lets a newcomer choose whether to learn to edit to the article they were visiting, or proceed directly to a copy-editing task. We suspect that by minimizing the interruption to newcomers' browsing, reducing the number of options provided, and by providing immediate access to work that newcomers can contribute productively to, we'll both increase newcomer contributions and increase their rate of success.
Since newcomers with OB6 will be brought back to the page they were looking at, we suspect that they will both be more likely to make an edit right after registering and will edit more than the control condition overall.
Hypothesis 1: Newcomers with OB6 will contribute more.
Since newcomers with OB6 will be directed toward copy-editing work -- a type of work that newcomers should be able to contribute productively to without learning much about Wikipedia -- we expect that this will increase the proportion of newcomers who manage to make productive contributions.
Hypothesis 2: Newcomers with OB6 will be more likely to make productive contributions.
Despite the fact that we hypothesize that newcomers will contribute more with OB6, our means for encouraging them to contribute focus on a low difficulty type of work: copy editing. Due to the low difficulty of this task, we expect two effects that minimize the possibility that newcomers will make contributions that lead to them being reverted or blocked.
For the week of Oct. 8-15th, 2013, we will randomly split newly registered users between a control (current, OB5-like) and a test condition (OB6) based on their user ids.
OB6 cohort: users which were presented with the new OB6 onboarding experience, and who elected to either edit the page they were redirected to, or accept a Getting Started suggested page to copyedit
Control cohort: users which were presented with the current default OB5-like onboarding experience, and who accept one of the three types of suggested tasks (copyediting, adding wiki links, clarifying content)
Metrics (quantitative)Edit
Based on the activities of these newcomers, we'll capture a set of behavioral measures from the Mediawiki database to check our hypotheses and generate some usage statistics from logging. See Schema:GettingStartedOnRedirect.
As in previous experiments, we'll observe the number of edits that newcomers save with a focus on two key thresholds:
1+ NS0 edits
Unlike previous experiments, we'll include some more intuitive measures of newcomers investment based on their edit sessions. Specifically we'll measure the amount of sessions newcomers complete in their first week and the amount of time they spend editing within those sessions.
In order to get a sense for the proportion of newcomers who make productive contributions in their session of editing, we'll look for NS0 edits that are not quickly reverted under the assumption (based on previous research[1]) that automated systems like ClueBot NG and semi-automated tools like Huggle will remove most damage within minutes. We'll determine a newcomers NS0 edit to be "productive" if their edit is not reverted within 48 hours.
In order to explore the quality of the contributions by newcomers, we'll measure whether users made at least one productive edit (i.e. an edit that was not reverted within 48hrs), as well as the long term proportion of reverts for users who continued editing.
We also examined the type of edits and the type of pages edited by users in the test.
In addition to the amount of time spent editing, number of edits, and related quality metrics, we'll compare whether new editors from each cohort stick around on Wikipedia. We'll measure survival based on whether newcomers continue editing past a week and throughout the following 30 days.
Funnel analysisEdit
Funnel analysis of these cohorts will be limited, as we are not tracking the full edit-preview-save funnel in this experiment. However, we can examine the click-through rate (CTR) for users presented with each test or control experience, with the funnel limited to the point at which they accept a call to action.
However, we may examine how many users elected to take the full guided tour of how to edit, in either test or control groups. Each tour step, including whether the user closed a tour, is logged as part of Schema:GuidedTour.
In order to get a sense for how newcomers were making use of the new version of onboarding, we generated the following funnel graphs.
Control funnel. The funnel graph for the control condition is presented
Test funnel. The funnel graph for the test condition (OB6) is presented
The control funnel has similar behavior compared to past experiments, such as the preceding A/B test. Overall, the Special page had a 34% click-through rate. The copyedit task ("Fix spelling and grammar") was the most popular, with add wikilinks the second most-clicked task type.
The test funnel demonstrates several interesting patterns.
Partial CTA
Roughly half of users were redirected to non-editable pages or non-article pages, resulting in seeing a CTA that only invited them to "Find pages that need easy fixes" (i.e. the copyediting task).
Of the users who were redirected back to editable articles, a small but important minority (337 users, 3%) were already editing, and skipped all CTAs.
Another minority were viewing Special pages (587, 5%), such as search, and also skipped all CTAs.
Full CTA
The rest of users (41.7%) were reading an editable article, and for these users, choosing to "Edit this page" with a guided tour was by far the most popular option (46%).
User who saw the Full CTA had an astoundingly high rate of edits, with 51% of them completing an edit to that page. This is one of the highest conversion rates we have observed in desktop or mobile experiments; compare to new mobile editors, another successful group.
However, we also saw that users who were redirected back to non-articles and presented with the Partial CTA were far less likely to accept a task suggestion (70-80% dismissed the modal, versus around 60% for the test group overall), and to complete any edits (17% completed 1+ article edits, compared to 22% in the test group overall.)
Newcomer productivityEdit
In order to compare the productivity between the experimental conditions, we gathered statistics for users who were bucketed into each condition. We filtered out users who had Javascript turned off (and therefore could not have seen the test condition) by limiting our analysis to users who had at least one log event stored. Note that log events for OB6 are stored via a javascript request.
Users in the test condition received a different experience based on where they were when they signed up (note the funnel analysis above). To bring a more nuanced view to our analysis, we split users based on this pre-registration page regardless of experimental condition in order to perform a fair comparison. Since this analysis affords a more nuanced explanation of the results, we opt to present graphs split by this return type.
First, we look at two metrics that have become a staple for the Growth team: NS0 24h 1+ and NS0 24h 5+. Here, we see no significant differenced between the cohorts for either the one article edit or five article edit thresholds. This suggests that, if OB6 changes newcomer behavior, it isn't visible in the first 24 hours of activity.
NS0 24h 1+. The proportion of newcomers who make at least one article edit within the first 24 hours is plotted with (normal approx.) standard error bars by experimental bucket.
NS0 24h 5+. The proportion of newcomers who make at least five article edits within the first 24 hours is plotted with (normal approx.) standard error bars by experimental bucket.
Next, we looked at the number of sessions and amount of time that newcomers spent editing in their first week since registration. The figures below show that neither the number of sessions nor the time spent editing differs between cohorts in a significant way for their first week. Combined with the results above, it seems clear that OB6 does not substantially affect the short- or mid-term activity level of newcomers.
Edit sessions. The geometric mean number of first week edit sessions is plotted with geometric standard error bars by experimental bucket.
Time spent editing. The geometric mean within-session seconds is plotted with geometric standard error bars by experimental bucket.
Next, we looked at the quality of work performed by newcomers by measuring the proportion of newcomers who managed to make an edit to an article that was not immediately reverted in their first week. Newcomers in the test condition were significantly less likely to make at least one productive contribution overall (
{\displaystyle X^{2}=4.2}
, p = 0.041). When we broke down the productive proportion by the user's return type, it seems clear that this drop in productivity occurred primarily in the case where users were redirected back to a non-Article page view (25.7% of newcomers in the test condition).
This result could suggest that a part of the process of making ones first contributions breaks down in the case that a newcomer is shown a partial CTA (as is done on non-main pages). A logical conclusion from the analysis is that these newcomers would perform better (as measured by productive edits) if they were shown Special:GettingStarted rather than the Partial CTA.
Productive editors. The proportion of newcomers who make at least one productive edit their first week is plotted with (normal approx.) standard error bars by experimental bucket.
Productive edits. The geometric mean number of productive edits made in newcomers' first weeks is plotted with geometric standard error bars by experimental bucket.
In this test, we set out to compare two very different workflows for onboarding new Wikipedians. In the control, we redirected all newly-registered users through a page with three suggestions for editing tasks (Special:GettingStarted). We compared this to a test workflow, where users were redirected back to the page they were on prior to account creation, and then either invited to edit the current page (if possible) or edit a suggested page that needed grammar and spelling fixes.
We made the following hypotheses:
unsupported: Statistically-speaking, newcomers in the test group contributed the same amount of content edits as the control group, when looking at the rate at which they reached 1+ and 5+ edits to articles.
rejected: When looking at the test group as a whole, they were slightly less likely to be productive editors than the control group. This result demonstrates one of the inherent risks in a more nuanced workflow. In order to understand why, we examined more detailed sub-groups (return type) in the test & control conditions, separating them out based on what kind of page they were redirected back to.
We observed that the overall lower productivity seems to have been caused by one particular minority of editors: those who we redirected back to non-articles, such as Help pages and policy (25.7% of test condition users). For other users, however, there are substantial benefits to the test version. For those already editing a page when they signed up, we sent them straight back to editing. Also, 51% of those who were reading an editable article and who accepted a guided tour contributed to that page successfully, which is one of the highest conversion rates we've ever observed.
Overall, we believe the improved flexibility of the test version outweighs the minor reduction productivity for some sub-groups of users. Rather than forcing all users through the same experience, tailoring the UX of onboarding to the user can produce substantial benefits for the users most motivated to edit. In future, we'll work on making specific improvements to help less productive workflows improve.
↑ When the Levee Breaks: Without Bots, What Happens to Wikipedia's Quality Control Processes? R. Stuart Geiger & Aaron Halfaker. (2013). WikiSym.
Retrieved from "https://meta.wikimedia.org/w/index.php?title=Research:Onboarding_new_Wikipedians/OB6&oldid=8419395"
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EUDML | Brownian bridge asymptotics for random -mappings. EuDML | Brownian bridge asymptotics for random -mappings.
Brownian bridge asymptotics for random
p
-mappings.
Aldous, David, Miermont, Grégory, and Pitman, Jim. "Brownian bridge asymptotics for random -mappings.." Electronic Journal of Probability [electronic only] 9 (2004): 37-56. <http://eudml.org/doc/124724>.
@article{Aldous2004,
author = {Aldous, David, Miermont, Grégory, Pitman, Jim},
keywords = {Brownian bridge; Brownian excursion; Joyal map; random mapping; random tree; weak convergence},
title = {Brownian bridge asymptotics for random -mappings.},
AU - Aldous, David
TI - Brownian bridge asymptotics for random -mappings.
KW - Brownian bridge; Brownian excursion; Joyal map; random mapping; random tree; weak convergence
Xinxing Chen, Jiangang Ying, The Markov chain asymptotics of random mapping graphs
Brownian bridge, Brownian excursion, Joyal map, random mapping, random tree, weak convergence
Articles by Aldous
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EUDML | Group Actions on the Chern Manifold. EuDML | Group Actions on the Chern Manifold.
Group Actions on the Chern Manifold.
Dariusz M. Wilcznski
Wilcznski, Dariusz M.. "Group Actions on the Chern Manifold.." Mathematische Annalen 281.2 (1988): 333-340. <http://eudml.org/doc/164423>.
@article{Wilcznski1988,
author = {Wilcznski, Dariusz M.},
keywords = {locally linear actions of finite groups on the Chern manifold; homotopy },
title = {Group Actions on the Chern Manifold.},
AU - Wilcznski, Dariusz M.
TI - Group Actions on the Chern Manifold.
KW - locally linear actions of finite groups on the Chern manifold; homotopy
locally linear actions of finite groups on the Chern manifold, homotopy
ℂ{P}^{2}
{E}^{4}
4
Articles by Dariusz M. Wilcznski
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Transition from Low to High-Fidelity UAV Models in Three Stages - MATLAB & Simulink - MathWorks Switzerland
Open Example and Project Files
Low-Fidelity Model
Medium-Fidelity Model
Medium-Fidelity Step Response
Simulate Path Following Algorithm
High-Fidelity Step Response
Simulate Path Following Algorithm for High-Fidelity
An unmanned aerial vehicle (UAV) design cycle provides incrementally better access to UAV characteristics as the design progresses. By increasing its fidelity, this information can be used to continuously evolve a plant model through a Model Based Design approach.
Towards the end of the design cycle, there is enough information to develop a high-fidelity plant. To accurately model the UAV, a high-fidelity model incorporates modeling all forces and moments, wind and environmental effects and sensors in detail. However, this level of information may be unavailable to a designer early in the design process. To build such a complex model, it can take several flight and wind tunnel tests to create enough detailed aerodynamic coefficients to compute all forces and moments that affect the UAV. These factors can potentially block guidance algorithm design until the end of the design process, when a more realistic estimate of UAV dynamics is obtained.
To concurrently design a guidance algorithm sooner, a UAV algorithm designer can start with a low-fidelity model and evolve their plant model as and when additional data becomes available.
Designing a guidance algorithm using only a low-fidelity model can also pose a risk. Without controller or aerodynamic constraints, an optimistic guidance technique can fail for a real UAV with slower aircraft dynamics.
This example highlights an alternative approach. You progress from the low-fidelity Guidance Block to a medium and then high-fidelity model by progressively adding layers of control and dynamics to the simulation. In this process, the medium-fidelity model becomes a useful tool for leveraging limited information about a plant model to tune and test guidance algorithms.
The medium-fidelity model is thus used to test a given path following an algorithm. Since the high-fidelity model is unavailable until the end of the design process, the high-fidelity model is only used later to validate our modelling approach by comparing step response and path following behavior.
To access the example files, click Open Live Script or use the openExample function.
openExample('shared_uav_aeroblks/UAVFidelityExample')
Open the Simulink™ project provided in this example.
cd fidelityExample
openProject('fidelityExample.prj')
The project contains three versions of a UAV model, low-fidelity, medium-fidelity and high-fidelity with steps to study their step response and path following behaviour.
Assume your UAV has the following design specifications shown in the table below. The low-fidelity variant provided in this model is tuned to achieve the desired response, but you can tune these gains for your specific requirements. The low-fidelity plant uses the UAV Guidance Block which is a reduced order model for a UAV. To run the low-fidelity variant, click the Simulate Plant shortcut under the Low Fidelity group of the project toolstrip.
This shortcut sets the FidelityStage parameter to 1, configures the FidelityStepResponse model to simulate the low-fidelity model, and outputs the step response. The step response is computed for height, airspeed, and roll response.
Open the UAV Fixed Wing Guidance Model block in the FidelityStepResponse/FixedWingModel/LowFidelity subsystem. In the Configuration tab, inspect the gains set for height, airspeed, and roll response. This guidance block integrates the controller with the dynamics of the aircraft. The low-fidelity variant gives a first estimate of how fast the UAV can realistically respond to help tune high-level planners.
As the UAV design progresses, the lift and drag coefficients become available. A motor for the aircraft is selected by the user, which defines the thrust curves. To test the validity of the guidance algorithm against this new information, the example adds this information to the plant model in this step.
To design a medium-fidelity model, the model needs only preliminary aerodynamic coefficients, thrust curves, and response time specifications. To model a medium-fidelity UAV, you can use the Fixed-Wing Point Mass Block. The block only requires lift, drag and thrust force inputs, which are much easier to approximate at an early design stage than detailed forces and moments of an aircraft. To set up the medium-fidelity variant, click the Setup Plant shortcut under the Medium Fidelity group of the project toolstrip.
Examine the Vehicle Dynamics tab in the model under FidelityStepResponse/FixedWingModel/Mid Fidelty/UAV Plant Dynamics/Vehicle Dynamics.
The medium-fidelity model represents the UAV as a point mass with the primary control variables being the angle of attack and roll. This medium-fidelity plant model takes in roll, pitch, thrust as control inputs. The point mass block assumes instantaneous dynamics of roll and angle of attack. This model uses a transfer function to model roll lag based on our roll-response specification shared in the table within the previous step.
The medium-fidelity aircraft controls pitch instead of angle of attack. Since the angle of attack is an input to the point mass block, the plant model converts pitch to alpha using the following equation.
\Theta ={\gamma }_{\mathit{a}}
\alpha
\Theta
{\gamma }_{\mathit{a}}
\alpha
represent pitch, flight path angle in the wind frame, and angle of attack respectively.
Unlike the low-fidelity model, the medium-fidelity model splits the autopilot from the plant dynamics. The medium-fidelity plant needs an outer-loop controller for height-pitch and airspeed-throttle control to be added. The predefined controllers provided are using standard PID-tuning loops to reach satisfactory response without overshoot. To inspect the outer-loop controller, open the Outer_Loop_Autopilot Simulink model.
The low-fidelity plant was tuned in the previous step by assuming that all response time specifications are met by the UAV. To test this assumption, use the medium-fidelity plant. The study of the step response of the improved plant is used to contrast the performance of the low-fidelity and medium-fidelity variant. To simulate the medium-fidelity step response, click the Simulate Plant shortcut under the Medium Fidelity group of the project toolstrip. The step response plots appear as figures.
Notice that the model meets the design criteria shown in the table below by achieving an air speed settling time of 0.6 seconds and a height response of 4.1 seconds. However, the height response is slower than the low-fidelity variant. This lag in response is expected due to the additional aerodynamic constraints placed on the medium-fidelity plant.
With a more accurate response from the UAV medium-fidelity model, you can now test waypoint follower or guidance algorithms to follow waypoints. For the guidance algorithm design, see the "Tuning Waypoint Follower for Fixed-Wing UAV" example.
To simulate and visualize the medium-fidelity UAV path following the model, click the Simulate Path Follower shortcut under the Medium Fidelity group of the project toolstrip.
Notice that the medium-fidelity UAV follows the desired path accurately.
The medium-fidelity model was used to test a path follower design using simple aircraft parameters available at an early design state. However, it is important to continue adding fidelity to capture UAV control response to study more complex situations. For example, the use of more detailed aerodynamics coefficients allows analysis of complex motions such as doublet maneuvers. Another example is, adding actuator dynamics lets you study the subsequent effect on inner loop controllers for attitude, which can cause destabilization. In this way, the high-fidelity plant allows refinement of control system design. In this step, to study the change in response, we look at a high-fidelity plant with these added dynamics.
The high-fidelity plant inputs all forces and moments to a 6-DOF block, adds on-board sensors, and models actuator dynamics for the UAV. Unlike the mid-fidelity plant, the high-fidelity version does not take attitude inputs directly. Instead, an inner loop controller is added to control attitude. Additionally, a yaw compensation loop balances the non-zero sideslip. The model reuses the outer-loop controller designed for the medium-fidelity model. To validate that the medium-fidelity model provided useful intermediate information, use the response of the higher fidelity model.
To simulate and visualize the high-fidelity step response, click the Simulate Plant shortcut under the High-Fidelity group of the project toolstrip. Notice that despite added complexity, the trajectory matches well with the medium-fidelity model. Also, notice the design specifications are relatively the same for the high-fidelity stage. This similarity shows that the medium-fidelity plant modelled UAV dynamics accurately.
Towards the end of the design cycle, the high-fidelity model finally becomes available. To get the final UAV path following characteristics, you can now test the guidance algorithm developed in previous steps on the high-fidelity plant. Click the Simulate Path Follower shortcut under the High-Fidelity group of the project toolstrip.
Notice that the model obtains a similar response to the medium-fidelity model using the guidance and outer-loop control parameters. This validates the guidance algorithm with a high-fidelity plant.
The medium-fidelity model accurately predicts the UAV dynamics making optimum use of limited information available during design. The example designs the outer loop controller and tests a waypoint follower without needing all the information in a high-fidelity plant model.
To model additional dynamics such as actuator lag, the medium-fidelity plant is flexible and can continuously evolve alongside design. The example obtains results under zero-wind conditions. In the presence of wind disturbances, the controller and path follower performance tracking might be adversely affected. To augment the autopilot controller to compensate for wind effects, leverage the atmospheric wind model in the high-fidelity plant model.
Guidance Model | Fixed-Wing UAV Point Mass
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{\displaystyle \mathbf {B} /\mu _{0}=\mathbf {H} }
1.1 The B-field
1.2 The H-field
2 Magnetic field of permanent magnets
2.1 Magnetic pole model
2.2 Amperian loop model
3 Interactions with magnets
3.1 Force between magnets
3.2 Magnetic torque on permanent magnets
4 Interactions with electric currents
4.1 Magnetic field due to moving charges and electric currents
4.2 Force on moving charges and current
4.2.1 Force on a charged particle
4.2.2 Force on current-carrying wire
5 Relation between H and B
5.2 H-field and magnetic materials
6 Stored energy
7 Appearance in Maxwell's equations
7.1 Gauss' law for magnetism
7.3 Ampère's Law and Maxwell's correction
8 Formulation in special relativity and quantum electrodynamics
8.1 Electric and magnetic fields: different aspects of the same phenomenon
9.2 Rotating magnetic fields
9.5 Largest magnetic fields
10.1 Early developments
10.2 Mathematical development
{\displaystyle \mathbf {F} =q\mathbf {E} +q(\mathbf {v} \times \mathbf {B} )}
{\displaystyle \mathbf {F} _{\text{electric}}=q\mathbf {E} .}
{\displaystyle \mathbf {F} _{\text{magnetic}}=q(\mathbf {v} \times \mathbf {B} ).}
{\displaystyle F_{\text{magnetic}}=qvB\sin(\theta )}
{\displaystyle \mathbf {\tau } =\mathbf {m} \times \mathbf {B} }
{\displaystyle \mathbf {H} \equiv {\frac {1}{\mu _{0}}}\mathbf {B} -\mathbf {M} }
{\displaystyle \mu _{0}}
Main article: Field line
Main article: Magnetic moment § Models
See also: Magnetic monopole
See also: Spin magnetic moment and Micromagnetism
{\displaystyle m=Ia,\,}
{\displaystyle \mathbf {F} ={\boldsymbol {\nabla }}\left(\mathbf {m} \cdot \mathbf {B} \right),}
Main article: Magnetic torque
{\displaystyle {\boldsymbol {\tau }}=\mathbf {m} \times \mathbf {B} =\mu _{0}\mathbf {m} \times \mathbf {H} ,\,}
Main articles: Electromagnet, Biot–Savart law, and Ampère's law
{\displaystyle \mathbf {B} ={\frac {\mu _{0}I}{4\pi }}\int _{\mathrm {wire} }{\frac {\mathrm {d} {\boldsymbol {\ell }}\times \mathbf {\hat {r}} }{r^{2}}},}
{\displaystyle |\mathbf {B} |={\frac {\mu _{0}}{2\pi r}}I}
{\displaystyle {I}}
{\displaystyle \oint \mathbf {B} \cdot \mathrm {d} {\boldsymbol {\ell }}=\mu _{0}I_{\mathrm {enc} },}
{\displaystyle {I}}
Main article: Lorentz force
{\displaystyle \mathbf {F} =q\mathbf {E} +q\mathbf {v} \times \mathbf {B} ,}
Main article: Laplace force
{\displaystyle F=qvB\sin \theta ,}
{\displaystyle N=n\ell A,}
{\displaystyle f=FN=qvBn\ell A\sin \theta =Bi\ell \sin \theta ,}
{\displaystyle \oint \mathbf {M} \cdot \mathrm {d} {\boldsymbol {\ell }}=I_{\mathrm {b} },}
{\displaystyle \oint _{S}\mu _{0}\mathbf {M} \cdot \mathrm {d} \mathbf {A} =-q_{\mathrm {M} },}
See also: Demagnetizing field
{\displaystyle \mathbf {H} \ \equiv \ {\frac {\mathbf {B} }{\mu _{0}}}-\mathbf {M} .}
{\displaystyle \oint \mathbf {H} \cdot \mathrm {d} {\boldsymbol {\ell }}=\oint \left({\frac {\mathbf {B} }{\mu _{0}}}-\mathbf {M} \right)\cdot \mathrm {d} {\boldsymbol {\ell }}=I_{\mathrm {tot} }-I_{\mathrm {b} }=I_{\mathrm {f} },}
{\displaystyle \left(\mathbf {H_{1}^{\parallel }} -\mathbf {H_{2}^{\parallel }} \right)=\mathbf {K} _{\mathrm {f} }\times {\hat {\mathbf {n} }},}
{\displaystyle {\hat {\mathbf {n} }}}
{\displaystyle \oint _{S}\mu _{0}\mathbf {H} \cdot \mathrm {d} \mathbf {A} =\oint _{S}(\mathbf {B} -\mu _{0}\mathbf {M} )\cdot \mathrm {d} \mathbf {A} =0-(-q_{\mathrm {M} })=q_{\mathrm {M} },}
{\displaystyle \mathbf {H} =\mathbf {H} _{0}+\mathbf {H} _{\mathrm {d} },}
{\displaystyle \mathbf {B} =\mu \mathbf {H} ,}
See also: Magnetic hysteresis
{\displaystyle u={\frac {\mathbf {B} \cdot \mathbf {H} }{2}}={\frac {\mathbf {B} \cdot \mathbf {B} }{2\mu }}={\frac {\mu \mathbf {H} \cdot \mathbf {H} }{2}}.}
{\displaystyle \delta W=\mathbf {H} \cdot \delta \mathbf {B} .}
{\displaystyle {\scriptstyle S}}
{\displaystyle \mathbf {B} \cdot \mathrm {d} \mathbf {A} =0}
{\displaystyle {\mathcal {E}}=-{\frac {\mathrm {d} \Phi }{\mathrm {d} t}}}
{\displaystyle {\mathcal {E}}}
{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}}
{\displaystyle \nabla \times \mathbf {B} =\mu _{0}\mathbf {J} +\mu _{0}\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}}
{\displaystyle \nabla \times \mathbf {H} =\mathbf {J} _{\mathrm {f} }+{\frac {\partial \mathbf {D} }{\partial t}}}
Main article: Magnetic vector potential
{\displaystyle {\begin{aligned}\mathbf {B} &=\nabla \times \mathbf {A} ,\\\mathbf {E} &=-\nabla \varphi -{\frac {\partial \mathbf {A} }{\partial t}}.\end{aligned}}}
Main articles: Rotating magnetic field and Alternator
Main article: Hall effect
Main article: Magnetic circuit
{\displaystyle \Phi ={\frac {F}{R}}_{\mathrm {m} },}
{\textstyle \Phi =\int \mathbf {B} \cdot \mathrm {d} \mathbf {A} }
{\textstyle F=\int \mathbf {H} \cdot \mathrm {d} {\boldsymbol {\ell }}}
Last update: October 2018 (July 2021)
Main article: History of electromagnetic theory
{\displaystyle \textstyle {\mathcal {E}}=-d\Phi /dt}
{\displaystyle \textstyle =\oint _{\partial \Sigma (t)}\left(\mathbf {E} (\mathbf {r} ,\ t)+\mathbf {v\times B} (\mathbf {r} ,\ t)\right)\cdot d{\boldsymbol {\ell }}\ }
{\displaystyle \textstyle =-{\frac {d}{dt}}\iint _{\Sigma (t)}d{\boldsymbol {A}}\cdot \mathbf {B} (\mathbf {r} ,\ t)}
Retrieved from "https://en.wikipedia.org/w/index.php?title=Magnetic_field&oldid=1085619251"
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5 posts tagged with "research" | Flashbots
5 posts tagged with "research"
Unity is Strength - A Formalization of Cross-Domain Maximal Extractable Value
The multi-chain future is upon us. Modular architectures are coming to maturity across the ecosystem to scale bandwidth and throughput of cryptocurrency. One example of such is the Ethereum modular architecture, with its beacon chain, its execution chain, its Layer 2s, and soon its shards. These can all be thought as separate blockchains, heavily inter-connected with one another, and together forming an ecosystem.
The incorporation of EIP-1559 in the London hardfork brings a major restructuring of the Ethereum fee mechanism, aiming to allow for easier fee estimation by users and consolidate ETH as the base currency of the network by burning part of the transaction fees. This post analyzes some of the consequences of this EIP under the light of the MEV (Maximal Extractable Value) phenomenon, that is, the permissionless extraction of value by the reordering, addition, or censoring of transactions.
MEV in eth2 - an early exploration
Ethereum will soon transition from a Proof of Work (PoW) to a Proof of Stake (PoS) consensus protocol. This transition has been worked on for years and is happening in multiple steps. The first step in December 2020 consisted in launching the beacon chain. It is now live, and, at the time of writing, has more than 160k validators or an equivalent of ~5m ETH staked on it.
Quantifying Realized Extractable Value
Maximal (formerly Miner) Extractable Value (
\textrm{MEV}
) is the value that can be extracted from a blockchain by any agent without special permissions. Considering this permissionless nature, any agent with transaction ordering rights will be in a privileged position to perform the extraction. In Proof of Work blockchains, it is miners who determine transaction ordering within a block, hence the former "miner" term. In practice, bot operators seek to extract
\textrm{MEV}
by either paying high fees to increase the likelihood that their transactions are mined, or by fine-tuning their gas price choices in order to "time" their transactions right, as is the case when backrunning an oracle update to perform a liquidation.
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Ask Answer - Determinants, Inverse Trigonometric Functions, Maths, Relations and Functions, Continuity and Differentiability, Probability, Vector Algebra - Popular Questions for School Students
Lovepreet Singh Johar
Linu Dash
Q.72. If sin (3x - 2y) = log (3x - 2y), then
\frac{dy}{dx}
If A = {1,2,3,4,5}, write the relation a R b such that a + b = 8, a ,b € A. Write the domain, range & co-domain.
Guitars R0ck
what is the value of e raised to infinity ?
Kwxyz
A={1,3,5}; B= {9,11} R = {(a,b) belongs to AxB:a-b is odd} Write the relation R
if f (x) = ln(x^2+7 |x|+10) is a single valued real function then range of f(x) in its natural domain will be
f(x) = x + 1/x, find
1. (fof)of
2. fo(fof)
Nikesh Chauhan
There is 80% chance that a problem will be solved by a statistics student and 60% chance that it will be solved independently by a mathematics student
find the probabolity that it will be solved.
Find the period of the function [sin3x] +
|cos6x| , where [] is greatest integer function and | | denotes modulus function . Answer is 2π/3
if any two function f and g : R→ R
and gof(x) = 2x-1
then find g(x) ?????
If f(x) = ax + 3sinx + 4cosx is injective then prove a ∈(∞,5] U5, ∞)
Sriju Ladashu Crma
Hardee Shah
The vector component of vector A=3i+4j+5k along vector B=I+j+k is
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EUDML | On rational approximations of algebraic numbers . EuDML | On rational approximations of algebraic numbers .
On rational approximations of algebraic numbers
\sqrt[3]{D}
Tasoev, B.G.
Tasoev, B.G.. "On rational approximations of algebraic numbers .." Vladikavkazskiĭ Matematicheskiĭ Zhurnal 3.3 (2001): 32-51. <http://eudml.org/doc/123796>.
@article{Tasoev2001,
author = {Tasoev, B.G.},
keywords = {rational approximation; algebraic number},
title = {On rational approximations of algebraic numbers .},
AU - Tasoev, B.G.
TI - On rational approximations of algebraic numbers .
KW - rational approximation; algebraic number
rational approximation, algebraic number
Approximation to algebraic numbers
Articles by Tasoev
|
EUDML | A remark on the uniform extendability of the Bergman kernel function. EuDML | A remark on the uniform extendability of the Bergman kernel function.
So-Chin Chen
Chen, So-Chin. "A remark on the uniform extendability of the Bergman kernel function.." Mathematische Annalen 291.3 (1991): 481-486. <http://eudml.org/doc/164881>.
author = {Chen, So-Chin},
keywords = {condition ; smoothly bounded domain; Bergman kernel function; uniformly holomorphic extendability},
title = {A remark on the uniform extendability of the Bergman kernel function.},
AU - Chen, So-Chin
TI - A remark on the uniform extendability of the Bergman kernel function.
KW - condition ; smoothly bounded domain; Bergman kernel function; uniformly holomorphic extendability
Q
, smoothly bounded domain, Bergman kernel function, uniformly holomorphic extendability
Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
Articles by So-Chin Chen
|
EUDML | The maximum unitary rank of some C*-algebras. EuDML | The maximum unitary rank of some C*-algebras.
The maximum unitary rank of some C*-algebras.
Mikael Rordam; Ian F. Putnam
Rordam, Mikael, and Putnam, Ian F.. "The maximum unitary rank of some C*-algebras.." Mathematica Scandinavica 63.2 (1988): 297-304. <http://eudml.org/doc/167059>.
@article{Rordam1988,
author = {Rordam, Mikael, Putnam, Ian F.},
keywords = {infinite dimensional separable abelian -algebras; infinite dimensional AF-algebras; irrational rotation -algebras; reduced group -algebra of the free group of n generators},
title = {The maximum unitary rank of some C*-algebras.},
AU - Rordam, Mikael
AU - Putnam, Ian F.
TI - The maximum unitary rank of some C*-algebras.
KW - infinite dimensional separable abelian -algebras; infinite dimensional AF-algebras; irrational rotation -algebras; reduced group -algebra of the free group of n generators
infinite dimensional separable abelian
{C}^{*}
-algebras, infinite dimensional AF-algebras, irrational rotation
{C}^{*}
-algebras, reduced group
{C}^{*}
-algebra of the free group of n generators
{C}^{*}
{W}^{*}
{C}^{*}
Articles by Mikael Rordam
Articles by Ian F. Putnam
|
EUDML | -convergence of modified complex trigonometric sums. EuDML | -convergence of modified complex trigonometric sums.
{L}^{1}
-convergence of modified complex trigonometric sums.
Bhatia, S.S.; Kaur, Kulwinder; Ram, Babu
Bhatia, S.S., Kaur, Kulwinder, and Ram, Babu. "-convergence of modified complex trigonometric sums.." Lobachevskii Journal of Mathematics 12 (2003): 3-10. <http://eudml.org/doc/225865>.
@article{Bhatia2003,
author = {Bhatia, S.S., Kaur, Kulwinder, Ram, Babu},
keywords = {-convergence of modified complex trigonometric sums; -convergence of Fourier series; Dirichlet kernel; -convergence of modified complex trigonometric sums; -convergence of Fourier series},
title = {-convergence of modified complex trigonometric sums.},
AU - Ram, Babu
TI - -convergence of modified complex trigonometric sums.
KW - -convergence of modified complex trigonometric sums; -convergence of Fourier series; Dirichlet kernel; -convergence of modified complex trigonometric sums; -convergence of Fourier series
{L}^{1}
-convergence of modified complex trigonometric sums,
{L}^{1}
-convergence of Fourier series, Dirichlet kernel,
{L}^{1}
{L}^{1}
-convergence of Fourier series
|
Development of a Semi-implicit Solver for Detailed Chemistry in Internal Combustion Engine Simulations | J. Eng. Gas Turbines Power | ASME Digital Collection
Long Liang,
, 1500 Engineering Drive, Madison, WI 53706
e-mail: lliang@wisc.edu
Song-Charng Kong,
Chulhwa Jung,
Chulhwa Jung
Liang, L., Kong, S., Jung, C., and Reitz, R. D. (February 28, 2006). "Development of a Semi-implicit Solver for Detailed Chemistry in Internal Combustion Engine Simulations." ASME. J. Eng. Gas Turbines Power. January 2007; 129(1): 271–278. https://doi.org/10.1115/1.2204979
An efficient semi-implicit numerical method is developed for solving the detailed chemical kinetic source terms in internal combustion (IC) engine simulations. The detailed chemistry system forms a group of coupled stiff ordinary differential equations (ODEs), which presents a very stringent time-step limitation when solved by standard explicit methods, and is computationally expensive when solved by iterative implicit methods. The present numerical solver uses a stiffly stable noniterative semi-implicit method. The formulation of numerical integration exploits the physical requirement that the species density and specific internal energy in the computational cells must be non-negative, so that the Lipschitz time-step constraint is not present and the computation time step can be orders of magnitude larger than that possible in standard explicit methods. The solver exploits the characteristics of the stiffness of the ODEs by using a sequential sort algorithm that ranks an approximation to the dominant eigenvalues of the system to achieve maximum accuracy. Subcycling within the chemistry solver routine is applied for each computational cell in engine simulations, where the subcycle time step is dynamically determined by monitoring the rate of change of concentration of key species, which have short characteristic time scales and are also important to the chemical heat release. The chemistry solver is applied in the KIVA-3V code to diesel engine simulations. Results are compared to those using the CHEMKIN package, which uses the VODE implicit solver. Good agreement was achieved for a wide range of engine operating conditions, and
40-70%
CPU time savings were achieved by the present solver compared to the standard CHEMKIN.
diesel engines, reaction kinetics, approximation theory, eigenvalues and eigenfunctions, differential equations, mechanical engineering computing
Chemical kinetics, Chemistry, Combustion, Engineering simulation, Engines, Heat, Pressure, Simulation, Algorithms, Diesel engines, Numerical analysis, Approximation, Differential equations, Cylinders, Eigenvalues, Internal combustion engines, Exhaust gas recirculation, Computation
Computations of Laminar Flame Propagation Using an Explicit Numerical Method
, Combust. Inst., Pittsburgh, PA, pp.
Ordinary Differential Equations: A Computational Approach
CHEMKIN-II: A FORTRAN Chemical Kinetics Package for the Analyses of Gas Phase Chemical Kinetics
,” Sandia Report, No. SAND 89-8009.
“VODE, A Variable-Coefficient ODE Solver
Application of Detailed Chemistry and CFD for Predicting Direct Injection HCCI Engine Combustion and Emissions
, Philadelphia, PA, Vol.
,” Los Alamos National Labs, LA-11560-MS.
, 2000, http:∕∕www.tfd.chalmers.se∕∼valeri∕MECH.html, Chalmers Univ. of Tech, Gothenburg, Sweden.
Development and Validation of a Reduced Reaction Mechanism for HCCI Engine Simulations
Particulate and NOx Reduction in a Heavy-Duty Diesel Engine Using High Levels of Exhaust Gas Recirculation and Very Early and Very Late Injection
Computationally Efficient Simulation of Multi-Component Fuel Combustion Using a Sparse Analytical Jacobian Chemistry Solver and High-Dimensional Clustering
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Pseudospectrum using eigenvector method - MATLAB peig - MathWorks Switzerland
Pseudospectrum of Sum of Sinusoids
Pseudospectrum of Real Signal
Pseudospectrum using eigenvector method
[S,wo] = peig(x,p)
[S,wo] = peig(x,p,wi)
[S,wo] = peig(___,nfft)
[S,wo] = peig(___,'corr')
[S,fo] = peig(x,p,nfft,fs)
[S,fo] = peig(x,p,fi,fs)
[S,fo] = peig(x,p,nfft,fs,nwin,noverlap)
[___] = peig(___,freqrange)
[___,v,e] = peig(___)
peig(___)
[S,wo] = peig(x,p) implements the eigenvector spectral estimation method and returns S, the pseudospectrum estimate of the input signal x, and a vector wo of normalized frequencies (in rad/sample) at which the pseudospectrum is evaluated. The pseudospectrum is calculated using estimates of the eigenvectors of a correlation matrix associated with the input data x. You can specify the signal subspace dimension using the input argument p.
[S,wo] = peig(x,p,wi) returns the pseudospectrum computed at the normalized frequencies specified in vector wi. The vector wi must have two or more elements, because otherwise the function interprets it as nfft.
[S,wo] = peig(___,nfft) specifies the integer length of the FFT, nfft, to use to estimate the pseudospectrum. This syntax can include any combination of input arguments from previous syntaxes.
[S,wo] = peig(___,'corr') forces the input argument x to be interpreted as a correlation matrix rather than a matrix of signal data. For this syntax, x must be a square matrix, and all of its eigenvalues must be nonnegative.
[S,fo] = peig(x,p,nfft,fs) returns the pseudospectrum computed at the frequencies specified in vector fo (in Hz). Supply the sample rate fs in Hz.
[S,fo] = peig(x,p,fi,fs) returns the pseudospectrum computed at the frequencies specified in the vector fi. The vector fi must have two or more elements, because otherwise the function interprets it as nfft.
[S,fo] = peig(x,p,nfft,fs,nwin,noverlap) returns the pseudospectrum S by segmenting the input data x using the window nwin and overlap length noverlap.
[___] = peig(___,freqrange) specifies the range of frequency values to include in fo or wo.
[___,v,e] = peig(___) returns the matrix v of noise eigenvectors, along with the associated eigenvalues in the vector e.
peig(___) with no output arguments plots the pseudospectrum in the current figure window.
Implement the eigenvector method to find the pseudospectrum of the sum of three sinusoids in noise. Use the default FFT length of 256. The inputs are complex sinusoids so you set p equal to the number of inputs. Use the modified covariance method for the correlation matrix estimate.
peig(X,3,'whole')
Generate a real signal that consists of the sum of two sinusoids embedded in white Gaussian noise of unit variance. The signal is sampled at 100 Hz for 1 second. The sinusoids have frequencies of 25 Hz and 35 Hz. The lower-frequency sinusoid has twice the amplitude of the other.
s = 2*sin(2*pi*25*t)+sin(2*pi*35*t)+randn(1,100);
Use the eigenvector method to compute the pseudospectrum of the signal between 0 and the Nyquist frequency. Specify a signal subspace dimension of 2 and a DFT length of 512.
peig(s,2,512,fs,'half')
It is not possible to resolve the two sinusoids because the signal is real. Repeat the computation using a signal subspace of dimension 4.
If the inputs to peig are real sinusoids, set the value of p to two times the number of sinusoids. If the inputs are complex sinusoids, set p equal to the number of sinusoids.
The eigenvector method estimates the pseudospectrum from a signal or a correlation matrix using a weighted version of the MUSIC algorithm derived from Schmidt's eigenspace analysis method [1] [2]. The algorithm performs eigenspace analysis of the signal's correlation matrix to estimate the signal's frequency content. If you do not supply the correlation matrix, the eigenvalues and eigenvectors of the signal's correlation matrix are estimated using svd. This algorithm is particularly suitable for signals that are the sum of sinusoids with additive white Gaussian noise.
The eigenvector method produces a pseudospectrum estimate given by
{P}_{\text{ev}}\left(f\right)=\frac{1}{\sum _{k=p+1}^{N}|{\text{v}}_{k}^{H}e\left(f\right){|}^{2}/{\lambda }_{k}}
where N is the dimension of the eigenvectors and vkis the kth eigenvector of the correlation matrix of the input signal. The integer p is the dimension of the signal subspace, so the eigenvectors vk used in the sum correspond to the smallest eigenvalues λk of the correlation matrix. The eigenvectors used span the noise subspace. The vector e(f) consists of complex exponentials, so the inner product vkHe(f) amounts to a Fourier transform. This is used for computation of the pseudospectrum. The FFT is computed for each vk and then the squared magnitudes are summed and scaled.
corrmtx | pburg | periodogram | pmtm | pmusic | prony | pwelch | rooteig | rootmusic
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The aim of this paper is to present a unifying approach to the computation of short addition chains. Our method is based upon continued fraction expansions. Most of the popular methods for the generation of addition chains, such as the binary method, the factor method, etc..., fit in our framework. However, we present new and better algorithms. We give a general upper bound for the complexity of continued fraction methods, as a function of a chosen strategy, thus the total number of operations required for the generation of an addition chain for all integers up to
n
is shown to be
O\left(n{log}^{2}n{\gamma }_{n}\right)
{\gamma }_{n}
is the complexity of computing the set of choices corresponding to the strategy. We also prove an analog of the Scholz-Brauer conjecture.
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Boundary value problem - zxc.wiki
Boundary value problems (short: RWP ) also boundary value problem (short: RWA ) or English boundary value problem (short: BVP ) is an important class of problems in mathematics in which solutions to a given differential equation (DGL) are sought that are based on the The edge of the definition range should assume predetermined function values ( boundary conditions ). The counterpart to this is the initial value problem , in which the solution is given for any point in the domain.
1.1 Dirichlet problem
1.2 Sturm Liouville RWP
1.3 Storm Liouville EWP
2.2 Neumann problem
2.3 Skewed boundary condition
4 Scientific application
Main article : Dirichlet boundary condition
Let and be real numbers. Boundary data or boundary conditions of a function of the form
{\ displaystyle \ alpha}
{\ displaystyle \ beta}
{\ displaystyle u \ colon [a, b] \ to \ mathbb {R}}
{\ displaystyle u (a) = \ alpha \ quad {\ text {and}} \ quad u (b) = \ beta}
are called boundary conditions of the first kind or Dirichlet boundary conditions. If so we speak of homogeneous Dirichlet boundary conditions. Otherwise we speak of inhomogeneous boundary conditions.
{\ displaystyle \ alpha = \ beta = 0}
So we are looking for a function that is a solution to the following problem:
{\ displaystyle u}
{\ displaystyle (N) {\ begin {cases} f (x, u (x), u '(x), u' '(x)) = 0, \ quad x \ in (a, b) & \\ u (a) = \ alpha, ~ u (b) = \ beta. & \ end {cases}}}
Here is a prescribed function and are the prescribed boundary conditions. Sufficient conditions for the existence (and uniqueness) of solutions of can be found in the article Dirichlet problem .
{\ displaystyle f}
{\ displaystyle \ alpha, \ beta}
{\ displaystyle (N)}
Storm Liouville RWP
Main article : Sturm-Liouville problem
Let be a self-adjoint linear differential operator of the 2nd order boundary operators with let
{\ displaystyle r, p, q \ in {\ mathcal {C}} ([a, b], \ mathbb {R})}
{\ displaystyle Lu: = (pu ')' + qu}
{\ displaystyle {\ alpha _ {0}} ^ {2} + {\ alpha _ {1}} ^ {2}> 0, ~ {\ beta _ {0}} ^ {2} + {\ beta _ { 1}} ^ {2}> 0}
{\ displaystyle R_ {a} u: = \ alpha _ {0} u (a) + \ alpha _ {1} p (a) u '(a)}
{\ displaystyle R_ {b} u: = \ beta _ {0} u (b) + \ beta _ {1} p (b) u '(b)}
{\ displaystyle (*) {\ begin {cases} (Lu) (x) = r (x) & \\ R_ {u} (a) = \ eta _ {a}, ~ R_ {u} (b) = \ eta _ {b} & \ end {cases}}}
is called Sturm-Liouville-RWP.
Storm Liouville EWP
See also : Eigenvalue Problem
{\ displaystyle (P _ {\ lambda}) {\ begin {cases} (Lu) (x) = \ lambda u (x) & \\ R_ {u} (a) = R_ {u} (b) = 0 & \ end {cases}}}
Those for which it is not clearly solvable are called eigenvalues . The corresponding solutions are called eigenfunctions.
{\ displaystyle \ lambda \ in \ mathbb {R}}
{\ displaystyle (P _ {\ lambda})}
Be open and restricted, be a Lebesgue-measurable function, describe the boundary specifications. Solutions are sought in each case . The partial differential equation is given by the differential operator . In particular, elliptic differential operators always lead to boundary value problems, such as the Laplace operator to the Poisson equation .
{\ displaystyle \ Omega \ subset \ mathbb {R} ^ {d}}
{\ displaystyle f}
{\ displaystyle \ Omega}
{\ displaystyle g}
{\ displaystyle u \ colon \ Omega \ rightarrow \ mathbb {R} ^ {n}}
{\ displaystyle L \ colon u \ mapsto L (u)}
With the Dirichlet problem , function values are specified on the edge.
{\ displaystyle L (u) (x) = f (x)}
{\ displaystyle x \ in \ Omega,}
{\ displaystyle u (x) = g (x)}
{\ displaystyle x \ in \ partial \ Omega.}
Instead of functional values, derivative values are prescribed for the Neumann problem .
{\ displaystyle L (u) (x) = f (x)}
{\ displaystyle x \ in \ Omega,}
{\ displaystyle {\ frac {\ partial u} {\ partial n}} (x) = g (x)}
{\ displaystyle x \ in \ partial \ Omega.}
Skewed boundary condition
The skewed boundary condition represents a combination of the two previous problems. Here, the function sought on the boundary should be equal to its normal derivative on the boundary.
{\ displaystyle L (u) (x) = f (x)}
{\ displaystyle x \ in \ Omega,}
{\ displaystyle u (x) = {\ frac {\ partial u} {\ partial n}} (x)}
{\ displaystyle x \ in \ partial \ Omega.}
Green's functions are an important theoretical aid for the investigation of boundary value problems .
In numerics , as a method for approximate solution z. B. the FDM ( finite difference method ), the FEM ( finite element method ), the shooting method and the multi-target method are used.
The modeling of many processes in nature and technology is based on differential equations. Typical simple examples of RWP are
vibrating string that is firmly clamped at both ends (= edge)
vibrating membrane (the edge is a circular ring here)
Equations of motion of satellites in Kepler orbits , see also orbit determination
the chain line of a chain hanging between two points or the seabed and the ship
the shape of the radii of the 3 lamellas that form when 2 independent soap bubbles first pair
the deformation of a trampoline surface when it bounces on.
Conversely, experiments with material models - made of a spring network, rubber blanket, soap bubble - can be used to solve mathematically formulated tasks or to illustrate them:
Gravitational potential represented by the central indentation of a rubber blanket clamped horizontally at the edge, (elliptical) circling movement by a small rolling ball
Tension optics
Martin Hermann : Numerics of ordinary differential equations. Initial and boundary value problems. Oldenbourg, Munich et al. 2004, ISBN 3-486-27606-9 .
This page is based on the copyrighted Wikipedia article "Randwertproblem" (Authors); it is used under the Creative Commons Attribution-ShareAlike 3.0 Unported License. You may redistribute it, verbatim or modified, providing that you comply with the terms of the CC-BY-SA.
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Grapevines - zxc.wiki
Real grapevine ( Vitis vinifera )
Order : Grapevine-like
Family : Grapevines
Grapevines (Vitaceae) form the only family of the order of the Vitales within the Rosids , they are flowering plants (Magnoliopsida). The approximately 16 genera with approximately 950 species (as of 2018) mainly thrive in tropical to subtropical areas. Some species are known as ornamental or useful plants .
All species are perennial plants . Either evergreen or deciduous climbing shrubs and lianas thrive , mostly with winding tendrils; or they are shrubs or succulent plants.
The leaves are alternate and arranged in two rows. The leaf blades are simple, palmately lobed or compound. The leaves are usually tomentose or hairy on the underside, these outer hairs consist of dead cells. Live, single or multicellular trichomes are often present on the veins . The leaf margins can be serrated. They have quickly perishable stipules .
Flowering diagram of Ampelopsis hederacea
Subfamily Vitoideae: inflorescence of Clematicissus angustissima with flowers in detail
The flowers are never single, but always in inflorescences , often complexly branched : in their basic structure, panicles or umbels (so botanically speaking, they are not grapes !) That arise in the axes of the leaves. There are always small bracts under the flower stalks .
The hermaphroditic or unisexual flowers are radial symmetry and are four or five-fold (rarely up to seven-fold). The species can be one ( monoecious ) or dioecious ( dioecious ). There is only one circle with four or five (up to seven) stamens each. The upper ovary is usually formed from two carpels . There is a mostly cup-shaped or bowl-shaped disc , which is a disc of nectar-secreting glands.
The basic flower formula is :, There are deviations from this for individual taxa .
{\ displaystyle \ star K_ {4-5} \; C_ {4-5} \; A_ {4-5} \; G _ {\ underline {(2)}}}
Mostly soft-fleshed berries with two, rarely three to eight compartments are formed. In each compartment there are two or one seeds with a hard shell.
Subfamily Vitoideae: succulent growing Cyphostemma elephantopus
Subfamily Vitoideae: Succulent Climber: Cissus quadrangularis
Subfamily Vitoideae: Tetrastigma species
Subfamily Leeoideae: Leea rubra that grows shrubby
The Vitaceae family was established in 1789 by Antoine-Laurent de Jussieu in Genera Plantarum , page 267 under the name "Vites". Type genus is Vitis L. Synonyms for Vitaceae Juss. are: Ampelopsidaceae Kostel. , Cissaceae Drejer , Leeaceae Dumort. nom. cons., Pterisanthaceae J. Agardh .
So that the Vitaceae family is monophyletic, the species of the Leeaceae Dumort family became . as subfamily Leeoideae Burmeister into the family Vitaceae Juss. posed. This was confirmed in APG IV. There the Vitaceae sl family is confirmed as the only family of the order Vitales. But some authors led as independent families Leeaceae and Vitaceae in the order Vitales.
The grapevine family (Vitaceae) contains 14 to 16 genera with 850 to 960 species, depending on the author:
Wen et al. In 2015, the two genera Causonis and Afrocayratia were spun off from Cayratia . Nekemias was spun off from Ampelopsis .
The family Vitaceae sl is divided into two subfamilies Leeoideae and Vitoideae. The subfamily Vitoideae can be divided into the five tribe Ampelopsideae J.Wen & ZLNie , Cisseae Rchb. , Cayratieae J.Wen & LMLu , Parthenocisseae J.Wen & ZDChen and Viteae Dumort. structure:
Subfamily Vitoideae Eaton : The basic chromosome number is x = 10–16, 19, 20. It is divided into five tribes and contains 14 to 15 genera:
The new tribe Ampelopsideae J.Wen & ZLNie was set up by J. Wen and ZL Nie in 2018 . It contains four to six genera:
Ampelopsis Michx. : The only about 18 species are found in Asia and North America (only three species) to Mexico . They thrive from tropical to temperate areas.
Clematicissus Planch. : It contains about six species as of 2018.
Nekemias Raf. : Jun Wen et al. separated this genus from the genus Ampelopsis in2014. Nekemias contains about nine species in East to Southeast Asia and eastern North America (only one species) and on Caribbean islands.
Nothocissus (Miq.) Latiff. : There is only one type:
Nothocissus spicifera (Griff.) Latiff. : It occurs on the Thai Peninsula, Malay Peninsula , Sumatra and Borneo .
Pterisanthes flower : The approximately 20 species are distributed from Thailand , Malaysia , Indonesia to the Philippines .
Pterocissus Urb. & Ekman : There is only one type:
Pterocissus mirabilis Urb. & Ekman : It only occurs in Hispaniola .
Rhoicissus Planch. : The approximately 14 species thrive in tropical to southern Africa.
The tribe of Cisseae Rchb. contains only one genus:
Cissus L .: The approximately 300 species are mostly found in the tropics of the Old and New World .
The new tribe Cayratieae J.Wen & LMLu was set up in 2018 by J. Wen and LM Lu . It contains about seven genera: Tetrastigma ,
Acareosperma Gagnep. : There is only one type:
Acareosperma spireanum Gagnep. : It only occurs in Laos .
Causonis Raf. : J. Wen et al. separated this genus from the genus Cayratia in2014. It contains about 15 species in East to Southeast Asia .
Cayratia Juss. : The only 50 to 60 species left since 2014 arewidespreadin Africa, Asia and Oceania .
Cyphostemma (Planch.) Alston : The approximately 250 species are mainly distributed in Africa and Madagascar , only a few species also extend to Thailand.
Pseudocayratia J.Wen, LMLu & ZDChen : It was established in 2018 and contains about five species in China and Japan.
Tetrastigma (Miq.) Planch. : The 90 to 100 species are distributed from Asia to Oceania.
The new Tribus Parthenocisseae J.Wen & ZDChen was set up in 2018 by J. Wen and ZD Chen . It contains only two genera:
Virgin vines ( Parthenocissus Planch. ): The approximately 14 species occur in Asia and North America.
Yua C.L.Li : The only two species are found in India, Nepal and China.
The tribe Viteae Dumort. contains two genera:
Ampelocissus Planch. : The 90 to 100 species are widespread in the tropics.
Grapevines ( Vitis L. ): The 60 to 75 species thrive from the temperate areas to the subtropics, with centers of biodiversity in China and eastern North America.
Subfamily Leeoideae Burmeister : Also as a separate family Leeaceae Dumort. guided: The basic chromosome number is x = (10-) 12 .:
It contains only one genus:
Leea L .: The approximately 34 species are widespread in tropical and subtropical Asia, extend into the Himalayas and Australia, only a few species exist in Africa and only one in Madagascar.
The family of Vitaceae in APWebsite . (Section systematics)
Description of the Vitaceae family at DELTA . (Section description)
Vitaceae at Tropicos.org. In: Flora of Pakistan . Missouri Botanical Garden, St. Louis (Description Section)
Zhiduan Chen, Hui Ren, Jun Wen: Vitaceae. In: Wu Zheng-yi, Peter H. Raven, Deyuan Hong (editors): Flora of China , Volume 12 - Hippocastanaceae through Theaceae , Science Press and Missouri Botanical Garden Press, Beijing and St. Louis, November 19, 2007, ISBN 978 -1-930723-64-1 . Pp. 173–177 - online with the same text as the printed work . (Description and identification key of the Chinese taxa)
Michael O. Moore, Jun Wen: Vitaceae. In: Flora of North America Editorial Committee (Editor): Flora of North America North of Mexico , Volume 12: Magnoliophyta: Vitaceae to Garryaceae , New York and Oxford - via eFloras.org, Missouri Botanical Garden, St. Louis and Harvard University Herbaria , Cambridge, 2016, ISBN 978-0-19-064372-0 . P. 3−23 - online with the same text as the printed work .
Jun Wen, Li ‐ Min Lu, Ze ‐ Long Nie, Xiu ‐ Qun Liu, Ning Zhang, Stefanie Ickert ‐ Bond, Jean Gerrath, Steven R. Manchester, John Boggan, Zhi ‐ Duan Chen: A new phylogenetic tribal classification of the grape family (Vitaceae). In: Journal of Systematicsand Evolution , Volume 56, 2018, pp. 262–272. doi : 10.1111 / jse.12427
↑ a b c d e f g h i j k l m n o p q r Jun Wen, Li ‐ Min Lu, Ze ‐ Long Nie, Xiu ‐ Qun Liu, Ning Zhang, Stefanie Ickert ‐ Bond, Jean Gerrath, Steven R. Manchester, John Boggan, Zhi ‐ Duan Chen: A new phylogenetic tribal classification of the grape family (Vitaceae). In: Journal of Systematicsand Evolution , Volume 56, 2018, pp. 262–272. doi : 10.1111 / jse.12427
↑ First publication scanned at biodiversitylibrary.org .
^ Vitaceae at Tropicos.org. Missouri Botanical Garden, St. Louis, accessed January 20, 2020.
^ A b c Vitaceae in the Germplasm Resources Information Network (GRIN), USDA , ARS , National Genetic Resources Program. National Germplasm Resources Laboratory, Beltsville, Maryland.
^ JE Molina, Jun Wen, L. Struwe: Systematics and biogeography of the non-viny grape relative Leea (Vitaceae). In: Botanical Journal of the Linnean Society , Volume 171, 2013, pp. 354-376.
↑ The Angiosperm Phylogeny Group: An update of the Angiosperm Phylogeny Group classification for the orders and families of flowering plants: APG IV. In: Botanical Journal of the Linnean Society , Volume 181, 2016, pp. 1-20. doi : 10.1111 / boj.12385
↑ a b c The family of Vitaceae in APWebsite .
↑ a b c Michael O. Moore, Jun Wen: Vitaceae. In: Flora of North America Editorial Committee (Editor): Flora of North America North of Mexico , Volume 12: Magnoliophyta: Vitaceae to Garryaceae , New York and Oxford - via eFloras.org, Missouri Botanical Garden, St. Louis and Harvard University Herbaria , Cambridge, 2016, ISBN 978-0-19-064372-0 . P. 3−23 - online with the same text as the printed work .
↑ a b Jun Wen, Li ‐ Min Lu, Ze ‐ Long Nie, Steven R. Manchester, Stefanie Ickert-Bond, Zhi-Duan Chen: Phylogenetics and a revised classification of Vitaceae. Presented at Botany 2015, Edmonton, Alberta. on-line.
↑ a b Jun Wen et al .: Synopsis of Nekemias Raf., A segregate genus from Ampelopsis Michx. (Vitaceae) disjunct between eastern / southeastern Asia and eastern North America, with ten new combinations. In: PhytoKeys , Volume 42, 2014, pp. 11-19.
↑ Akiko Soejima, Jun Wen: Phylogenetic analysis of the grape family (Vitaceae) based on three chloroplast markers. In: American Journal of Botany , Volume 93, Issue 2, 2006, pp. 278-287. doi : 10.3732 / ajb.93.2.278 full text online.
↑ Jun Wen, Li ‐ Min Lu, Tsai-Wen Hsu, Viet Dang, Sadaf Habib, John Boggan, Hiroshi Okada, Iju Chen, Zhi ‐ Duan Chen: Pseudocayratia, a new genus of Vitaceae from China and Japan with two new species and three new combinations. In: Journal of Systematics and Evolution , Volume 56, 2018, pp. 374–393. doi : 10.1111 / jse.12448
Commons : Grapevine Family (Vitaceae) - Collection of images, videos and audio files
Vitaceae at Tropicos.org. In: IPCN Chromosome Reports . Missouri Botanical Garden, St. Louis
Vitaceae at Tropicos.org. In: Catalog of the Vascular Plants of Madagascar . Missouri Botanical Garden, St. Louis
Vitaceae at Tropicos.org. In: 83 . Missouri Botanical Garden, St. Louis
Vitaceae at Tropicos.org. In: Flora Mesoamericana . Missouri Botanical Garden, St. Louis
Family description in the Western Australian flora . (English)
Profile at the Botanical Garden in Tübingen.
List of links to pictures of species from the family.
Sadaf Habib, Viet-Cuong Dang, Stefanie M. Ickert-Bond, Jin-Long Zhang, Li-Min Lu, Jun Wen, Zhi-Duan Chen: Robust Phylogeny of Tetrastigma (Vitaceae) Based on Ten Plastid DNA Regions: Implications for Infrageneric Classification and Seed Character Evolution. In: Frontiers in Plant Science , Volume 8, April 2017, p. 590. doi : 10.3389 / fpls.2017.00590
This page is based on the copyrighted Wikipedia article "Weinrebengew%C3%A4chse" (Authors); it is used under the Creative Commons Attribution-ShareAlike 3.0 Unported License. You may redistribute it, verbatim or modified, providing that you comply with the terms of the CC-BY-SA.
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LMIs in Control/Matrix and LMI Properties and Tools/Young’s Relation-Based Properties - Wikibooks, open books for an open world
LMIs in Control/Matrix and LMI Properties and Tools/Young’s Relation-Based Properties
Young’s Relation-Based PropertiesEdit
1. Consider
{\displaystyle X}
{\displaystyle Y\in \mathbb {R} ^{n\times m}}
{\displaystyle Z\in \mathbb {S} ^{m}}
{\displaystyle {\begin{aligned}Z+XTY+YTX>0,\end{aligned}}}
is satisfied if and only if there exist
{\displaystyle Q\in \mathbb {S} ^{m}}
{\displaystyle P\in \mathbb {S} ^{n}}
{\displaystyle G1\in \mathbb {R} ^{n\times n}}
{\displaystyle G2\in \mathbb {R} ^{n\times m}}
{\displaystyle F\in \mathbb {R} ^{m\times n}}
{\displaystyle H\in \mathbb {R} ^{m\times m}}
{\displaystyle Q>0}
{\displaystyle P>0}
{\displaystyle {\begin{bmatrix}P&Y\\*&Q\end{bmatrix}}>0}
{\displaystyle {\begin{bmatrix}Z+Q+X^{T}PX&F-X^{T}G_{2}&H-X^{T}G_{1}\\*&G_{1}+G_{1}^{T}-P&F^{T}+G_{2}-Y\\*&*&H^{T}+H-Q\end{bmatrix}}}
{\displaystyle X}
{\displaystyle Y\in \mathbb {R} ^{n\times n}}
{\displaystyle W\in \mathbb {S} ^{m}}
{\displaystyle X}
is full rank and
{\displaystyle W>0}
{\displaystyle {\begin{aligned}X^{T}-W>0,\end{aligned}}}
is satisfied if there exist
{\displaystyle \lambda \in \mathbb {R} _{>0}}
{\displaystyle {\begin{bmatrix}\lambda \mathbf {1} &\lambda \mathbf {1} &\mathbf {0} \\*&\mathbf {X} +\mathbf {X} ^{T}&\mathbf {W} ^{\frac {1}{2}}\\*&*&\lambda \mathbf {1} \end{bmatrix}}>0}
Retrieved from "https://en.wikibooks.org/w/index.php?title=LMIs_in_Control/Matrix_and_LMI_Properties_and_Tools/Young’s_Relation-Based_Properties&oldid=4010499"
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Charles's law — Wikipedia Republished // WIKI 2
Relationship between volume and temperature of a gas at constant pressure
An animation demonstrating the relationship between volume and temperature
{\displaystyle J=-D{\frac {d\varphi }{dx}}}
Relationships between Boyle's, Charles's, Gay-Lussac's, Avogadro's, combined and ideal gas laws, with the Boltzmann constant kB = R/NA = n R/N (in each law, properties circled are variable and properties not circled are held constant)
Charles's law (also known as the law of volumes) is an experimental gas law that describes how gases tend to expand when heated. A modern statement of Charles's law is:
When the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be in direct proportion.[1]
This relationship of direct proportion can be written as:
{\displaystyle V\propto T}
{\displaystyle {\frac {V}{T}}=k,\quad {\text{or}}\quad V=kT}
V is the volume of the gas,
T is the temperature of the gas (measured in kelvins), and
k is a non-zero constant.
This law describes how a gas expands as the temperature increases; conversely, a decrease in temperature will lead to a decrease in volume. For comparing the same substance under two different sets of conditions, the law can be written as:
2 Relation to absolute zero
3 Relation to kinetic theory
The law was named after scientist Jacques Charles, who formulated the original law in his unpublished work from the 1780s.
In two of a series of four essays presented between 2 and 30 October 1801,[2] John Dalton demonstrated by experiment that all the gases and vapours that he studied expanded by the same amount between two fixed points of temperature. The French natural philosopher Joseph Louis Gay-Lussac confirmed the discovery in a presentation to the French National Institute on 31 Jan 1802,[3] although he credited the discovery to unpublished work from the 1780s by Jacques Charles. The basic principles had already been described by Guillaume Amontons[4] and Francis Hauksbee[5] a century earlier.
Dalton was the first to demonstrate that the law applied generally to all gases, and to the vapours of volatile liquids if the temperature was well above the boiling point. Gay-Lussac concurred.[6] With measurements only at the two thermometric fixed points of water, Gay-Lussac was unable to show that the equation relating volume to temperature was a linear function. On mathematical grounds alone, Gay-Lussac's paper does not permit the assignment of any law stating the linear relation. Both Dalton's and Gay-Lussac's main conclusions can be expressed mathematically as:
{\displaystyle V_{100}-V_{0}=kV_{0}\,}
where V100 is the volume occupied by a given sample of gas at 100 °C; V0 is the volume occupied by the same sample of gas at 0 °C; and k is a constant which is the same for all gases at constant pressure. This equation does not contain the temperature and so is not what became known as Charles's Law. Gay-Lussac's value for k (1⁄2.6666), was identical to Dalton's earlier value for vapours and remarkably close to the present-day value of 1⁄2.7315. Gay-Lussac gave credit for this equation to unpublished statements by his fellow Republican citizen J. Charles in 1787. In the absence of a firm record, the gas law relating volume to temperature cannot be attributed to Charles. Dalton's measurements had much more scope regarding temperature than Gay-Lussac, not only measuring the volume at the fixed points of water but also at two intermediate points. Unaware of the inaccuracies of mercury thermometers at the time, which were divided into equal portions between the fixed points, Dalton, after concluding in Essay II that in the case of vapours, “any elastic fluid expands nearly in a uniform manner into 1370 or 1380 parts by 180 degrees (Fahrenheit) of heat”, was unable to confirm it for gases.
Charles's law appears to imply that the volume of a gas will descend to zero at a certain temperature (−266.66 °C according to Gay-Lussac's figures) or −273.15 °C. Gay-Lussac was clear in his description that the law was not applicable at low temperatures:
but I may mention that this last conclusion cannot be true except so long as the compressed vapours remain entirely in the elastic state; and this requires that their temperature shall be sufficiently elevated to enable them to resist the pressure which tends to make them assume the liquid state.[3]
At absolute zero temperature, the gas possesses zero energy and hence the molecules restrict motion. Gay-Lussac had no experience of liquid air (first prepared in 1877), although he appears to have believed (as did Dalton) that the "permanent gases" such as air and hydrogen could be liquified. Gay-Lussac had also worked with the vapours of volatile liquids in demonstrating Charles's law, and was aware that the law does not apply just above the boiling point of the liquid:
I may, however, remark that when the temperature of the ether is only a little above its boiling point, its condensation is a little more rapid than that of atmospheric air. This fact is related to a phenomenon which is exhibited by a great many bodies when passing from the liquid to the solid-state, but which is no longer sensible at temperatures a few degrees above that at which the transition occurs.[3]
The first mention of a temperature at which the volume of a gas might descend to zero was by William Thomson (later known as Lord Kelvin) in 1848:[7]
This is what we might anticipate when we reflect that infinite cold must correspond to a finite number of degrees of the air-thermometer below zero; since if we push the strict principle of graduation, stated above, sufficiently far, we should arrive at a point corresponding to the volume of air being reduced to nothing, which would be marked as −273° of the scale (−100/.366, if .366 be the coefficient of expansion); and therefore −273° of the air-thermometer is a point which cannot be reached at any finite temperature, however low.
However, the "absolute zero" on the Kelvin temperature scale was originally defined in terms of the second law of thermodynamics, which Thomson himself described in 1852.[8] Thomson did not assume that this was equal to the "zero-volume point" of Charles's law, merely that Charles's law provided the minimum temperature which could be attained. The two can be shown to be equivalent by Ludwig Boltzmann's statistical view of entropy (1870).
However, Charles also stated:
The volume of a fixed mass of dry gas increases or decreases by 1⁄273 times the volume at 0 °C for every 1 °C rise or fall in temperature. Thus:
{\displaystyle V_{T}=V_{0}+({\tfrac {1}{273}}\times V_{0})\times T}
{\displaystyle V_{T}=V_{0}(1+{\tfrac {T}{273}})}
where VT is the volume of gas at temperature T, V0 is the volume at 0 °C.
The kinetic theory of gases relates the macroscopic properties of gases, such as pressure and volume, to the microscopic properties of the molecules which make up the gas, particularly the mass and speed of the molecules. To derive Charles's law from kinetic theory, it is necessary to have a microscopic definition of temperature: this can be conveniently taken as the temperature being proportional to the average kinetic energy of the gas molecules, Ek:
{\displaystyle T\propto {\bar {E_{\rm {k}}}}.\,}
{\displaystyle PV={\frac {2}{3}}N{\bar {E_{\rm {k}}}}\,}
Boyle's law – Relationship between pressure and volume in a gas at constant temperature
Combined gas law – Combination of Charles', Boyle's and Gay-Lussac's gas laws
Gay-Lussac's law – Relationship between pressure and temperature of a gas at constant volume.
Avogadro's law – Relationship between volume and number of moles of a gas at constant temperature and pressure.
Ideal gas law – Equation of the state of a hypothetical ideal gas
Hand boiler
Thermal expansion – Tendency of matter to change volume in response to a change in temperature
^ Fullick, P. (1994), Physics, Heinemann, pp. 141–42, ISBN 978-0-435-57078-1 .
^ J. Dalton (1802), "Essay II. On the force of steam or vapour from water and various other liquids, both in vacuum and in air" and Essay IV. "On the expansion of elastic fluids by heat," Memoirs of the Literary and Philosophical Society of Manchester, vol. 8, pt. 2, pp. 550–74, 595–602.
^ a b c Gay-Lussac, J. L. (1802), "Recherches sur la dilatation des gaz et des vapeurs" [Researches on the expansion of gases and vapors], Annales de Chimie, 43: 137–75 . English translation (extract).
Amontons, G. (presented 1699, published 1732) "Moyens de substituer commodément l'action du feu à la force des hommes et des chevaux pour mouvoir les machines" (Ways to conveniently substitute the action of fire for the force of men and horses to power machines), Mémoires de l’Académie des sciences de Paris (presented 1699, published 1732), 112–26; see especially pp. 113–17.
Amontons, G. (presented 1702, published 1743) "Discours sur quelques propriétés de l'Air, & le moyen d'en connoître la température dans tous les climats de la Terre" (Discourse on some properties of air and on the means of knowing the temperature in all climates of the Earth), Mémoires de l’Académie des sciences de Paris, 155–74.
Review of Amontons' findings: "Sur une nouvelle proprieté de l'air, et une nouvelle construction de Thermométre" (On a new property of the air and a new construction of thermometer), Histoire de l'Academie royale des sciences, 1–8 (submitted: 1702 ; published: 1743).
^ * Englishman Francis Hauksbee (1660–1713) independently also discovered Charles's law: Francis Hauksbee (1708) "An account of an experiment touching the different densities of air, from the greatest natural heat to the greatest natural cold in this climate," Archived 2015-12-14 at the Wayback Machine Philosophical Transactions of the Royal Society of London 26(315): 93–96.
^ Gay-Lussac (1802), from p. 166:
From p. 174:
^ Thomson, William (1848), "On an Absolute Thermometric Scale founded on Carnot's Theory of the Motive Power of Heat, and calculated from Regnault's Observations", Philosophical Magazine: 100–06 .
^ Thomson, William (1852), "On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam", Philosophical Magazine, 4 . Extract.
Krönig, A. (1856), "Grundzüge einer Theorie der Gase", Annalen der Physik, 99 (10): 315–22, Bibcode:1856AnP...175..315K, doi:10.1002/andp.18561751008 . Facsimile at the Bibliothèque nationale de France (pp. 315–22).
Clausius, R. (1857), "Ueber die Art der Bewegung, welche wir Wärme nennen", Annalen der Physik und Chemie, 176 (3): 353–79, Bibcode:1857AnP...176..353C, doi:10.1002/andp.18571760302 . Facsimile at the Bibliothèque nationale de France (pp. 353–79).
Joseph Louis Gay-Lussac – Liste de ses communications, archived from the original on October 23, 2005 . (in French)
The Wikibook School Science has a page on the topic of: Making Charles' law tubes
Charles's law simulation from Davidson College, Davidson, North Carolina
Charles's law demonstration by Prof. Robert Burk, Carleton University, Ottawa, Canada
Charles's law animation from the Leonardo Project (GTEP/CCHS, UK)
Avogadro constant
Boltzmann constant
Gas constant
Mass concentration
Molar concentration
Mole fraction
Mass fraction
Amount of substance
Molar mass
Atomic mass
Particle number
Molar volume
Specific volume
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EUDML | Powers of -hyponormal operators. EuDML | Powers of -hyponormal operators.
p
-hyponormal operators.
Aluthge, Ariyadasa, and Wang, Derming. "Powers of -hyponormal operators.." Journal of Inequalities and Applications [electronic only] 3.3 (1999): 279-284. <http://eudml.org/doc/120218>.
@article{Aluthge1999,
author = {Aluthge, Ariyadasa, Wang, Derming},
keywords = {-hyponormal operator; inequalities; -hyponormal operator},
title = {Powers of -hyponormal operators.},
AU - Aluthge, Ariyadasa
AU - Wang, Derming
TI - Powers of -hyponormal operators.
KW - -hyponormal operator; inequalities; -hyponormal operator
p
-hyponormal operator, inequalities,
p
-hyponormal operator
Articles by Aluthge
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EUDML | A stability result for -harmonic systems with discontinuous coefficients. EuDML | A stability result for -harmonic systems with discontinuous coefficients.
p
Stroffolini, Bianca. "A stability result for -harmonic systems with discontinuous coefficients.." Electronic Journal of Differential Equations (EJDE) [electronic only] 2001 (2001): Paper No. 02, 7 p., electronic only-Paper No. 02, 7 p., electronic only. <http://eudml.org/doc/121109>.
@article{Stroffolini2001,
author = {Stroffolini, Bianca},
keywords = {-harmonic systems; bounded mean oscillation; linear and nonlinear commutators; Hodge decomposition; -harmonic systems},
title = {A stability result for -harmonic systems with discontinuous coefficients.},
TI - A stability result for -harmonic systems with discontinuous coefficients.
KW - -harmonic systems; bounded mean oscillation; linear and nonlinear commutators; Hodge decomposition; -harmonic systems
p
-harmonic systems, bounded mean oscillation, linear and nonlinear commutators, Hodge decomposition,
p
-harmonic systems
Articles by Stroffolini
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platinum - Simple English Wiktionary
{\displaystyle \longleftarrow }
{\displaystyle \longrightarrow }
(UK) IPA (key): /ˈplætɪnəm/
(US) IPA (key): /ˈplætənəm/ or /ˈplætnəm/
Hyphenation: plat‧i‧num
Pieces of platinum
(uncountable) Platinum is an element of the periodic table with the atomic number 78. Its symbol is Pt.
(uncountable) Platinum is also the silver-grey metal made of platinum atoms.
With a density of 21,4, platinum is one of the densest materials known to Earth.
(countable) Atom of the element platinum.
(uncountable) Platinum is the silver-grey color of the metal.
(countable); (music) A platinum is a musical recording that has sold over one million copies (for singles), or two million (for albums)
Something platinum has the silver-grey color of the metal.
She has always had her strange platinum hair.
Retrieved from "https://simple.wiktionary.org/w/index.php?title=platinum&oldid=444702"
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Some Basic Concepts of Chemistry (English) - Live Session - NEET 2020
Some Basic Concepts of Chemistry (English) - Live Session - NEET 2020Contact Number: 9667591930 / 8527521718
{\mathrm{O}}_{4}^{-}
The total number of valence electrons in 4.2g of
{\mathrm{N}}_{3}^{-}
ion is (NA is the Avogadro's number)
1. 2.1NA
The mass of carbon anode consumed (giving only carbon dioxide) in the production of 270 kg of aluminium metal from bauxite by the Hall process is (at. mass of Al = 27)
A metal oxide has the formula Z2O3. It can be reduced by hydrogen to give free metal and water. 0.1596g of the metal oxide requires 6 mg of hydrogen for complete reduction. The atomic weight of the metal is
In the Haber process, 30 L of dihydrogen and 30L of dinitrogen were taken for the reaction which yielded only 50% of the expected product. What will be the composition of the gaseous mixture under the above-said condition in the end?
1. 20L ammonia, 10L nitrogen, 30L hydrogen
A partially dried clay mineral contains 8% water. The original sample contained 12% water and 45% silica. The % of silica in the partially dried sample is nearly:
One mole of a mixture of CO and CO2 requires exactly 20g of NaOH in solution for complete conversion of all the CO2 into Na2CO3. How much NaOH would it require for conversion into Na2CO3, if the mixture (one mole) is completely oxidised to CO2?
100 mL of PH3 when decomposed produces phosphorus and hydrogen. The change in volume is:
1. 50 mL increase
2. 500 mL decrease
Mass of sucrose C12H22O11 produced by mixing 84 gm of carbon, 12gm of hydrogen and 56L. O2 at 1atm & 273 K according to give reaction, is C(s) + H2(g) +O2(g)
\to
C12H22O11 (s)
1.0 mol of Fe reacts completely with 0.65 mol of O2 to give a mixture of only FeO and Fe2O3. The mole ratio of ferrous oxide to ferric oxide is
KClO3 on heating decomposes to KCl and O2. The volume of O2 at STP liberated by 0.1 mole KClO3 is
Total number of moles of oxygen atoms in 3 litre
{\mathrm{O}}_{3}\left(\mathrm{g}\right)
°
C and 8.21 atm are:
The equivalent weight of
\mathrm{HCl}
in the given reaction is:
{\mathrm{K}}_{2}{\mathrm{Cr}}_{2}{\mathrm{O}}_{7}+14\mathrm{HCl}\quad \to \quad 2\mathrm{KCl}+2{\mathrm{CrCl}}_{3}+3{\mathrm{Cl}}_{2}+{\mathrm{H}}_{2}\mathrm{O}
Cisplatin, an anticancer drug, has the molecular formula
\mathrm{Pt}{\left({\mathrm{NH}}_{3}\right)}_{2} {\mathrm{Cl}}_{2}
. What is the mass (in gram) of one molecule? (Atomic weights : Pt=195, H=1.0, N=14, Cl=35.5)
4.98×{10}^{-21}
4.98×{10}^{-22}
6.55×{10}^{-21}
3.85×{10}^{-22}
A gaseous compound is composed of 85.7% by mass carbon and 14.3% by mass hydrogen. It's density is 2.28 g/litre at 300 K and 1.0 atm pressure. Determine the molecular formula of the compound:
{\mathrm{C}}_{2}{\mathrm{H}}_{2}
{\mathrm{C}}_{2}{\mathrm{H}}_{4}
{\mathrm{C}}_{4}{\mathrm{H}}_{8}
{\mathrm{C}}_{4}{\mathrm{H}}_{10}
Copper forms two oxides. For the same amount of copper, twice as much oxygen was used to form first oxide than to form second one. What is the ratio of the valencies of copper in first and second oxides?
The average molar mass of the mixture of
{\mathrm{CH}}_{4}\quad
{\mathrm{C}}_{2}{\mathrm{H}}_{4}
present in the mole ratio of a:b is 20 g mol-1.
The molar mass of the mixture when the mole ratio gets reversed, will be -
The vapour density of a volatile chloride of a metal is 95 and the specific heat of the metal is 0.13 cal/g. The equivalent mass of the metal will be:
{\mathrm{H}}_{3}{\mathrm{PO}}_{2}
{\mathrm{PH}}_{3}
{\mathrm{H}}_{3}{\mathrm{PO}}_{3}
\sqrt{6} \overline{)\mathrm{h}}
\sqrt{2} \mathrm{h}
2\sqrt{3} \mathrm{h}
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"Charge distribution" redirects here. This article is about the physical quantity in electromagnetism. For other uses see charge and density.
In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in coulombs per cubic meter (C⋅m−3), at any point in a volume.[1][2][3] Surface charge density (σ) is the quantity of charge per unit area, measured in coulombs per square meter (C⋅m−2), at any point on a surface charge distribution on a two dimensional surface. Linear charge density (λ) is the quantity of charge per unit length, measured in coulombs per meter (C⋅m−1), at any point on a line charge distribution. Charge density can be either positive or negative, since electric charge can be either positive or negative.
Like mass density, charge density can vary with position. In classical electromagnetic theory charge density is idealized as a continuous scalar function of position
{\displaystyle {\boldsymbol {x}}}
, like a fluid, and
{\displaystyle \rho ({\boldsymbol {x}})}
{\displaystyle \sigma ({\boldsymbol {x}})}
{\displaystyle \lambda ({\boldsymbol {x}})}
are usually regarded as continuous charge distributions, even though all real charge distributions are made up of discrete charged particles. Due to the conservation of electric charge, the charge density in any volume can only change if an electric current of charge flows into or out of the volume. This is expressed by a continuity equation which links the rate of change of charge density
{\displaystyle \rho ({\boldsymbol {x}})}
and the current density
{\displaystyle {\boldsymbol {J}}({\boldsymbol {x}})}
Since all charge is carried by subatomic particles, which can be idealized as points, the concept of a continuous charge distribution is an approximation, which becomes inaccurate at small length scales. A charge distribution is ultimately composed of individual charged particles separated by regions containing no charge.[4] For example, the charge in an electrically charged metal object is made up of conduction electrons moving randomly in the metal's crystal lattice. Static electricity is caused by surface charges consisting of ions on the surface of objects, and the space charge in a vacuum tube is composed of a cloud of free electrons moving randomly in space. The charge carrier density in a conductor is equal to the number of mobile charge carriers (electrons, ions, etc.) per unit volume. The charge density at any point is equal to the charge carrier density multiplied by the elementary charge on the particles. However, because the elementary charge on an electron is so small (1.6⋅10−19 C) and there are so many of them in a macroscopic volume (there are about 1022 conduction electrons in a cubic centimeter of copper) the continuous approximation is very accurate when applied to macroscopic volumes, and even microscopic volumes above the nanometer level.
At even smaller scales, of atoms and molecules, due to the uncertainty principle of quantum mechanics, a charged particle does not have a precise position but is represented by a probability distribution, so the charge of an individual particle is not concentrated at a point but is 'smeared out' in space and acts like a true continuous charge distribution.[4] This is the meaning of 'charge distribution' and 'charge density' used in chemistry and chemical bonding. An electron is represented by a wavefunction
{\displaystyle \psi ({\boldsymbol {x}})}
whose square is proportional to the probability of finding the electron at any point
{\displaystyle {\boldsymbol {x}}}
in space, so
{\displaystyle |\psi ({\boldsymbol {x}})|^{2}}
is proportional to the charge density of the electron at any point. In atoms and molecules the charge of the electrons is distributed in clouds called orbitals which surround the atom or molecule, and are responsible for chemical bonds.
2 Free, bound and total charge
2.1 Total charge densities
2.2 Bound charge
2.3 Free charge density
3 Homogeneous charge density
4 Discrete charges
5 Charge density in special relativity
6 Charge density in quantum mechanics
Continuous chargesEdit
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (three dimensional), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P. Position vector r is a point to calculate the electric field; r′ is a point in the charged object.
{\displaystyle \lambda _{q}={\frac {dQ}{d\ell }}\,,}
{\displaystyle \sigma _{q}={\frac {dQ}{dS}}\,,}
{\displaystyle \rho _{q}={\frac {dQ}{dV}}\,,}
{\displaystyle Q=\int _{L}\lambda _{q}(\mathbf {r} )\,d\ell }
{\displaystyle Q=\int _{S}\sigma _{q}(\mathbf {r} )\,dS}
{\displaystyle Q=\int _{V}\rho _{q}(\mathbf {r} )\,dV}
{\displaystyle \langle \lambda _{q}\rangle ={\frac {Q}{\ell }}\,,\quad \langle \sigma _{q}\rangle ={\frac {Q}{S}}\,,\quad \langle \rho _{q}\rangle ={\frac {Q}{V}}\,.}
Free, bound and total chargeEdit
In dielectric materials, the total charge of an object can be separated into "free" and "bound" charges.
Total charge densitiesEdit
In terms of volume charge densities, the total charge density is:
{\displaystyle \rho =\rho _{\text{f}}+\rho _{\text{b}}\,.}
{\displaystyle \sigma =\sigma _{\text{f}}+\sigma _{\text{b}}\,.}
Bound chargeEdit
The bound surface charge is the charge piled up at the surface of the dielectric, given by the dipole moment perpendicular to the surface:[6]
{\displaystyle q_{b}={\frac {\mathbf {d} \cdot \mathbf {\hat {n}} }{|\mathbf {s} |}}}
where s is the separation between the point charges constituting the dipole,
{\displaystyle \mathbf {d} }
{\displaystyle \mathbf {\hat {n}} }
is the unit normal vector to the surface.
Taking infinitesimals:
{\displaystyle dq_{b}={\frac {d\mathbf {d} }{|\mathbf {s} |}}\cdot \mathbf {\hat {n}} }
{\displaystyle \sigma _{b}={\frac {dq_{b}}{dS}}={\frac {d\mathbf {d} }{|\mathbf {s} |dS}}\cdot \mathbf {\hat {n}} ={\frac {d\mathbf {d} }{dV}}\cdot \mathbf {\hat {n}} =\mathbf {P} \cdot \mathbf {\hat {n}} \,.}
{\displaystyle q_{b}=\iiint \rho _{b}dV=-}
{\displaystyle {\scriptstyle S}}
{\displaystyle \mathbf {P} \cdot \mathbf {\hat {n}} dS=-\iiint \nabla \cdot \mathbf {P} dV}
{\displaystyle \rho _{b}=-\nabla \cdot \mathbf {P} \,.}
{\displaystyle \varphi ={\frac {1}{4\pi \varepsilon _{0}}}{\frac {(\mathbf {r} -\mathbf {r} ')\cdot \mathbf {d} }{|\mathbf {r} -\mathbf {r} '|^{3}}}}
{\displaystyle d\mathbf {d} =\mathbf {P} dV=\mathbf {P} d^{3}\mathbf {r} }
{\displaystyle \varphi ={\frac {1}{4\pi \varepsilon _{0}}}\iiint {\frac {(\mathbf {r} -\mathbf {r} ')\cdot \mathbf {P} }{|\mathbf {r} -\mathbf {r} '|^{3}}}d^{3}\mathbf {r'} }
{\displaystyle \nabla '\left({\frac {1}{|\mathbf {r} -\mathbf {r} '|}}\right)\equiv \left(\mathbf {e} _{x}{\frac {\partial }{\partial x'}}+\mathbf {e} _{y}{\frac {\partial }{\partial y'}}+\mathbf {e} _{z}{\frac {\partial }{\partial z'}}\right)\left({\frac {1}{|\mathbf {r} -\mathbf {r} '|}}\right)={\frac {\mathbf {r} -\mathbf {r} '}{|\mathbf {r} -\mathbf {r} '|^{3}}}}
{\displaystyle \varphi ={\frac {1}{4\pi \varepsilon _{0}}}\iiint \mathbf {P} \cdot \nabla '\left({\frac {1}{|\mathbf {r} -\mathbf {r} '|}}\right)d^{3}\mathbf {r'} }
{\displaystyle \varphi ={\frac {1}{4\pi \varepsilon _{0}}}\iiint \left[\nabla '\cdot \left({\frac {\mathbf {P} }{|\mathbf {r} -\mathbf {r} '|}}\right)-{\frac {1}{\mathbf {r} -\mathbf {r} '}}(\nabla '\cdot \mathbf {P} )\right]d^{3}\mathbf {r'} }
{\displaystyle \varphi ={\frac {1}{4\pi \varepsilon _{0}}}}
{\displaystyle {\scriptstyle S}}
{\displaystyle {\frac {\mathbf {P} \cdot \mathbf {\hat {n}} dS'}{|\mathbf {r} -\mathbf {r} '|}}-{\frac {1}{4\pi \varepsilon _{0}}}\iiint {\frac {\nabla '\cdot \mathbf {P} }{|\mathbf {r} -\mathbf {r} '|}}d^{3}\mathbf {r'} }
{\displaystyle \varphi ={\frac {1}{4\pi \varepsilon _{0}}}}
{\displaystyle {\scriptstyle S}}
{\displaystyle {\frac {\sigma _{b}dS'}{|\mathbf {r} -\mathbf {r} '|}}+{\frac {1}{4\pi \varepsilon _{0}}}\iiint {\frac {\rho _{b}}{|\mathbf {r} -\mathbf {r} '|}}d^{3}\mathbf {r'} }
{\displaystyle \sigma _{b}=\mathbf {P} \cdot \mathbf {\hat {n}} \,,\quad \rho _{b}=-\nabla \cdot \mathbf {P} }
Free charge densityEdit
{\displaystyle \Phi _{D}=}
{\displaystyle {\scriptstyle S}}
{\displaystyle \mathbf {D} \cdot \mathbf {\hat {n}} dS=\iiint \rho _{f}dV}
Homogeneous charge densityEdit
{\displaystyle Q=V\rho _{0}.}
Start with the definition of a continuous volume charge density:
{\displaystyle Q=\int _{V}\rho _{q}(\mathbf {r} )\,dV.}
{\displaystyle Q=\rho _{q,0}\int _{V}\,dV=\rho _{0}V}
{\displaystyle Q=V\rho _{q,0}.}
Discrete chargesEdit
{\displaystyle \rho _{q}(\mathbf {r} )=q\delta (\mathbf {r} -\mathbf {r} _{0})}
{\displaystyle \int _{R}d^{3}\mathbf {r} f(\mathbf {r} )\delta (\mathbf {r} -\mathbf {r} _{0})=f(\mathbf {r} _{0})}
{\displaystyle Q=\int _{R}d^{3}\mathbf {r} \,\rho _{q}=\int _{R}d^{3}\mathbf {r} \,q\delta (\mathbf {r} -\mathbf {r} _{0})=q\int _{R}d^{3}\mathbf {r} \,\delta (\mathbf {r} -\mathbf {r} _{0})=q}
{\displaystyle \rho _{q}(\mathbf {r} )=\sum _{i=1}^{N}\ q_{i}\delta (\mathbf {r} -\mathbf {r} _{i})}
{\displaystyle Q=\int _{R}d^{3}\mathbf {r} \sum _{i=1}^{N}\ q_{i}\delta (\mathbf {r} -\mathbf {r} _{i})=\sum _{i=1}^{N}\ q_{i}\int _{R}d^{3}\mathbf {r} \delta (\mathbf {r} -\mathbf {r} _{i})=\sum _{i=1}^{N}\ q_{i}}
{\displaystyle \rho _{q}(\mathbf {r} )=qn(\mathbf {r} )\,.}
Charge density in special relativityEdit
In special relativity, the length of a segment of wire depends on velocity of observer because of length contraction, so charge density will also depend on velocity. Anthony French[7] has described how the magnetic field force of a current-bearing wire arises from this relative charge density. He used (p 260) a Minkowski diagram to show "how a neutral current-bearing wire appears to carry a net charge density as observed in a moving frame." When a charge density is measured in a moving frame of reference it is called proper charge density.[8][9][10]
Charge density in quantum mechanicsEdit
{\displaystyle \rho _{q}(\mathbf {r} )=q|\psi (\mathbf {r} )|^{2}}
{\displaystyle Q=\int _{R}q|\psi (\mathbf {r} )|^{2}\,d^{3}\mathbf {r} }
The charge density appears in the continuity equation for electric current, and also in Maxwell's Equations. It is the principal source term of the electromagnetic field; when the charge distribution moves, this corresponds to a current density. The charge density of molecules impacts chemical and separation processes. For example, charge density influences metal-metal bonding and hydrogen bonding.[11] For separation processes such as nanofiltration, the charge density of ions influences their rejection by the membrane.[12]
^ P.M. Whelan, M.J. Hodgeson (1978). Essential Principles of Physics (2nd ed.). John Murray. ISBN 0-7195-3382-1.
^ "Physics 2: Electricity and Magnetism, Course Notes, Ch. 2, p. 15-16" (PDF). MIT OpenCourseware. Massachusetts Institute of Technology. 2007. Retrieved December 3, 2017.
^ Serway, Raymond A.; Jewett, John W. (2013). Physics for Scientists and Engineers, Vol. 2, 9th Ed. Cengage Learning. p. 704. ISBN 9781133954149.
^ a b Purcell, Edward (2011-09-22). Electricity and Magnetism. Cambridge University Press. ISBN 9781107013605.
^ a b I.S. Grant; W.R. Phillips (2008). Electromagnetism (2nd ed.). Manchester Physics, John Wiley & Sons. ISBN 978-0-471-92712-9.
^ a b c d D.J. Griffiths (2007). Introduction to Electrodynamics (3rd ed.). Pearson Education, Dorling Kindersley. ISBN 978-81-7758-293-2.
^ A. French (1968) Special Relativity, chapter 8 Relativity and electricity, pp 229–65, W. W. Norton.
^ Richard A. Mould (2001) Basic Relativity, §62 Lorentz force, Springer Science & Business Media ISBN 0-387-95210-1
^ Derek F. Lawden (2012) An Introduction to Tensor Calculus: Relativity and Cosmology, page 74, Courier Corporation ISBN 0-486-13214-5
^ Jack Vanderlinde (2006) Classical Electromagnetic Theory, § 11.1 The Four-potential and Coulomb's Law, page 314, Springer Science & Business Media ISBN 1-4020-2700-1
^ R. J. Gillespie & P. L. A. Popelier (2001). "Chemical Bonding and Molecular Geometry". Environmental Science & Technology. Oxford University Press. 52 (7): 4108–4116. Bibcode:2018EnST...52.4108E. doi:10.1021/acs.est.7b06400. PMID 29510032.
^ Razi Epsztein, Evyatar Shaulsky, Nadir Dizge, David M Warsinger, Menachem Elimelech (2018). "Ionic Charge Density-Dependent Donnan Exclusion in Nanofiltration of Monovalent Anions". Environmental Science & Technology. 52 (7): 4108–4116. Bibcode:2018EnST...52.4108E. doi:10.1021/acs.est.7b06400. PMID 29510032. {{cite journal}}: CS1 maint: multiple names: authors list (link)
[1] - Spatial charge distributions
Retrieved from "https://en.wikipedia.org/w/index.php?title=Charge_density&oldid=1070186476"
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Distributive law - zxc.wiki
Visualization of the distributive law for positive numbers
The distributive laws (lat. Distribuere "distribute") are mathematical rules that indicate how two two- digit links relate to each other when brackets are broken, namely that one link is compatible in a certain way with the other link .
In school mathematics in particular, the use of the distributive law to convert a sum into a product is referred to as factoring out or singling out. Solving parentheses by applying the distributive law is known as multiplying .
The distributive law, together with the associative law and the commutative law, form fundamental rules of algebra .
Let two two- digit links and be defined on a set . The link is called
{\ displaystyle A}
{\ displaystyle {\ diamond} \ colon A \ times A \ to A}
{\ displaystyle * \ colon A \ times A \ to A}
{\ displaystyle *}
linksdistributiv about if for all true
{\ displaystyle \ diamond,}
{\ displaystyle a, b, c \ in A}
{\ displaystyle a * (b \ diamond c) = (a * b) \ diamond (a * c)}
rechtsdistributiv about if for all true
{\ displaystyle \ diamond,}
{\ displaystyle a, b, c \ in A}
{\ displaystyle (a \ diamond b) * c = (a * c) \ diamond (b * c)}
distributive over if it is left and right distributive over .
{\ displaystyle \ diamond,}
{\ displaystyle \ diamond}
If the connection is commutative, then these three conditions are equivalent .
{\ displaystyle *}
The two-digit links for the addition and multiplication of numbers can serve as an example .
{\ displaystyle (+)}
{\ displaystyle (\ cdot)}
A distinction between linksdistributiven and rechtsdistributiven links:
{\ displaystyle a \ cdot \ left (b \ pm c \ right) = a \ cdot b \ pm a \ cdot c}
(left-hand distribution)
{\ displaystyle (a \ pm b) \ cdot c = a \ cdot c \ pm b \ cdot c}
(legal distributive)
A sum (or difference) is multiplied by a factor by multiplying each summand (or minuend and subtrahend) with this factor and adding (or subtracting) the product values.
If the “superordinate” link, in this case the multiplication, is commutative , one can infer from the left distributivity also the right distributivity and vice versa.
An example of "only" legal distributivity is division , which is not commutative:
{\ displaystyle (a \ pm b): c = a: c \ pm b: c}
The following generally applies here:
{\ displaystyle a: (b \ pm c) \ neq a: b \ pm a: c}
In school mathematics, mostly only the bilateral (commutative) distributive laws are designated as such and the law of division is circumvented. It is then only calculated:
be and
{\ displaystyle a = m \ cdot c}
{\ displaystyle b = n \ cdot c}
{\ displaystyle (a \ pm b): c = (m \ cdot c \ pm n \ cdot c): c = (m \ pm n) \ cdot c: c = m \ pm n}
The distributive laws are among the axioms for rings and bodies . Examples of structures in which two functions are distributively related to one another are Boolean algebras , such as the algebra of sets or the switching algebra . But there are also combinations of links that are not distributively related to one another; for example, addition is not distributive to multiplication.
The multiplication of sums can also be put into words as follows: A sum is multiplied by a sum by multiplying each addend of one sum by each addend of the other sum - taking into account the signs - and adding the resulting products.
The following examples illustrate the use of the distributive law on the set of real numbers . In school mathematics, these examples are usually referred to as multiplying. From the point of view of algebra , the real numbers form a field , which ensures the validity of the distributive law.
{\ displaystyle \ mathbb {R}}
First example (mental arithmetic and writing multiplication)
In mental arithmetic, the distributive law is often used unconsciously:
{\ displaystyle 6 \ times 16 = 6 \ times (10 + 6) = 6 \ times 10 + 6 \ times 6 = 60 + 36 = 96}
You want to compute 6 · 16 in your head. To do this, multiply 6 · 10 and 6 · 6 and add the intermediate results. Even the written multiplication based on the distributive law.
{\ displaystyle 3a ^ {2} b \ cdot (4a-5b) = 3a ^ {2} b \ cdot 4a-3a ^ {2} b \ cdot 5b = 12a ^ {3} b-15a ^ {2} b ^ {2}}
{\ displaystyle {\ begin {aligned} (a + b) \ cdot (ab) & = a \ cdot (ab) + b \ cdot (ab) = a ^ {2} -ab + ba-b ^ {2} = a ^ {2} -b ^ {2} \\ & = (a + b) \ cdot a- (a + b) \ cdot b = a ^ {2} + ba-ab-b ^ {2} = a ^ {2} -b ^ {2} \ end {aligned}}}
Here the distributive law was applied twice and the result was summarized. It does not matter which bracket is multiplied out first or whether in one step each addend of the first bracket is multiplied with each addend of the second bracket. The result is the third binomial formula .
Here the distributive law is applied the other way around than in the previous examples. Consider
{\ displaystyle 12a ^ {3} b ^ {2} -30a ^ {4} bc + 18a ^ {2} b ^ {3} c ^ {2} \ ,.}
Since the factor occurs in all summands , it can be excluded. That means, based on the distributive law, applies
{\ displaystyle 6a ^ {2} b}
{\ displaystyle 12a ^ {3} b ^ {2} -30a ^ {4} bc + 18a ^ {2} b ^ {3} c ^ {2} = 6a ^ {2} b (2ab-5a ^ {2nd } c + 3b ^ {2} c ^ {2}) \ ,.}
The distributive law is also valid for the matrix multiplication . More precisely, it applies
{\ displaystyle (A + B) \ cdot C = A \ cdot C + B \ cdot C}
for all matrices and matrices as well
{\ displaystyle l \ times m}
{\ displaystyle A, B}
{\ displaystyle m \ times n}
{\ displaystyle C}
{\ displaystyle A \ cdot (B + C) = A \ cdot B + A \ cdot C}
for all matrices and matrices . Since the commutative law does not apply to matrix multiplication , the second law does not follow from the first law. In this case there are two different laws.
{\ displaystyle l \ times m}
{\ displaystyle A}
{\ displaystyle m \ times n}
{\ displaystyle B, C}
Distributive Association
Boolean algebra (classical propositional logic )
DM Smirnov: Distributivity . In: Michiel Hazewinkel (Ed.): Encyclopaedia of Mathematics . Springer-Verlag , Berlin 2002, ISBN 978-1-55608-010-4 (English, online ).
This page is based on the copyrighted Wikipedia article "Distributivgesetz" (Authors); it is used under the Creative Commons Attribution-ShareAlike 3.0 Unported License. You may redistribute it, verbatim or modified, providing that you comply with the terms of the CC-BY-SA.
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RSVP 101 - ccie.nyquist.eu
RSVP (Resource Reservation Protocol) is an industry standard protocol used to implement IntServ QoS architecture. RSVP is used by the sender to request a certain QoS level from the routers along the path to the receiver. Devices along the way should be RSVP aware and they will let the sender know if they can implement its requirements. The sender first sends an RSVP request message (PATH). This message will identify the flows and what QoS level they require. The first router in the path towards destination will receive this message and if it can offer the desired QoS level it will forward the traffic to the next router towards the destination. If all routers along the path can deliver the required QoS level, the PATH message will arrive at the destination router. If it can also deliver the QoS level, it will start to send RESV messages towards the sender, letting it and all the routers along the path that the network can offer the required QoS level. By sending RESV messages, the receiver is the one that actually requests the QoS level, now that we know that the network can implement it. In order for the routers to maintain the reservation, senders must send PATH messages every 30 seconds.
RSVP Sender
To configure a Cisco router as an RSVP sender, we must configure it to sende PATH messages.
R(config)#ip rsvp sender-host DESTINATION-IP SOURCE-IP {udp|tcp|PROTOCOL} PORT-DST PORT-SRC CIR BC
! SOURCE-IP must exist locally
! DESTINATION-IP, SOURCE-IP, PROTOCOL, PORT-DST, PORT-SRC define the flow
! CIR, BC - define the flow's requirements
Similarly, you can configure a router to act as a Sender Proxy and use RSVP to request QoS for a non-RSVP enabled source. This time the SOURCE-IP doesn’t have to be locally defined:
R(config)# ip rsvp sender DESTINATION-IP SOURCE-IP {PROTOCOL|tcp|udp} DST-PORT SRC-PORT PREVIOUS-HOP-IP PREVIOUS-INTERFACE CIR BC
RSVP Receiver
To respond to PATH messages and start sending RESV messages, a receiver has to be configured accordingly:
R(config)# ip rsvp receiver-host DESTINATION-IP SOURCE-IP {udp|tcp|PROTOCOL} PORT-DST PORT-SRC {ff|se|wf} {load|rate} CIR BC
! DESTINATION-IP must exist locally
! ff|se| wf - Filter Type (FilterSpec)
! load|rate - Reservation Type/Service Type
As you can see, the source must define the Reservation Type and the Service Type that this flow will require. An RSVP flow is characterized by 2 data structures: FlowSpec and FilterSpec. FlowSpec contains the RSpec (Reservation Type – the class of service that the flow requires) and TSpec(Traffic Info – the Token Bucket parameters used for metering: CIR, Bc). FilterSpec defines the sources that can make use of the QoS reserved for the flow. There are 3 types of filters that can be used:
ff – Fixed Filter – allows only 1 source, explicitly defined.
sf – Shared Filter – allows multiple sources, explicitly defined.
wf – Wildcard Filter – allows any source, no explicit info.
The Reservation Type can be one of the following options:
Guaranteed Rate Service, which allows applications to reserve bandwidth to meet their requirements. Cisco IOS QoS uses RSVP with WFQ for this Service Type
Controlled Load Service, which allows applications to have low delay and high throughput even during times of congestion. Cisco IOS QoS uses RSVP with WRED for this Service Type
As before, you can configure a router to act as a Receiver Proxy and use RSVP to respond to PATH messages in the name of a non-RSVP enabled receiver. This time the DESTINATION-IP doesn’t have to be locally defined:
R(config)# ip rsvp receiver DESTINATION-IP SOURCE-IP {PROTOCOL|tcp|udp} DST-PORT SRC-PORT NEXT-HOP-IP NEXT-INTERFACE {ff|se|wf} {load|rate} CIR BC
Routers along the path
In order to process RSVP messages, all routers between sender and receiver must define the interfaces that are RSVP enabled and what is the maximum bandwidth reservation that RSVP flows can use. The command to enable this is:
R(config-if)# ip rsvp bandwidth TOTAL-RSVP-BW [SINGLE-FLOW-BW]
! RSVP-BW can also be defined as percentage of interface bandwidth
This command configure the Total Bandwidth that RSVP can use and the maximum bandwidth that a single RSVP flow can request You can verify the RSVP flows that have been installed in the QoS Database with:
R# show ip rsvp installed
RSVP and Fair Queueing
RSVP only works with interfaces that use a form of Fair Queueing: WFQ or CBWFQ. The RSVP flow with the highest CIR will be assigned a weight of 6, While the other flows will have a weight equal to
W_{ThisFlow}= 6\frac{max(BW_{AllRSVPFlows})}{BW_{ThisFlow}}
However, if the traffic is more than what was reserved for it, everything that is over the requirement is treated as traffic with IP_Precedence 0.
You can enable some RSVP flows to make use of the priority queue of LLQ. This is used primarily for voice traffic, but you can also specify flow characteristics to identify the flows that can use the priority queue.
! Voice Like identifies most voice traffic:
R(config)# ip rsvp pq-profile voice-like
! Or you can define your own characteristics:
R(config)# ip rsvp pq-profile RATE [BURST [PEAK-RATE|ignore-peak-value]]
On shared media, like Ethernet, one router can act as the Designated Subnetwork Bandwidth Manager. The reason we need such a Bandwidth Manager is that not all routers will be aware of the reservations made by other routers on the same media. By proxy-ing all RSVP requests to the DSBM, it will be aware of all reservations. To configure a rotuer as a DSBM candidate, use:
R(config-if)#ip rsvp dsbm candidate [PRIORITY]
! Default PRIORITY: 64
The highest PRIORITY wins and in case of ties the highest IP Address wins. There is no preemption. The DSBM can be configured to implement a form of Admission Control by specifying the amount of traffic that can be forwarded to the shared segment without reservation:
R(config-if)# ip rsvp dsbm non-resv-send-limit rate KBPS
R(config-if)#ip rsvp dsbm non-resv-send-limit burst KBYTES
R(config-if)#ip rsvp dsbm non-resv-send-limit peak KBPS
R(config-if)#ip rsvp dsbm non-resv-send-limit min-unit BYTES
R(config-if)#ip rsvp dsbm non-resv-send-limit max-unit BYTES
The DSBM will distribute this information to the other RSVP routers on the segment.
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The displacement x in meter of a particle of mass m kg moving in one direction under the action of a force is related to the time t in second by the equation x=(t-3)2. The work done by the force (in joules) in first six seconds is
\frac{Mgh}{2}
-\frac{Mgh}{2}
\frac{3Mgh}{2}
-\frac{3Mgh}{2}
\stackrel{\to }{F}=2x\stackrel{^}{i}+2\stackrel{^}{j}+3{z}^{2}\stackrel{^}{k} N
is acting on a particle. Find the work done by this force in displacing the body from (1, 2, 3) m to (3, 6, 1)m.
1. -10 J
If we shift a body in equilibrium from A to C gravitational field via path AC or ABC,
1. The work done by the force
\stackrel{\to }{F}
for both paths will be same
{W}_{AC}>{W}_{ABC}
{W}_{AC}<{W}_{ABC}
An engine pumps up 100 kg of water through a height of 10 m in 5 s. Given that the efficiency of the engine is 60%, what is the power of the engine? Take g= 10 ms-2.
2. 3.3 kW
4. 0.033 kW
An engine pumps water continuously through a hole. Speed with which water passes through the hole nozzle is v, and k is the mass per unit length of the water jet as it leaves the nozzle. Find the rate at which kinetic energy is being imparted to the water.
\frac{1}{2} k{v}^{2}
\frac{1}{2} k{v}^{3}
\frac{{v}^{2}}{2k}
\frac{{v}^{3}}{2k}
A bus can be stopped by applying a retarding force F when it is moving with speed v on a level road. The distance covered by it before coming to rest is s. If the load of the bus increases by 50% because of passengers, for the same speed and same retarding force, the distance covered by the bus to come to rest shall be
A heavy weight is suspended from a spring. A person raises the weight till the spring becomes slack. The work done by him is W. The energy stored in the stretched spring was E. What will be the gain in gravitational potential energy?
3. W + E
4. W - E
The speed v reached by a car of mass m in traveling a distance x, driven with constant power P, is givenby
v=\frac{3xP}{m}
v={\left(\frac{3xP}{m}\right)}^{1/2}
v={\left(\frac{3xP}{m}\right)}^{1/3}
v={\left(\frac{3xP}{m}\right)}^{2}
Figure shows the verticl section of a frictionless surface. A block of mass 2 kg is released from rest from position A; its KE as it reaches position C is (g= 10 m s-2)
The kinetic energy K of a particle moving along a circle of radius R depends upon the distance s as K=as2. The force acting on the particle is
2a\frac{{s}^{2}}{R}
2as{\left[1+\frac{{s}^{2}}{{R}^{2}}\right]}^{1/2}
A block of 4 kg mass starts at rest and slides a distance d down a friction less incline (angle 30
°
) where it runs into a spring of negligible mass. The block slides an additional 25 cm before it is brought to rest momentarily by compressing the spring. The force constant of the spring is 400 Nm-1. The value of d is (take g= 10 ms-2)
A particle is released one by one from the top of two inclined rough surfaces of height h each. The angles of inclination of the two planes are 30
°
°
, respectively. All other factors (e.g., coefficient of friction, mass of block, etc.) are same in the both the cases. Let K1 and K2 be the kinetic energies of the particle at the bottom of the plane in the two cases. Then
1. K1 = K2
2. K1 > K2
3. K1 < K2
The system shown in the figure is released from rest with mass 2 kg in contact with the ground. Pulley and spring are massless, and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with the ground is (found constant of the spring k= 40 Nm-1 and g= 10 m s-2)
\sqrt{2} m {s}^{-1}
2\sqrt{2}m {s}^{-1}
2 m {s}^{-1}
\sqrt{2} m {s}^{-1}
A particle of mass m is projected at an angle
\alpha
to the horizontal with an initial velocity u. The work done by the gravity during the time it reaches its highest point is
{u}^{2}{\mathrm{sin}}^{2}\alpha
\frac{m{u}^{2}{\mathrm{cos}}^{2}\alpha }{2}
\frac{m{u}^{2}{\mathrm{sin}}^{2}\alpha }{2}
-\frac{m{u}^{2}{\mathrm{sin}}^{2}\alpha }{2}
\alpha
to the horizontal with an initial velocity u, the average power delivered by gravity is
-mg u \mathrm{cos} \alpha
-mgu \mathrm{sin} \alpha
-\frac{mgu \mathrm{cos} \alpha }{2}
-\frac{mgu \mathrm{sin} \alpha }{2}
A person of mass 70 kg jumps from a stationary helicopter with the parachute open. As he falls through 50 m height, he gains a speed of 20 m s-1.The work done by the viscous air drag is
2. -21000 J
A particle located in a one-dimensional potential field has its potential energy function as
U\left(x\right)=\frac{a}{{x}^{4}}-\frac{b}{{x}^{2}}
, where a and b are positive constants. The position of equilibrium x corresponds to
\frac{b}{2a}
\sqrt{\frac{2a}{b}}
\sqrt{\frac{2b}{a}}
\frac{a}{2b}
A collar B of mass 2 kg is constrained to move along a horizontal smooth and fixed circular track of radius 5 m. The spring lying in the plane of the circular track and having spring constant 200 N m-1 is underformed when the collar is at A. If the collar starts from rest at B, the normal reaction exerted by the track on the collar when it passes through A is
A particle of mass m slides on a frictionless surface ABCD, starting from rest as shown in figure. The part BCD is a circular arc. If it looses contact at point P, the maximum height attained by the particle from point C is
R\left[2+\frac{1}{2\sqrt{2}}\right]
R\left[2+\frac{1}{2\sqrt{2}}\right]R
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Select model order for single-output ARX models - MATLAB selstruc - MathWorks Switzerland
\begin{array}{c}{V}_{\mathrm{mod}}=\mathrm{log}\left(V\left(1+\frac{2d}{N}\right)\right)\\ =\mathrm{log}\left(V\right)+\frac{2d}{N},N\gg d\end{array}
\mathrm{log}\left(V\right)+\frac{2d}{N}
{V}_{\text{mod}}=V\left(1+\frac{d\mathrm{log}\left(N\right)}{N}\right)
{V}_{\mathrm{mod}}=V\left(1+\frac{cd}{N}\right)
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{\displaystyle {dI \over dt}={V_{B} \over L}}
{\displaystyle I=V_{B}/R}
Induction at the opening of a contactEdit
{\displaystyle V_{L}=-{d\Phi _{B} \over dt}=-L{dI \over dt}}
{\displaystyle V_{R_{2}}=R_{2}\cdot I}
{\displaystyle V_{L}=V_{R_{2}}}
{\displaystyle -L{dI \over dt}=R_{2}\cdot I}
{\displaystyle I(t)=I_{0}\cdot e^{-{R_{2} \over L}t}}
{\displaystyle V_{D}=\mathrm {constant} }
{\displaystyle V_{L}=V_{R_{1}}+V_{D}}
{\displaystyle -L{dI \over dt}=R_{1}\cdot I+V_{D}}
{\displaystyle I(t)=(I_{0}+{1 \over R_{1}}V_{D})\cdot e^{-{R_{1} \over L}t}-{1 \over R_{1}}V_{D}}
{\displaystyle t={-L \over R_{1}}\cdot ln{\left({V_{D} \over {V_{D}+I_{0}{R_{1}}}}\right)}}
{\displaystyle t={-L \over R_{1}}\cdot ln{\left({1 \over {{\frac {V_{CC}}{V_{D}}}+1}}\right)}={L \over R_{1}}\cdot ln{\left({{\frac {V_{CC}}{V_{D}}}+1}\right)}}
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Determine if digital filter coefficients are double precision - MATLAB isdouble - MathWorks India
Double- and Single-Precision Filter
Determine if digital filter coefficients are double precision
flag = isdouble(d) returns true if the coefficients of a digital filter, d, are double precision.
Use designfilt to design a sixth-order highpass IIR filter. Specify a normalized passband frequency of
0.6\pi
Digital filter, specified as a digitalFilter object. Use designfilt to generate d. If you want a single-precision filter, apply single to the output of designfilt.
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Chemical Bonding - Live Session (Aggressive Schedule) - NEET 2020Contact Number: 9667591930 / 8527521718
Calculate the maximum ionic character possible in a bond between two atoms in the periodic table according to Hanny Smith equation. [Electronegativeity of Li=1.0, Na=0.9, K=0.8, Rb=0.8, Cs=0.7, Fr=0.7]
~90%
~97%
~80%
~75%
Choose the correct order from the following:
{\mathrm{N}}_{2}\mathrm{O}<{\mathrm{N}}_{2}{\mathrm{O}}_{3}<\mathrm{NO}
; Acidic character
\mathrm{MgO}>{\mathrm{Al}}_{2}{\mathrm{O}}_{3}>{\mathrm{SiO}}_{2}
; Basic character
{\mathrm{Fe}}^{3+}<{\mathrm{Fe}}^{2+}<{\mathrm{Mn}}^{2+}
; Ionic radius order
\mathrm{Sc}>\mathrm{La}>\mathrm{Y}
; Ionisation energy order
Statement-1 : Fluorine (F) act as stronger oxidizing agent than oxygen (O).
\left|∆{\mathrm{H}}_{\mathrm{e}.\mathrm{g}.\mathrm{e}}\right|
of Fluorine (F) is higher than oxygen (O).
1. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
2. Statement-1 is true, statement-2 is true and statement-2 is not the correct explanation for statement-1.
3. Statement-1 is true, statement-2 is false.
4. Statement-1 is false, statement-2 is true.
1. Lattice energy
\mathrm{\alpha }\frac{1}{{\mathrm{r}}^{2}}
. [where r is the interionic distance]
\mathrm{\alpha }\quad {\mathrm{q}}_{1}{\mathrm{q}}_{2}
. [where
{\mathrm{q}}_{1}\quad \&\quad {\mathrm{q}}_{2}
are the charges of co-ions]
3. Ionic mobility of the ions in aqueous state
\mathrm{\alpha }\frac{1}{\mathrm{radius}\quad \mathrm{of}\quad \mathrm{ions}\quad \mathrm{in}\quad \mathrm{gaseous}\quad \mathrm{state}}
4. Heat of formation of a compound depends on the number of steps involved in its formation reaction.
Statement-1: Glycerol is more viscous than methanol.
Statement-2: This is due to intramolecular H-bonding.
{\mathrm{AsF}}_{5}
molecule is trigonal bipyramidal. The hybrid orbitals used by As-atoms for bonding are
{\mathrm{d}}_{{\mathrm{x}}^{2}-{\mathrm{y}}^{2}},\quad {\mathrm{d}}_{{\mathrm{z}}^{2}},\quad \mathrm{s},\quad {\mathrm{p}}_{\mathrm{x}},\quad {\mathrm{p}}_{\mathrm{y}}
{\mathrm{d}}_{\mathrm{xy}},\quad \mathrm{s},\quad {\mathrm{p}}_{\mathrm{x}},\quad {\mathrm{p}}_{\mathrm{y}},\quad {\mathrm{p}}_{\mathrm{z}}
\mathrm{s},\quad {\mathrm{p}}_{\mathrm{x}},\quad {\mathrm{p}}_{\mathrm{y}},\quad {\mathrm{p}}_{\mathrm{z}},\quad {\mathrm{d}}_{{\mathrm{z}}^{2}}
{\mathrm{d}}_{{\mathrm{x}}^{2}-{\mathrm{y}}^{2}},\quad \mathrm{s},\quad {\mathrm{p}}_{\mathrm{x}},\quad {\mathrm{p}}_{\mathrm{y}},\quad {\mathrm{p}}_{\mathrm{z}}
Choose the incorrect statement among the following.
\mathrm{HF}
is the most volatile acid among
\mathrm{HX}
{\mathrm{Na}}_{2}{\mathrm{O}}_{2}
is having ionic and covalent type of bonds.
{\mathrm{CH}}_{3}{\mathrm{CO}}_{2}\mathrm{Na}
is having identical
\mathrm{C}-\mathrm{O}
bond lengths while it is not true for
{\mathrm{CH}}_{3}{\mathrm{CO}}_{2}\mathrm{H}
4. p-p overlap is more stronger compared to s-s overlap in axial type of bond formation.
Find out the molecule species which is not electron deficient.
{\mathrm{AlCl}}_{3}
{\mathrm{BeH}}_{2}
{{\mathrm{BH}}_{4}}^{-}
{\mathrm{BF}}_{3}
Choose the correct
{1}^{\mathrm{st}}
ionisation potential order of the given elements.
\mathrm{B}<\mathrm{Be}<\mathrm{N}<\mathrm{O}
\mathrm{Be}<\mathrm{B}<\mathrm{N}<\mathrm{O}
\mathrm{N}>\mathrm{Be}>\mathrm{O}>\mathrm{B}
\mathrm{N}>\mathrm{O}>\mathrm{Be}>\mathrm{B}
1. Electronegativity of
\mathrm{Cl}
\mathrm{F}
2. Electron affinity of
\mathrm{Cl}
\mathrm{F}
3. Bond energy of
\mathrm{\sigma }
-bond is greater than
\mathrm{\pi }
4. The net dipole moment direction of
{\mathrm{NF}}_{3}
is toward
\mathrm{l}.\mathrm{p}.
of N-atom.
If y-axis is the approaching axis between two atoms, then which of the set of orbitals cannot form the
\mathrm{\pi }
bond between two atoms in general.
{\mathrm{P}}_{\mathrm{y}}-{\mathrm{P}}_{\mathrm{z}}
{\mathrm{P}}_{\mathrm{x}}-{\mathrm{P}}_{z}
{\mathrm{P}}_{\mathrm{x}}-{\mathrm{P}}_{\mathrm{y}}
In which of the following molecule the intramolecular hydrogen bonding is not existing.
\mathrm{P}-\mathrm{O}-\mathrm{P}
linkages in
{\mathrm{P}}_{4}{\mathrm{O}}_{10}
{\mathrm{P}}_{4}{\mathrm{O}}_{6}
are respectively -
The state of hybridisation of 'B' atoms in borax
\left({\mathrm{Na}}_{2}{\mathrm{B}}_{4}{\mathrm{O}}_{7} · 10{\mathrm{H}}_{2}\mathrm{O}\right)
1. All sp2 hybridised
2. Three sp2 and one sp3 hybridised
3. One sp2 and three sp3 hybridised
4. Two sp2 and two sp3 hybridised
Which of the following forces does not contribute to the van der Waal's forces of attraction.
2. Dipole-induced dipole interaction
3. Instantaneous dipole induced dipole interaction
4. ELectrostatic forces of attraction releasing the energy 72 kJ/mole
For the molecule
{\mathrm{MA}}_{2}{\mathrm{L}}_{\mathrm{n}}
(where A is number of single bonded surrounding atoms, L indicates lone pair and 'n' is the number of lone pair and M is the central atom of 's' or 'p' block element) the possible range of 'n' is
1. '1' to '4'
2. zero to '4'
The total number of
\mathrm{\pi }
-bond electrons in the following structure is
\left({\mathrm{C}}_{3}{\mathrm{O}}_{2}\right)
3. Trigonal structure
4. Distorted tetrahedral structure
Which of the following gas is least polarizable?
Which of the following is correct order of dipole moment of the following?
2. I = II = III
{\mathrm{PCl}}_{5}
is highly unstable and in solid state it exists as into
{\left[{\mathrm{PCl}}_{4}\right]}^{+} \mathrm{and} {\left[{\mathrm{PCl}}_{6}\right]}^{-}
The geometry of
{\left[{\mathrm{PCl}}_{6}\right]}^{-}
4. square planar
In an octahedral structure, the pair of d orbitals involved in
{\mathrm{d}}^{2}{\mathrm{sp}}^{3}
-hybridisation is
{\mathrm{d}}_{{\mathrm{x}}^{2}-{\mathrm{y}}^{2}}, {\mathrm{d}}_{{\mathrm{z}}^{2}}
{\mathrm{d}}_{\mathrm{xy}}, {\mathrm{d}}_{{\mathrm{x}}^{2}-{\mathrm{y}}^{2}}
{\mathrm{d}}_{{\mathrm{z}}^{2}}, {\mathrm{d}}_{\mathrm{xz}}
{\mathrm{d}}_{\mathrm{xy}}, {\mathrm{d}}_{\mathrm{yz}}
{\mathrm{PO}}_{4}^{3-}
ion, the formal charge on each oxygen atom and P-O bond order respectively are :
1. -0.75, 0.6
3. -0.75, 1.25
4. -3.1, 1.25
The correct order of increasing bond angles in t
he following species is
{\mathrm{Cl}}_{2}\mathrm{O} < {\mathrm{ClO}}_{2} < {\mathrm{ClO}}_{2}^{-}
{\mathrm{ClO}}_{2} < {\mathrm{Cl}}_{2}\mathrm{O} < {\mathrm{ClO}}_{2}^{-}
{\mathrm{Cl}}_{2}\mathrm{O} < {\mathrm{ClO}}_{2}^{-} < {\mathrm{ClO}}_{2}
{\mathrm{ClO}}_{2}^{-} < {\mathrm{Cl}}_{2}\mathrm{O} <{\mathrm{ClO}}_{2}
Which of the following compounds has the lowest melting point?
{\mathrm{CaBr}}_{2}
{\mathrm{Cal}}_{2}
{\mathrm{CaF}}_{2}
{\mathrm{CaCl}}_{2}
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Multivariate normal regression with missing data - MATLAB ecmmvnrmle - MathWorks Australia
ecmmvnrmle
Compute Multivariate Normal Regression With Missing Data
TolParam
[Param,Covar] = ecmmvnrmle(Data,Design)
[Param,Covar,Resid,Info] = ecmmvnrmle(___,MaxIterations,TolParam,TolObj,Param0,Covar0,CovarFormat)
[Param,Covar] = ecmmvnrmle(Data,Design) estimates a multivariate normal regression model with missing data. The model has the form
Dat{a}_{k}\sim N\left(Desig{n}_{k}×Parameters,\text{\hspace{0.17em}}Covariance\right)
for samples k = 1, ... , NUMSAMPLES.
[Param,Covar,Resid,Info] = ecmmvnrmle(___,MaxIterations,TolParam,TolObj,Param0,Covar0,CovarFormat) adds an optional arguments for MaxIterations, TolParam, TolObj, Param0, Covar0, and CovarFormat.
This example shows how to estimate a multivariate normal regression model with missing data.
First, load dates, total returns, and ticker symbols for the twelve stocks from the MAT-file.
% Estimate the multivariate normal regression for each asset separately.
[Param, Covar] = ecmmvnrmle(TestData, TestDesign)
Covar = 0.0010
Covar = 8.8911e-04
Data, specified as an NUMSAMPLES-by-NUMSERIES matrix with NUMSAMPLES samples of a NUMSERIES-dimensional random vector. Missing values are indicated by NaNs. Only samples that are entirely NaNs are ignored. (To ignore samples with at least one NaN, use mvnrmle.)
Design — Design model
Design model, specified as a matrix or a cell array that handles two model structures:
MaxIterations — Maximum number of iterations for the estimation algorithm
(Optional) Maximum number of iterations for the estimation algorithm, specified as a numeric.
TolParam — Convergence tolerance for estimation algorithm based on changes in model parameter estimates
(Optional) Convergence tolerance for estimation algorithm based on changes in model parameter estimates, specified as a numeric. The convergence test for changes in model parameters is
‖Para{m}_{k}-Para{m}_{k-1}‖<TolParam×\left(1+‖Para{m}_{k}‖\right)
where Param represents the output Parameters, and iteration k = 2, 3, ... . Convergence is assumed when both the TolParam and TolObj conditions are satisfied. If both TolParam ≤ 0 and TolObj ≤ 0, do the maximum number of iterations (MaxIterations), whatever the results of the convergence tests.
TolObj — Convergence tolerance for estimation algorithm based on changes in objective function
1.0e-12 (default) | numeric
(Optional) Convergence tolerance for estimation algorithm based on changes in the objective function, specified as a numeric. The convergence test for changes in the objective function is
|Ob{j}_{k}-Ob{j}_{k-1}|<\text{\hspace{0.17em}}TolObj×\left(1+|Ob{j}_{k}|\right)
for iteration k = 2, 3, ... . Convergence is assumed when both the TolParam and TolObj conditions are satisfied. If both TolParam ≤ 0 and TolObj ≤ 0, do the maximum number of iterations (MaxIterations), whatever the results of the convergence tests.
Param0 — Estimate for the parameters of regression model
(Optional) Estimate for the parameters of the regression model, specified as an NUMPARAMS-by-1 column vector.
Covar0 — Estimate for the covariance matrix of regression residuals
(Optional) Estimate for the covariance matrix of the regression residuals, specified as NUMSERIES-by-NUMSERIES matrix.
CovarFormat — Format for the covariance matrix
'full' (default) | character vector
(Optional) Format for the covariance matrix, specified as a character vector. The choices are:
'full' — Compute the full covariance matrix.
'diagonal' — Force the covariance matrix to be a diagonal matrix.
Param — Estimates for parameters of the regression model
Estimates for the parameters of the regression model, returned as a NUMPARAMS-by-1 column vector.
Covar — Estimates for the covariance of regression model's residuals
Estimates for the covariance of the regression model's residuals, returned as a NUMSERIES-by-NUMSERIES matrix.
Resid — Residuals from regression
Residuals from the regression, returned as a NUMSAMPLES-by-NUMSERIES matrix. For any missing values in Data, the corresponding residual is the difference between the conditionally imputed value for Data and the model, that is, the imputed residual.
The covariance estimate Covariance cannot be derived from the residuals.
Info — Additional information from regression
Additional information from the regression, returned as a structure. The structure has these fields:
Info.Obj — A variable-extent column vector, with no more than MaxIterations elements, that contain each value of the objective function at each iteration of the estimation algorithm. The last value in this vector, Obj(end), is the terminal estimate of the objective function. If you do maximum likelihood estimation, the objective function is the log-likelihood function.
Info.PrevParameters — NUMPARAMS-by-1 column vector of estimates for the model parameters from the iteration just prior to the terminal iteration.Info.PrevCovariance – NUMSERIES-by-NUMSERIES matrix of estimates for the covariance parameters from the iteration just prior to the terminal iteration.
ecmmvnrobj | mvnrmle
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Calculus Problem on Telescoping Series - Product: Who's gonna be the topper from our community! RA vs SA - Parth Lohomi | Brilliant
Who's gonna be the topper from our community! RA vs SA
A
B
A = \displaystyle\prod\limits_{n=2}^{\infty} \left(1-\frac{1}{n^3}\right), \quad B =\displaystyle\prod\limits_{n=1}^{\infty}\left(1+\frac{1}{n(n+1)}\right).
\frac{A}{B} = \frac{m}{k},
m
k
100m+k
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Hazen–Williams equation - Wikipedia
(Redirected from Hazen-Williams)
The Hazen–Williams equation is an empirical relationship which relates the flow of water in a pipe with the physical properties of the pipe and the pressure drop caused by friction. It is used in the design of water pipe systems[1] such as fire sprinkler systems,[2] water supply networks, and irrigation systems. It is named after Allen Hazen and Gardner Stewart Williams.
The Hazen–Williams equation has the advantage that the coefficient C is not a function of the Reynolds number, but it has the disadvantage that it is only valid for water. Also, it does not account for the temperature or viscosity of the water,[3] and therefore is only valid at room temperature and conventional velocities.[4]
2 Pipe equation
2.1 U.S. customary units (Imperial)
Henri Pitot discovered that the velocity of a fluid was proportional to the square root of its head in the early 18th century. It takes energy to push a fluid through a pipe, and Antoine de Chézy discovered that the hydraulic head loss was proportional to the velocity squared.[5] Consequently, the Chézy formula relates hydraulic slope S (head loss per unit length) to the fluid velocity V and hydraulic radius R:
{\displaystyle V=C{\sqrt {RS}}=C\,R^{0.5}\,S^{0.5}}
The variable C expresses the proportionality, but the value of C is not a constant. In 1838 and 1839, Gotthilf Hagen and Jean Léonard Marie Poiseuille independently determined a head loss equation for laminar flow, the Hagen–Poiseuille equation. Around 1845, Julius Weisbach and Henry Darcy developed the Darcy–Weisbach equation.[6]
The Darcy-Weisbach equation was difficult to use because the friction factor was difficult to estimate.[7] In 1906, Hazen and Williams provided an empirical formula that was easy to use. The general form of the equation relates the mean velocity of water in a pipe with the geometric properties of the pipe and slope of the energy line.
{\displaystyle V=k\,C\,R^{0.63}\,S^{0.54}}
V is velocity (in ft/s for US customary units, in m/s for SI units)
k is a conversion factor for the unit system (k = 1.318 for US customary units, k = 0.849 for SI units)
C is a roughness coefficient
R is the hydraulic radius (in ft for US customary units, in m for SI units)
S is the slope of the energy line (head loss per length of pipe or hf/L)
The equation is similar to the Chézy formula but the exponents have been adjusted to better fit data from typical engineering situations. A result of adjusting the exponents is that the value of C appears more like a constant over a wide range of the other parameters.[8]
The conversion factor k was chosen so that the values for C were the same as in the Chézy formula for the typical hydraulic slope of S=0.001.[9] The value of k is 0.001−0.04.[10]
Typical C factors used in design, which take into account some increase in roughness as pipe ages are as follows:[11]
C Factor low
C Factor high
Asbestos-cement 140 140 -
Cast iron new 130 130 [11]
Cast iron 10 years 107 113 [11]
Cast iron 20 years 89 100 [11]
Cement-Mortar Lined Ductile Iron Pipe 140 140 –
Concrete 100 140 [11]
Copper 130 140 [11]
Steel 90 110 –
Galvanized iron 120 120 [11]
Polyethylene 140 140 [11]
Polyvinyl chloride (PVC) 150 150 [11]
Fibre-reinforced plastic (FRP) 150 150 [11]
Pipe equationEdit
The general form can be specialized for full pipe flows. Taking the general form
{\displaystyle V=k\,C\,R^{0.63}\,S^{0.54}}
and exponentiating each side by 1/0.54 gives (rounding exponents to 3–4 decimals)
{\displaystyle V^{1.852}=k^{1.852}\,C^{1.852}\,R^{1.167}\,S}
{\displaystyle S={V^{1.852} \over k^{1.852}\,C^{1.852}\,R^{1.167}}}
The flow rate Q = V A, so
{\displaystyle S={V^{1.852}A^{1.852} \over k^{1.852}\,C^{1.852}\,R^{1.167}\,A^{1.852}}={Q^{1.852} \over k^{1.852}\,C^{1.852}\,R^{1.167}\,A^{1.852}}}
The hydraulic radius R (which is different from the geometric radius r) for a full pipe of geometric diameter d is d/4; the pipe's cross sectional area A is π d2 / 4, so
{\displaystyle S={4^{1.167}\,4^{1.852}\,Q^{1.852} \over \pi ^{1.852}\,k^{1.852}\,C^{1.852}\,d^{1.167}\,d^{3.7034}}={4^{3.019}\,Q^{1.852} \over \pi ^{1.852}\,k^{1.852}\,C^{1.852}\,d^{4.8704}}={4^{3.019} \over \pi ^{1.852}\,k^{1.852}}{Q^{1.852} \over C^{1.852}\,d^{4.8704}}={7.8828 \over k^{1.852}}{Q^{1.852} \over C^{1.852}\,d^{4.8704}}}
U.S. customary units (Imperial)Edit
When used to calculate the pressure drop using the US customary units system, the equation is:[12]
{\displaystyle S_{\mathrm {psi\ per\ foot} }={\frac {P_{d}}{L}}={\frac {4.52\ Q^{1.852}}{C^{1.852}\ d^{4.8704}}}}
Spsi per foot = frictional resistance (pressure drop per foot of pipe) in psig/ft (pounds per square inch gauge pressure per foot)
Pd = pressure drop over the length of pipe in psig (pounds per square inch gauge pressure)
Q = flow, gpm (gallons per minute)
C = pipe roughness coefficient
d = inside pipe diameter, in (inches)
Note: Caution with U S Customary Units is advised. The equation for head loss in pipes, also referred to as slope, S, expressed in "feet per foot of length" vs. in 'psi per foot of length' as described above, with the inside pipe diameter, d, being entered in feet vs. inches, and the flow rate, Q, being entered in cubic feet per second, cfs, vs. gallons per minute, gpm, appears very similar. However, the constant is 4.73 vs. the 4.52 constant as shown above in the formula as arranged by NFPA for sprinkler system design. The exponents and the Hazen-Williams "C" values are unchanged.
SI unitsEdit
When used to calculate the head loss with the International System of Units, the equation becomes:[13]
{\displaystyle S={\frac {h_{f}}{L}}={\frac {10.67\ Q^{1.852}}{C^{1.852}\ d^{4.8704}}}}
S = Hydraulic slope
hf = head loss in meters (water) over the length of pipe
L = length of pipe in meters
Q = volumetric flow rate, m3/s (cubic meters per second)
d = inside pipe diameter, m (meters)
Note: pressure drop can be computed from head loss as hf × the unit weight of water (e.g., 9810 N/m3 at 4 deg C)
Darcy–Weisbach equation and Prony equation for alternatives
^ "Hazen–Williams Formula". Archived from the original on 22 August 2008. Retrieved 6 December 2008.
^ "Hazen–Williams equation in fire protection systems". Canute LLP. 27 January 2009. Archived from the original on 6 April 2013. Retrieved 27 January 2009.
^ Brater, Ernest F.; King, Horace W.; Lindell, James E.; Wei, C. Y. (1996). "6". Handbook of Hydraulics (Seventh ed.). New York: McGraw Hill. p. 6.29. ISBN 0-07-007247-7.
^ Pumping station design. Jones, Garr M. (3rd ed.). Burlington, MA: Butterworth-Heinemann. 2006. p. 3.4. ISBN 978-0-08-094106-6. OCLC 144609617. {{cite book}}: CS1 maint: others (link)
^ Walski, Thomas M. (March 2006), "A history of water distribution", Journal of the American Water Works Association, American Water Works Association, 98 (3): 110–121, doi:10.1002/j.1551-8833.2006.tb07611.x , p. 112.
^ Walski 2006, p. 112
^ Williams & Hazen 1914, p. 1, stating "Exponents can be selected, however, representing approximate average conditions, so that the value of c for a given condition of surface will vary so little as to be practically constant."
^ Williams & Hazen 1914, p. 1
^ Williams & Hazen 1914, pp. 1–2
^ a b c d e f g h i j Hazen-Williams Coefficients, Engineering ToolBox, retrieved 7 October 2012
^ 2007 version of NFPA 13: Standard for the Installation of Sprinkler Systems, page 13-213, eqn 22.4.2.1
^ "Comparison of Pipe Flow Equations and Head Losses in Fittings" (PDF). Retrieved 6 December 2008.
Finnemore, E. John; Franzini, Joseph B. (2002), Fluid Mechanics (10th ed.), McGraw Hill
Mays, Larry W. (1999), Hydraulic Design Handbook, McGraw Hill
Watkins, James A. (1987), Turf Irrigation Manual (5th ed.), Telsco
Williams, Gardner Stewart; Hazen, Allen (1905), Hydraulic tables: showing the loss of head due to the friction of water flowing in pipes, aqueducts, sewers, etc. and the discharge over weirs (first ed.), New York: John Wiley and Sons
Williams and Hazen, Second edition, 1909
Williams, Gardner Stewart; Hazen, Allen (1914), Hydraulic tables: the elements of gagings and the friction of water flowing in pipes, aqueducts, sewers, etc., as determined by the Hazen and Williams formula and the flow of water over sharp-edged and irregular weirs, and the quantity discharged as determined by Bazin's formula and experimental investigations upon large models. (2nd revised and enlarged ed.), New York: John Wiley and Sons
Williams, Gardner Stewart; Hazen, Allen (1920), Hydraulic tables: the elements of gagings and the friction of water flowing in pipes, aqueducts, sewers, etc., as determined by the Hazen and Williams formula and the flow of water over sharp-edged and irregular weirs, and the quantity discharged as determined by Bazin's formula and experimental investigations upon large models. (3rd ed.), New York: John Wiley and Sons, OCLC 1981183
Engineering Toolbox reference
Engineering toolbox Hazen–Williams coefficients
Online Hazen–Williams calculator for gravity-fed pipes.
Online Hazen–Williams calculator for pressurized pipes.
https://books.google.com/books?id=DxoMAQAAIAAJ&pg=PA736&hl=en&sa=X&ved=0CEsQ6AEwAA#v=onepage&f=false
https://books.google.com/books?id=RAMX5xuXSrUC&pg=PA145&lpg=PA145&source=bl&ots=RucWGKXVYx&hl=en&sa=X&ved=0CDkQ6AEwAjgU States pocket calculators and computers make calculations easier. H-W is good for smooth pipes, but Manning better for rough pipes (compared to D-W model).
Retrieved from "https://en.wikipedia.org/w/index.php?title=Hazen–Williams_equation&oldid=1072629546"
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Compact multiclass model for support vector machines (SVMs) and other classifiers - MATLAB - MathWorks Switzerland
\begin{array}{cccc}& \text{Learner 1}& \text{Learner 2}& \text{Learner 3}\\ \text{Class 1}& 1& 1& 0\\ \text{Class 2}& -1& 0& 1\\ \text{Class 3}& 0& -1& -1\end{array}
\stackrel{^}{k}
\stackrel{^}{k}=\underset{k}{\text{argmin}}\frac{\sum _{l=1}^{B}|{m}_{kl}|g\left({m}_{kl},{s}_{l}\right)}{\sum _{l=1}^{B}|{m}_{kl}|}.
{L}_{d}\approx ⌈10{\mathrm{log}}_{2}K⌉
{L}_{s}\approx ⌈15{\mathrm{log}}_{2}K⌉
\Delta \left({k}_{1},{k}_{2}\right)=0.5\sum _{l=1}^{L}|{m}_{{k}_{1}l}||{m}_{{k}_{2}l}||{m}_{{k}_{1}l}-{m}_{{k}_{2}l}|,
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4IN6FN8492 Y
UN number 3288 2291 3077
InChI=1S/O.Pb
Key: YEXPOXQUZXUXJW-UHFFFAOYSA-N
O=[Pb]
Appearance red or yellow powder
Solubility insoluble in dilute alkalis, alcohol
soluble in HCl, ammonium chloride
4.20×10−5 cm3/mol
Tetragonal, tP4
P4/nmm, No. 129
H302, H332, H351, H360Df, H362, H373, H410
P201, P202, P260, P261, P263, P264, P270, P271, P273, P281, P301+P312, P304+P312, P304+P340, P308+P313, P312, P314, P330, P391, P405, P501
1400 mg/kg (dog, oral)[2]
Lead(II,II,IV) oxide
Lead(II) oxide, also called lead monoxide, is the inorganic compound with the molecular formula PbO. PbO occurs in two polymorphs: litharge having a tetragonal crystal structure, and massicot having an orthorhombic crystal structure. Modern applications for PbO are mostly in lead-based industrial glass and industrial ceramics, including computer components. It is an amphoteric oxide.[3]
4.1 Niche or declining uses
PbO may be prepared by heating lead metal in air at approximately 600 °C (1,100 °F). At this temperature it is also the end product of oxidation of other oxides of lead in air:[4]
{\displaystyle {\ce {PbO2->[{293 °C}] Pb12O19 ->[{351 °C}] Pb12O17 ->[{375 °C}] Pb3O4 ->[{605 °C}] PbO}}}
Thermal decomposition of lead(II) nitrate or lead(II) carbonate also results in the formation of PbO:
3 → PbO + CO2
PbO is produced on a large scale as an intermediate product in refining raw lead ores into metallic lead. The usual lead ore is galena (lead(II) sulfide). At a temperature of around 1,000 °C (1,800 °F) the sulfide is converted to the oxide:[5]
2 → 2 PbO + 2 SO2
Metallic lead is obtained by reducing PbO with carbon monoxide at around 1,200 °C (2,200 °F):[6]
As determined by X-ray crystallography, both polymorphs, tetragonal and orthorhombic feature a pyramidal four-coordinate lead center. In the tetragonal form the four lead–oxygen bonds have the same length, but in the orthorhombic two are shorter and two longer. The pyramidal nature indicates the presence of a stereochemically active lone pair of electrons.[7] When PbO occurs in tetragonal lattice structure it is called litharge; and when the PbO has orthorhombic lattice structure it is called massicot. The PbO can be changed from massicot to litharge or vice versa by controlled heating and cooling.[8] The tetragonal form is usually red or orange color, while the orthorhombic is usually yellow or orange, but the color is not a very reliable indicator of the structure.[9] The tetragonal and orthorhombic forms of PbO occur naturally as rare minerals.
Crystal structure of the litharge form of lead(II) oxide[4][10][11]
Lead coordination
Oxygen coordination
3×3×3 unit cells viewed along the a axis viewed along the c axis square pyramidal distorted tetrahedral
The red and yellow forms of this material are related by a small change in enthalpy:
PbO(red) → PbO(yellow) ΔH = 1.6 kJ/mol
PbO is amphoteric, which means that it reacts with both acids and with bases. With acids, it forms salts of Pb2+
via the intermediacy of oxo clusters such as [Pb
6O(OH)
. With strong bases, PbO dissolves to form plumbite (also called plumbate(II)) salts:[12]
PbO + H2O + OH−
→ [Pb(OH)
The kind of lead in lead glass is normally PbO, and PbO is used extensively in making glass. Depending on the glass, the benefit of using PbO in glass can be one or more of increasing the refractive index of the glass, decreasing the viscosity of the glass, increasing the electrical resistivity of the glass, and increasing the ability of the glass to absorb X-rays. Adding PbO to industrial ceramics (as well as glass) makes the materials more magnetically and electrically inert (by raising their Curie temperature) and it is often used for this purpose.[13] Historically PbO was also used extensively in ceramic glazes for household ceramics, and it is still used, but not extensively any more. Other less dominant applications include the vulcanization of rubber and the production of certain pigments and paints.[3] PbO is used in cathode ray tube glass to block X-ray emission, but mainly in the neck and funnel because it can cause discoloration when used in the faceplate. Strontium oxide and Barium oxide are preferred for the faceplate.[14]
The consumption of lead, and hence the processing of PbO, correlates with the number of automobiles, because it remains the key component of automotive lead–acid batteries.[15]
Niche or declining uses[edit]
A mixture of PbO with glycerine sets to a hard, waterproof cement that has been used to join the flat glass sides and bottoms of aquariums, and was also once used to seal glass panels in window frames. It is a component of lead paints.
PbO was used to speed up the process to turn more profit for less time and artificially increase the quality of century eggs, a type of Chinese preserved egg. It was an unscrupulous practice in some small factories but it became rampant in China and forced many honest manufacturers to label their boxes "lead-free" after the scandal went mainstream in 2013.
In powdered tetragonal litharge form, it can be mixed with linseed oil and then boiled to create a weather-resistant sizing used in gilding. The litharge would give the sizing a dark red color that made the gold leaf appear warm and lustrous, while the linseed oil would impart adhesion and a flat durable binding surface.
PbO is used in certain condensation reactions in organic synthesis.[16]
PbO is the input photoconductor in a video camera tube called the Plumbicon.
Lead oxide may be fatal if swallowed or inhaled. It causes irritation to skin, eyes, and respiratory tract. It affects gum tissue, the central nervous system, the kidneys, the blood, and the reproductive system. It can bioaccumulate in plants and in mammals.[17]
^ Blei(II)-oxid. Merck
^ a b Carr, Dodd S. (2005). "Lead Compounds". Ullmann's Encyclopedia of Industrial Chemistry. Weinheim: Wiley-VCH. doi:10.1002/14356007.a15_249.
^ Abdel-Rehim, A. M. (2006). "Thermal and XRD analysis of Egyptian galena". Journal of Thermal Analysis and Calorimetry. 86 (2): 393–401. doi:10.1007/s10973-005-6785-6. S2CID 96393940.
^ Lead Processing @ Universalium.academic.ru. Alt address: Lead processing @ Enwiki.net.
^ Wells, A. F. (1984), Structural Inorganic Chemistry (5th ed.), Oxford: Clarendon Press, ISBN 0-19-855370-6 [page needed]
^ A simple example is given in Anil Kumar De (2007). "§9.2.6 Lead (Pb): Lead Monoxide PbO". A Textbook Of Inorganic Chemistry. New Age International. p. 383. ISBN 978-81-224-1384-7. A more complex example is in Turova, N.Y. (2002). "§9.4 Germanium, tin, lead alkoxides". The Chemistry of Metal Alkoxides. Springer. p. 115. ISBN 978-0-7923-7521-0.
^ Rowe, David John (1983). Lead Manufacturing in Britain: A History. Croom Helm. p. 16. ISBN 978-0-7099-2250-6.
^ Pirovano, Caroline; Islam, M. Saiful; Vannier, Rose-Noëlle; Nowogrocki, Guy; Mairesse, Gaëtan (2001). "Modelling the crystal structures of Aurivillius phases". Solid State Ion. 140 (1–2): 115–123. doi:10.1016/S0167-2738(01)00699-3.
^ "ICSD Entry: 94333". Cambridge Structural Database: Access Structures. Cambridge Crystallographic Data Centre. Retrieved 2021-06-01.
^ Holleman, Arnold Frederik; Wiberg, Egon (2001), Wiberg, Nils (ed.), Inorganic Chemistry, translated by Eagleson, Mary; Brewer, William, San Diego/Berlin: Academic Press/De Gruyter, ISBN 0-12-352651-5 [page needed]
^ Chapter 9, "Lead Compounds", in the book Ceramic and Glass Materials: Structure, Properties and Processing, published by Springer, year 2008.
^ Compton, Kenneth (5 December 2003). Image Performance in CRT Displays. SPIE Press. ISBN 9780819441447 – via Google Books.
^ Sutherland, Charles A.; Milner, Edward F.; Kerby, Robert C.; Teindl, Herbert; Melin, Albert; Bolt, Hermann M. "Lead". Ullmann's Encyclopedia of Industrial Chemistry. Weinheim: Wiley-VCH. doi:10.1002/14356007.a15_193.pub2.
^ Corson, B. B. (1936). "1,4-Diphenylbutadiene". Organic Syntheses. 16: 28. ; Collective Volume, vol. 2, p. 229
^ "Lead(II) oxide". International Occupational Safety and Health Information Centre. Archived from the original on 2011-12-15. Retrieved 2009-06-06.
Webelements PbO
Pb(BiO3)2
Retrieved from "https://en.wikipedia.org/w/index.php?title=Lead(II)_oxide&oldid=1075231148"
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B(0)+\int_0^{364}B^\prime(t)dt=212
B
represents the number of “buddies” you have in your buddyzone.com account
is days since your
16
th birthday.
In the context of the problem, write a complete description about what the integral is computing. Use correct units and be sure to mention the meaning of the bounds in your description.
Recall that integrals can be considered accumulation functions.
\int _ { 0 } ^ { 364 } B ^ { \prime } ( t ) d t = 115
, how many buddies did you have on your
16
th birthday? Justify your answer.
B(0)
represents the number of buddies you have on your
16
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EUDML | On the Banach principle. EuDML | On the Banach principle.
On the Banach principle.
Zaharopol, Radu. "On the Banach principle.." Portugaliae Mathematica 54.2 (1997): 229-253. <http://eudml.org/doc/47862>.
@article{Zaharopol1997,
author = {Zaharopol, Radu},
keywords = {Banach principle; sequences of operators; Archimedean-Riesz space; almost everywhere convergence; individual convergence; absence of a measure; -order continuous dual of the Dedekind completion; -order continuous dual of the Dedekind completion},
title = {On the Banach principle.},
AU - Zaharopol, Radu
TI - On the Banach principle.
KW - Banach principle; sequences of operators; Archimedean-Riesz space; almost everywhere convergence; individual convergence; absence of a measure; -order continuous dual of the Dedekind completion; -order continuous dual of the Dedekind completion
Banach principle, sequences of operators, Archimedean-Riesz space, almost everywhere convergence, individual convergence, absence of a measure,
\sigma
-order continuous dual of the Dedekind completion,
\sigma
-order continuous dual of the Dedekind completion
Articles by Zaharopol
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EIGRP Metric - ccie.nyquist.eu
Metric_{EIGRP} =\begin{cases}[\frac{K_1B+K_2B}{256-L}+K3D)*{\frac{K_5}{R+K_4}}]*256 & K_5!=0\\ [\frac{K_1B+K_2B}{256-L}+K3D)]*256 & K_5=0\end{cases}
you will have to round down to the nearest integer
default K values: (K1,K2,K3,K4,K5) = (1,0,1,0,0)
default EIGRP metric: B+D
remember it as BuiLDeR 20
The EIGRP metric is 256 times larger than IGRP metric.
Bandwidth – B
inverse lowest bandwidth along the path in kbps, scaled by 10^7
Interfaces with bandwidth higher than 10Gbps (10^7 kbps) are considered similar from EIGRP’s metric standpoint (B=1).
B = \frac{10^7}{\min_{path}(Bandwidth[kbps])}
Load – L
Highest load along the path
Dynamically determined by the router. It has values starting from 1 (no usage) to 255(fully utilized)
L = \max_{path}(Load)
Delay – D
cumulative delay along the path in 10s of microseconds
EIGRP uses Delay to signal an unreachable route, by using the Delay value of 0xFFFFFF
D = \sum_{path}(Delay[10 \mu s]
Reliability – R
Lowest reliability along the path
Dynamically determined by the router as the percentage of successfully received packets on the interface scaled by 255. The maximum value of 255 means 100% reliability.
R=\min_{path} (Reliability)
MTU is used as a tiebreaker if the metric is the same for more paths
Largest MTU wins the tiebreak
MTU = \min_{path}(MTU_{interface})
Not used in the actual metric, but the value is passed from router to router
There is a default limit of 100 to the number of hops to a destination, but this can be changed up to 255.
Hop_{count}=\sum_{path}(Hops)
When route information for a destination is received, it also contains the metric parameters used by the advertising router: Bandwidth, Delay, Load, Reliability, MTU. The receiving router compares the received information with the data it has for the incoming interface so it can find the lowest Bandwidth along the path, the highest Load along the path, the sum of Delays along the path, the lowest Reliability along the path and the lowest MTU along the path. Then, it can apply the formula to find the metric value for each path. The router that advertised the best path is considered the Successor, and the metric for that path is known as „Feasible Distance” (FD)
For each destination, the router also applies the formula on the parameters it received from the advertising router to calculate the metric from that router towards the destination. This is known as the Advertised Distance (AD) or Reported Distance (RD).
Using the DUAL algortithm, EIGRP will consider all paths that have a RD<FD as loop free backup paths and will call the routers advertising them Feasable Successors(FS) for the route. The FS will be kept in the topology table and when the route through the successor fails, the router will imediately use the best FS. For all other routes, DUAL will not consider them as backup paths, because they can be part of a routing loop (even if they aren’t actually). The idea is that if RD>FD, then that router is closer to the destination then us and it should route through us. If we use it as our next hop then it could send it back to us resulting in a routing loop.
How to modify metric
Changing metric components
R(config-if)# bandwidth BANDWIDTH
! in kbps
R(config-if)# delay DELAY
! in 10s of usec
Load and Reliability cannot be changed manually. They are caculated by the router based on a 5 minute average. The values can be seen using:
R# show interface INTERFACE
R3#sh int fa0/0 | i MTU|load
Changing K values
R(config-router)# metric weights TOS K1 K2 K3 K4 K5
Default values for (K1,K2,K3,K4,K5) is (1,0,1,0,0) and only 0 is supported for TOS. K values must match between neighbors.
Using offset lists
Adds the OFFSET to the metric. It can be used to create multiple equal cost links.
Even though EIGRP doesn’t use hop count in it’s metric calculation, it still counts how many hops away is the router that first advertised this network. You can see the hop count value using:
IP-EIGRP (AS 10): Topology entry for 4.4.4.0/24
You can invalidate routes that are more than a number of hops away by running:
R(config-router)# metric maximum-hops HOPS
!Default: 100
All routes that have a hop-count greater than the maximum-hops, will not be added to the routing table.
Newer IOS implementations support wide metrics, which can differentiate between interfaces higher than 10Gbps. Wide metric uses the following formula: [pmath size=12]K5!WideMetric_EIGRP = [(K1B+K2B/{256-L}+K3D+K6E)*{K5/{R+K4}}]*65535[/pmath]
Metric_{EIGRP} =\begin{cases}[\frac{K_1T+K_2T}{256-L}+K3D+K_6E)*{\frac{K_5}{R+K_4}}]*256 & K_5!=0\\ [\frac{K_1T+K_2T}{256-L}+K3D+K_6E)]*256 & K_5=0\end{cases}
where T = Throughput and E = Extended Attributes. See here for details. Supporting Wide metric, requires changes in the EIGRP packets to add the additional information. For this reason, a router will send packets for both standard metric and wide metric, so additional bandwidth will be used. If it detects that all neighbors on an interface support wide metrics, then it will only send this version.
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Sandbox - Synth DIY Wiki
1 Anything on this page may be altered or deleted by other users
1.1 Numbered list
4 Citing references
5 Multiple references
Anything on this page may be altered or deleted by other users
An example of a classic analog synthesizer
sound – a sawtooth bass filter sweep with
gradually increasing resonance.
Use this page to play around and experiment with editing. Any content here won't be preserved. You can also create your own sandbox area by appending "/sandbox" to the URL for your user page, or click this link to go there. Your own sandbox is where to rough out articles until they're ready for posting.Sandboxes will be indexed by search engines like any other page, unless the first line is __NOINDEX__.
Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum. Curabitur pretium tincidunt lacus. Nulla gravida orci a odio. See Wikipedia:Web colors for a list of colors.
Breadboarding a Theremin, (from HeatSync Labs)
Some indented text. In a discussion thread don't forget to sign your post.
Some text another indentation in.
More text and a further indentation.
Use tags <math> for formulae, eg, (click edit to see the source):
{\displaystyle \operatorname{erfc}(x) = \frac{2}{\sqrt{\pi}} \int_x^{\infty} e^{-t^2}\,dt = \frac{e^{-x^2}}{x\sqrt{\pi}}\sum_{n=0}^\infty (-1)^n \frac{(2n)!}{n!(2x)^{2n}}}
Such references are particularly useful when citing sources, if different statements come from the same source.
A concise way to make multiple references is to use empty ref tags, which have a slash at the end. Although this may reduce redundant work, please be aware that if a future editor removes the first reference, this will result in the loss of all references using the empty ref tags.[3]This part of the text requires clarification,[note 1] whereas the entire text is cited.[4]
^ This note is listed separately from the references.
^ E. Miller, The Sun, (New York: Academic Press, 2005), 23-5.
^ Wikipedia:Virtual Studio Technology
^ a b Remember that when you refer to the same footnote multiple times, the text from the first reference is used.
^ Analog Days by by Trevor Pinch and Frank Trocco, 2004
Retrieved from "https://sdiy.info/w/index.php?title=Sandbox&oldid=8907"
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Solve system of nonlinear equations - MATLAB fsolve - MathWorks Switzerland
c
\begin{array}{c}2{x}_{1}+{x}_{2}=\mathrm{exp}\left(c{x}_{1}\right)\\ -{x}_{1}+2{x}_{2}=\mathrm{exp}\left(c{x}_{2}\right).\end{array}
c=-1
c
c
c
c
\begin{array}{c}2{x}_{1}-{x}_{2}={e}^{-{x}_{1}}\\ -{x}_{1}+2{x}_{2}={e}^{-{x}_{2}}.\end{array}
F\left(x\right) = 0
\begin{array}{c}2{x}_{1}-{x}_{2}-{e}^{-{x}_{1}}=0\\ -{x}_{1}+2{x}_{2}-{e}^{-{x}_{2}}=0.\end{array}
X
X*X*X=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]
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Home > Course Outline > Lesson 6 - Maximizing the Solar Utility for the Client in a Locale > 6.8 Electric Incentives in SAM
Try This! SAM Financing, Incentives and Utility Rate
We just talked about all these things that affect the cost of an energy system, and now let's take a look to see how the real data can fit into our simulation software for project design. Time to break out SAM again and do some exploration!
Click on "Photovoltaics (Detailed)" on the left of the pop-up window ("Choose a performance model").
Click on "Residential (Distributed)" on the right of the pop-up window ("then choose from the available financial models").
You will now have a default residential PV project, based in Phoenix, AZ, just like the last example we tried.
Next, we are going to explore three tabs: Financial Parameters, Incentives, and Electricity Rates.
Click on the shortcut tab called "Financial Parameters."
This opens a field of data entry for "Loan Type," "Residential Loan Parameters," "Analysis Parameters," "Tax and Insurance Rates," "Property Rates," and "Salvage Value."
The first few things to notice is that the Loan Term (and Analysis Period) is 25 years as a default. This is the standard period of covered life for a PV module. Much like your computers, the actual life will be longer than the warrantee, but 25 years is the most risk that the manufacturers will currently take on to guarantee their products. In general, all the SAM defaults are going to be conservative, and you can indeed adjust them for your own projects.
You want to enclose your period of loan or mortgage (
{n}_{L}
) within the full period of evaluation (
{n}_{e}
, years of analysis), so that
{n}_{e}\ge {n}_{L}
. The loan rates are assumed to be a bit high, but you could change it to a lower rate if appropriate.
Tax, insurance, and property rates can be left at the defaults unless you know better from practical experience. When working with a full team in industry, you will need to be working with an expert knowledgeable in these areas to accurately represent them for the client.
The salvage value will almost never be zero in a real project. Just think, a PV system at the end of 25 years may be operating at 60-80 percent of its original peak performance, but will not catastrophically fail that year. In fact, it will likely keep on truckin' for decades more. Even a 20-year-old operational truck has a resale value that is a significant percentage of the original value. So, change it to something greater than zero, but less than 100, and you can still be conservative.
Now, click on the tab for "Incentives." You can see at the top that there is a direct link for the DSIRE website [2].
There are five types of incentives listed, each with Federal and State entries. Some also have open fields to enter utility incentives or space for an alternative incentive from another source. They also have time horizons within which the credits or incentives are valid. Check the DSIRE site for the credits and incentives in your locale!
Investment Tax Credit [3](ITC): this is the standard federal tax credit of 30% for installed solar systems, for both residential and commercial properties.
Production Tax Credit [4] (PTC): this is very common for wind farms (and landfill gas, biomass, Hydroelectric, geothermal power, tidal energy...effectively everything but solar energy power). This is an incentive to produce through corporate tax credit. Again, the PTC has not been enacted Federally for solar, but is an open field if such credits become available.
Investment Based Incentive (IBI): an incentive to reduce annual expenditures of a project for Year One cash flow (see help menu in SAM).
Capacity Based Incentive (CBI): similar to an IBI, in that it is an incentive to reduce annual expenditures of a project for Year One cash flow. However, the CBI can be expressed as a function of the system's rated capacity in Watts (see help menu in SAM).This is a direct cash incentive.
Production Based Incentive [5] (PBI): This is another direct cash incentive, and a PBI reduces the project's annual tax liability from years one through the period of valid application (which you can specify). The PBI is a dollar amount per kilowatt-hour of annual electric output. You can use the PBI inputs for SRECs that are paid on a $/MWh basis. The PBI also can accept Performance Based Incentives [6] such as a Feed-In Tariff.
Now, click on the "Electricity Rates" tab. You will see whether or not "Net Metering" is occurring in your model. In most cases, this will be "Enabled" with a check box and a Year end sell rate (this is low, not the rate that you pay).
The top left box is a handy link to search for electricity rates in the USA from the OpenEI utility rate repository [7]. The Open Energy Information (OpenEI) [8] provides powerful centralized access to the latest data and energy information, and an opportunity to make new tools to interpret those data and dynamic information sets.
There is a middle hidden box (Blue plus sign) for "Description and Applicability" that is for your own record keeping, to assign the locale information for your client's site.
You can select "Net Metering" if the locale permits electricity from a SECS to enter the grid. The Solar Energy Industry Association has a good site describing net metering in the USA [9]. Obviously, this is important to a residential or commercial PV system, but has to be adapted for a solar thermal hot water scenario (all SAM inputs are in terms of electricity).
The electricity rates can either be "Flat" (same $/kWh charge in a month, regardless of time of day) or "Time of Use (Energy Charge)." The local electricity provider will be able to specify the selection.
On top of electricity rates, there are charges for services, bundled as "Fixed Monthly Charges."
Some utilities will specify "Peak Demand Charges" for high demand blocks of time (high LMP periods for the locale), and "Tiered Rates (Energy Charge)" for various scales of electric demand in kWh.
Finally, notice that little box in the upper right called "Annual Electricity Cost Escalation". The default is for SAM to assume that the price of electricity will not go up in the next 25 years. The rate is set to zero. I will pose that this is not really an appropriate guess given our future in energy demand. A conservative increase of 1-3% is probably a better estimate.
If you have any questions or comments, please post them to the Lesson 6 General Questions and Comments Discussion Forum. I will check the forum regularly to respond. While you are in a discussion, feel free to post your own responses if you, too, are able to help out a classmate.
[3] http://programs.dsireusa.org/system/program/detail/658
[5] http://en.openei.org/wiki/Performance-Based_Incentive
[6] http://programs.dsireusa.org/system/program/detail/5698
[7] http://en.openei.org/wiki/Gateway:Utilities
[8] http://en.openei.org/wiki/Main_Page
[9] https://www.seia.org/research-resources/net-metering-facts
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Electric Potential and Capacitance - Live Session - NEET 2020
Electric Potential and Capacitance - Live Session - NEET 2020Contact Number: 9667591930 / 8527521718
64 charged drops of capacity C and potential V are put together to form a bigger drop. If each small drop had a charge q, then the charge on bigger drop will be
(2) 4q
(3) 16q
A positively charged pendulum is oscillating in a uniform electric field as shown in figure. Its time period as compared to that when it was uncharged
(a) will increase (b) will decrease
(c) will not change (d) will first increase then decrease
A thin metal plate P is inserted between the plates of a parallel-plate capacitor of capacitance C in such a ways that its edges touch the two plates (see the figure). The capacitance now becomes
(a) C/2 (b) 2C
\infty
Two charged metal spheres of capacitances C1 and C2 are brought in contact and then separated. The final charges Q1 and Q2 on them will satisfy the condition
(1) Q1C1 = Q2C2
(2) Q1C2 > Q2C1
(3) Q1C2 < Q2C1
The charge on a drop of water is 3
\times
10–8 C. If its surface potential is 500 V, its radius must be equal to
A and B are two thin concentric hollow conductors having radii a and b and charges Q1 and Q2 respectively. Given that a > b and P is a point between the two spheres and distance of P from the common centre is r (b < r < a). The potential at P is proportional to
\frac{{\mathrm{Q}}_{1}+{\mathrm{Q}}_{2}}{\mathrm{r}}
\frac{{\mathrm{Q}}_{1}}{\mathrm{a}}+\frac{{\mathrm{Q}}_{2}}{\mathrm{r}}
\frac{{\mathrm{Q}}_{1}}{\mathrm{a}}+\frac{{\mathrm{Q}}_{2}}{b }
\frac{{\mathrm{Q}}_{1}}{b }+\frac{{\mathrm{Q}}_{2}}{a}
How should 5 capacitors each of value 1
\mathrm{\mu }
F be connected so as to produce a total capacitance
\frac{3}{7}\mathrm{\mu }
(1) Two capacitors in parallel and the combination in series with other three capacitors
(2) Three capacitors in parallel and the combination in series with other two capacitors
(3) Four capacitors in parallel and combination in series with fifth capacitor
(4) All capacitors in parallel
\frac{\mathrm{C}}{2}
Four plates of area A are arranged as shown. The equivalent capacitance between A and B is
\frac{2{\mathrm{A\epsilon }}_{0}}{3\mathrm{d}}
\frac{3{\mathrm{A\epsilon }}_{0}}{2\mathrm{d}}
\frac{4{\mathrm{A\epsilon }}_{0}}{3\mathrm{d}}
One plate of a capacitor having charge Q, and plate area A, is pulled by a man keeping one plate at fix position, as shown in the figure. What force should be applied by the man such that, the plate moves with constant velocity?
\frac{{\mathrm{Q}}^{2}}{{\mathrm{A\epsilon }}_{0}}
\frac{2}{3}\frac{{\mathrm{Q}}^{2}}{{\mathrm{A\epsilon }}_{0}}
\frac{{\mathrm{Q}}^{2}}{2{\mathrm{A\epsilon }}_{0}}
In the circuit shown, a potential difference of 60 V is applied across AB. The potential difference between the points M and N is
Two thin different dielectrics are inserted between a parallel plate capacitor. Then electric field verses separation graph is (k1 < k2)
An electron having a charge – e located at A in the presence of a point charge +Q located at B is moved to a point C so that ABC is an equilateral triangle. The work done in this process is
\frac{1}{4{\mathrm{\pi \epsilon }}_{0}}\frac{\mathrm{Q}}{\mathrm{AC}}
\frac{1}{4{\mathrm{\pi \epsilon }}_{0}}\frac{\mathrm{Qe}}{\mathrm{AC}}
\frac{1}{4{\mathrm{\pi \epsilon }}_{0}}\frac{-\mathrm{Qe}}{\mathrm{AB}}
An infinite number of charges each equal to q are placed along the x-axis at x = 1, x =2,
x = 4, x = 8 and so on. The resultant potential at x = 0 will be
\frac{\mathrm{q}}{2{\mathrm{\pi \epsilon }}_{0}}
\frac{\mathrm{q}}{4{\mathrm{\pi \epsilon }}_{0}}
\frac{\mathrm{q}}{8{\mathrm{\pi \epsilon }}_{0}}
\frac{\mathrm{q}}{{\mathrm{\epsilon }}_{0}}
A solid conducting sphere of charge Q is surrounded by an uncharged concentric conducting spherical shell. The potential difference between the sphere and the shell is V. If the shell is now given a charge of –3Q, the new potential difference between them will be
(a) V (b) 2 V
(c) 4 V (d) –2 V
In a parallel plate capacitor, the plate separation of 10 mm is very small compared with the size of the plates. A potential difference of 5.0 kV is maintained across the plates. The electric field intensity between the plates is
(1) 500 V/m
×
105 V/m
×
×
Three uncharged capacitors of capacities C1 , C2 , C3 are connected as shown in figure to one another and to points A, B and C at potentials V1 , V2 and V3 . Then the potential at O will be
\frac{{\mathrm{V}}_{1}{\mathrm{C}}_{1}+{\mathrm{V}}_{2}{\mathrm{C}}_{2}+{\mathrm{V}}_{3}{\mathrm{C}}_{3}}{{\mathrm{C}}_{1}+{\mathrm{C}}_{2}+{\mathrm{C}}_{3}}
\frac{{\mathrm{V}}_{1}+{\mathrm{V}}_{2}+{\mathrm{V}}_{3}}{{\mathrm{C}}_{1}+{\mathrm{C}}_{2}+{\mathrm{C}}_{3}}
\frac{{\mathrm{V}}_{1}\left({\mathrm{V}}_{2}+{\mathrm{V}}_{3}\right)}{{\mathrm{C}}_{1}\left({\mathrm{C}}_{2}+{\mathrm{C}}_{3}\right)}
\frac{{\mathrm{V}}_{1}{\mathrm{V}}_{2}{\mathrm{V}}_{3}}{{\mathrm{C}}_{1}{\mathrm{C}}_{2}{\mathrm{C}}_{3}}
Two capacitors A (2
\mathrm{\mu }
F) and B(5
\mathrm{\mu }
F) are connected to two batteries as shown in the figure. Then the potential difference in volts between the plates of A is
The effective capacitance between A and B is ( each capacitor is of 1
\mathrm{\mu }
\frac{15}{2}\mathrm{\mu F}
\frac{17}{3}\mathrm{\mu F}
\frac{13}{8}\mathrm{\mu F}
\frac{19}{8}\mathrm{\mu F}
Two identical thin rings, each of radius R metres are coaxially placed at a distance R metres apart. If Q1 and Q2 charges are spread uniformly on the two rings, the work done in moving a charge q from the centre of one ring to that of the other is
\mathrm{q}\left({\mathrm{Q}}_{1}-{\mathrm{Q}}_{2}\right)\left(\sqrt{2}-1\right)/\sqrt{2}\left(4{\mathrm{\pi \epsilon }}_{0}\mathrm{R}\right)
\mathrm{q}\sqrt{2}\left({\mathrm{Q}}_{1}+{\mathrm{Q}}_{2}\right)/\left(4{\mathrm{\pi \epsilon }}_{0}\mathrm{R}\right)
\mathrm{q}\left({\mathrm{Q}}_{1}+{\mathrm{Q}}_{2}\right)\left(\sqrt{2}+1\right)/\sqrt{2}\left(4{\mathrm{\pi \epsilon }}_{0}\mathrm{R}\right)
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User talk:The Wicked Twisted Road - Wikinews, the free news source
User talk:The Wicked Twisted Road
(Redirected from User talk:C628)
For previous messages, see User talk:C628/archive
1 election certificate
4 Handy template and gadget
5 Request to review
6 Power line to Japanese nuclear plant completed
9 Category:Goodluck Jonathan
10 Re Bob Dylan plays first concert in Vietnam
11 "Last night" on the main page
12 Schoolboy dies in Israel after bus hit by rocket from Gaza
13 "quiet" train car
14 How did you find "Related news"?
17 21 people killed and 113 reported injured in three blasts in Mumbai
18 Reviewer revocation
19 FR/RFP
20 FR/RFP Reconfirmation Failed
election certificateEdit
{\displaystyle {\color {Blue}{\mathfrak {Wikinews}}}:{\color {Sepia}The\;Free\;News\;Source}}
The election committee for the 2010 Arbitration Committee election certifies that this user was elected to be an Arbitrator until July 31, 2011.
Benny the mascot (talk) 19:07, 2 August 2010 (UTC)
FarewellEdit
Hey C628! I'm sorry to see that you've become dissatisfied with Wikinews. I do hope things work out for you in the near future; our door is always open. :) Benny the mascot (talk) 19:07, 2 August 2010 (UTC)
Sigh... Yet another great user leaves. I'll take this to mean that you no longer plan to serve as an Arb. —fetch·comms 20:26, 2 August 2010 (UTC)
Sorry to see you go, I can't say I blame you :( the wub "?!" 20:34, 2 August 2010 (UTC)
*sigh* Sad to see you leave. :( —Mikemoral♪♫ 20:54, 2 August 2010 (UTC)
How's it going? —fetch·comms 22:11, 12 March 2011 (UTC)
Oh, not too bad. How about you? C628 (talk) 22:19, 12 March 2011 (UTC)
Welcome back! I saw you created an article. Nice to see this project getting a bit of a revival. Tempodivalse [talk] 16:53, 13 March 2011 (UTC)
Thanks. I have to say, it's nice to be back. C628 (talk) 17:04, 13 March 2011 (UTC)
Welcome back. I'll make sure I'm not mean to you this time. Sorry about before:(. Gopher65talk 05:15, 25 March 2011 (UTC)
Handy template and gadgetEdit
Hey there. (Sorry I didn't welcome you back sooner.)
Thought I'd put in a good word for a handy template we've only had for a little over a month. It's got the same name as a notoriously pointless legacy template from the ancient past of wiki software: {{w}}. It uses one or two parameters like a [[w:...]] but
it checks for a local target first, and only goes to Wikipedia if no local target is found; and
if it does link to Wikipedia, it acts like w:Template:Sec link auto in that from the secure server it links to the secure server. (I haven't wired it to do anchors, though; they don't seem to fit into the intended purpose of {{w}}.)
There's also a neat gadget Microchip08 whipped up so that when you look at a page, if there's a {{w}} link on it that links locally, the link is underlined in green. --Pi zero (talk) 23:26, 13 March 2011 (UTC)
Request to reviewEdit
Could you please review my article, entitled Japan earthquake shifts Earth's axis 10 centimetres? There isn't much time left before this article goes stale. --Rayboy8 (my talk) (my contributions) 21:28, 14 March 2011 (UTC)
I'll see what I can do with Google translate. C628 (talk) 21:40, 14 March 2011 (UTC)
Power line to Japanese nuclear plant completedEdit
The final quotes in the article are not as long as shown in the sources. The one prior to the last one isn't even a quote. Do you have another source to say they did say that. Also I think you should reword to be similar to the actual quote in the source. --[[::User:Nascar1996|Nascar1996]] ([[::User talk:Nascar1996|talk]] • [[::Special:Contributions/Nascar1996|contribs]]) 01:19, 18 March 2011 (UTC)
I intended for the quotes to be only partial compared to the sources, since I think it's generally better for the article to not be entirely dependent on quotes for its content. On the other hand, the BBC seems to have modified its article since I looked at it, and it's taken out some of the quotes I lifted from it. I've added some more sources to cover that. C628 (talk) 01:30, 18 March 2011 (UTC)
I seen that. After a final review over the article to check for any mistakes it will be published since everythings sourced. I seen your edits in the recent changes. --[[::User:Nascar1996|Nascar1996]] ([[::User talk:Nascar1996|talk]] • [[::Special:Contributions/Nascar1996|contribs]]) 01:35, 18 March 2011 (UTC)
Re [1] Not wanting to argue but "democracy" is mentioned in the source.
Jeffrey Fleishman and Amro Hassan. "Egyptians overwhelmingly approve constitutional changes" — Los Angeles Times, March 20, 2911
"The referendum, which calls for judicial oversight of elections and limited presidential terms, was the first step to bring Egypt closer to a democracy after decades of corrupt one-party rule."
The date has changed on the article, but it is the same one I used. Regards, Mattisse (talk) 22:25, 21 March 2011 (UTC)
Oh, blast, I never even saw the text on that article, only the video. That appears to also be where a bit I removed because I couldn't find it in the sources came from...sorry about that. Feel free to re-add that. C628 (talk) 22:30, 21 March 2011 (UTC)
Actually, it may be just as well. Just abstract words when a list of the main changes is clearer. The less words the better! Thanks, Mattisse (talk) 22:35, 21 March 2011 (UTC)
Hi! I'd appreciate your comments on this thread for reviving the project. I really want to get recent proposals implemented and get Wikinews going on the path to success. The more people help brainstorm and discuss constructively, the better. Tempodivalse [talk] 19:18, 29 March 2011 (UTC)
Category:Goodluck JonathanEdit
...is now fully populated. :-) --Pi zero (talk) 22:29, 9 April 2011 (UTC)
Thank you very much. C628 (talk) 22:32, 9 April 2011 (UTC)
Re Bob Dylan plays first concert in VietnamEdit
What you removed (as far as I can tell) is sourced by [2]. There are no videos in the sources, or if there are, they are not necessary to source the article. Also, the quotebox is in the article and is sourced by [3] I hope you don't mind that I restored the quotebox, although the other sourced material you removed I will just leave out. Thanks, Mattisse (talk) 21:11, 13 April 2011 (UTC)
Oh, yeah, the quotebox is fine. I'd removed the Examiner-sourced stuff because I don't consider the Examiner to be a reliable source, since it's written by random people (kinda like Wikinews), but as far as I can tell it's not reviewed or edited by anyone. C628 (talk) 21:21, 13 April 2011 (UTC)
Oh, OK. I wasn't familiar with the source, and assumed it was as reliable as any for such things. It wasn't really obviously unreliable, like the National Enquirer, and I took it at face value. Normally, I would have been more thorough, but I really ought to go deal with this personal stuff. (Damn Internet's so appealing). DENDODGE 21:28, 13 April 2011 (UTC)
Greg Kohs writes for the Examiner. And they let me in, too (although I declined to join because I only applied to see if I could get in). It's like a Wikinews that reviews users' "experience" before giving them an account. —fetch·comms 03:45, 14 April 2011 (UTC)
"Last night" on the main pageEdit
Re this, just a reminder that WN:ML says "Please remember to not use time-sensitive phrasing in Main Page leads, such as "yesterday" or "today" – the leads are sometimes around for several days after publication, and the phrasing becomes out of date quickly." And, yes, this is virtually the only thing I bother doing on Wikinews these days... Regards, Bencherlite (talk) 15:53, 14 April 2011 (UTC)
Noted, thanks for letting me know. C628 (talk) 02:00, 19 April 2011 (UTC)
Schoolboy dies in Israel after bus hit by rocket from GazaEdit
Hi. Just a note, a couple of slips that got past review on this one (diff). --Pi zero (talk) 14:14, 19 April 2011 (UTC)
"quiet" train carEdit
Yes, this is a name - File:Quiet.car.jpg. I restored the phrase "quiet car" at the article over here if you don't mind - if you find it vague, feel free to rephrase, but I think it's important for this news. --Gryllida (talk) 11:39, 24 May 2011 (UTC)
I do mind, it's factually inaccurate. Amtrak only operates designated quiet cars on some of its corridor routes; the train this happened on is a long-distance route that doesn't have a quiet car. I don't know why the rest of the media insists on calling it one, but that's dead wrong. If you look at Amtrak's website, its page on Northeast Regional corridor service, it explicitly notes that there's a designated quiet car. If you look at the page for the Coast Starlight, that's not present. The way the article is now is wrong. C628 (talk) 12:02, 24 May 2011 (UTC)
How did you find "Related news"?Edit
I looked and looked for Related news for Brazil spots unknown tribe of indigenous people in Amazon jungle. What was your technique in finding those? Thanks, Mattisse (talk) 23:20, 22 June 2011 (UTC)
I didn't add those, user:William S. Saturn did in this edit; you'd want to ask him. I only formatted them better. Cheers, C628 (talk) 23:26, 22 June 2011 (UTC)
Thanks for passing my article on the Philippine foreign secretary's visit to China. I appreciate the diligence you showed in reviewing such a lengthy article with many sources. Ragettho (talk) 00:08, 4 July 2011 (UTC)
Can you please review British Gas to increase electricity, gas prices? I'd be grateful if you could. --Rayboy8 (my talk) (my contributions) 22:20, 10 July 2011 (UTC)
Done. :) C628 (talk) 23:37, 10 July 2011 (UTC)
21 people killed and 113 reported injured in three blasts in MumbaiEdit
Weren't you rather heavily involved in this article, to submit a review of it? Admittedly, some kinds of changes create a diff that makes the change look bigger than it is...
(Btw, I'd really like to believe I'd have thought to insist on a rename before publication, to not have specific numbers built into it that are sure to change; it's a recipe for a mess going forward.) --Pi zero (talk) 20:07, 13 July 2011 (UTC)
I was involved, yeah, but I though the importance of publishing the thing outweighed the importance of following policy to the letter. It's the biggest news story of the day, it's a little pathetic for us not to have something on it published, and I was comfortable enough that I didn't make a huge error that I was willing to publish it. The title, yes, I can see there'd be a problem with that. C628 (talk) 20:26, 13 July 2011 (UTC)
If a story is especially important, failing to maintain our standards on it is especially damaging to our reputation — says we can't even maintain our standards when it really matters. One doesn't even get far enough for that to kick in, though, because the very fact a reviewer is involved disqualifies them from judging how important it is (COI).
Note that the detailed text of WN:IAR explicitly identifies independent review as the prime example of a policy not subject to being ignored. --Pi zero (talk) 22:49, 13 July 2011 (UTC)
Further to the above conversation and our exchange on IRC, please be advised (with apologies for forgetting to notify you on here) that a thread at the admin alerts board has been opened concerning the above issue. You are welcome to comment there. BarkingFish (talk) 21:39, 13 July 2011 (UTC)
Reviewer revocationEdit
Further to the above discussions, and notes on the Admin alerts board, your reviewer rights on this site have been temporarily withdrawn for a period of 2 weeks from today, 15th July 2011. You are welcome to reapply for these rights from 29th July onwards. BarkingFish (talk) 00:48, 15 July 2011 (UTC)
Worse things have happened. C628 (talk) 13:41, 16 July 2011 (UTC)
Maybe so, but hopefully we won't have to do this again. BarkingFish (talk) 13:43, 16 July 2011 (UTC)
FR/RFPEdit
I've asked a question of you at your RFP. --Pi zero (talk) 11:22, 8 August 2011 (UTC)
FR/RFP Reconfirmation FailedEdit
Hello C628. After 18 days, I've closed your Reconfirmation request at the FR/RFP, and I'm sorry to say that your rights have not been reconfirmed at this time. The final tally in your RFP was 2 support, 2 oppose, 3 neutral. As a result of this, your right to use the reviewer bit has been withdrawn indefinitely, pending a full, new application for the bit at some point in the future. You may read a summary of my closing comments at this link. If you feel this is not an accurate assessment of the matter, you are welcome to refer this issue to the Admin Alerts Area or to another administrator for review. BarkingFish (talk) 20:46, 25 August 2011 (UTC)
And my fall from grace is complete...ah, well, so be it. C628 (talk) 21:23, 25 August 2011 (UTC)
Retrieved from "https://en.wikinews.org/w/index.php?title=User_talk:The_Wicked_Twisted_Road&oldid=4288848"
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Vapor Chamber Acting as a Heat Spreader for Power Module Cooling | J. Thermal Sci. Eng. Appl. | ASME Digital Collection
Y. P. Zhang,
, Xi'an, Shaanxi 710049, China; School of Energy,
X. L. Yu,
X. L. Yu
Q. K. Feng,
Q. K. Feng
Zhang, Y. P., Yu, X. L., Feng, Q. K., and Zhang, L. H. (November 4, 2009). "Vapor Chamber Acting as a Heat Spreader for Power Module Cooling." ASME. J. Thermal Sci. Eng. Appl. June 2009; 1(2): 021003. https://doi.org/10.1115/1.4000285
This paper presents an integrated power electronics module with a vapor chamber (VC) acting as a heat spreader to transfer the heat from the insulated gate bipolar transistor (IGBT) module to the base of the heat-sink. The novel VC integrated in a power module instead of a metal substrate is proposed. Compared with a conventional metal heat spreader, the VC significantly diffuses the concentrated heat source to a larger condensing area. The experimental results indicate that the VC based heat-sink will maintain the IGBT junction temperature
20°C
cooler than a non-VC based heat-sink with high power density. The junction-to-case thermal resistance of the power module based on the VC is about 50% less than that of the power module based on a copper substrate with the same weight. The chip overshooting temperature of the copper substrate module with the same weight goes beyond
10°C
against the junction temperature of the VC module at a given impulse power of 225 W. Consequently, thanks to a longer time duration to reach the same temperature, a power surge for the chip can be avoided and the ability to resist thermal impact during the VC module startup can be improved as well. The investigation shows that the VC power module is an excellent candidate for the original metal substrate, especially for an integrated power module with high power density.
cooling, heat sinks, insulated gate bipolar transistors, integrated circuit packaging, thermal resistance, VC, heat dissipation, thermal characteristic, power module, electronics cooling
Cooling, Copper, Flat heat pipes, Heat, Heat sinks, Junctions, Temperature, Thermal resistance, Vapors, Heat flux, Weight (Mass), Metals, Heat transfer, Gates (Closures), Transistors
Microchannel Heat Sinks for Electronics Cooling A Review
18th National and 7th ISHMT ASME Heat and Mass Transfer Conference
, Guwahati, India, Jan. 4–6, pp.
Power Electronics Technology at the Dawn of a New Century-Past Achievements and Future Expectations
Proceedings of the Third International Power Electronics and Motion Control Conference (PEMC 2000)
, Aug. 15–18, Vol.
G. -Q.
IEEE Circuits Syst. Mag.
Spreading in the Heat Sink Base: Phase Change Systems or Solid Metals
Measurement of Vapor Chamber Performance
IEEE Semiconductor Thermal Measurement and Management Symposium
Heat Pipe Integrated in Direct Bonded Copper Technology for Cooling of Power Electronics Packaging
Thermal Response of a Flat Heat Pipe Sandwich Structure to a Localized Heat Flux
An Experimental Investigation on a Novel High-Performance Integrated Heat Pipe-Heat Sink for High-Flux Chip Cooling
Transient Characteristics of Flat-Plate Heat Pipe During Startup and Shutdown Operations
Thermal Management of Sintered Copper Heat Pipe Integrated in Stacked 3D Electronic Package
36th IEEE Power Electronics Specialists Conference (PESC '05)
, Recife, Brazil, pp.
Vapor and Liquid Flow in an Asymmetrical Flat Plate Heat Pipe: A Three-Dimensional Analytical and Numerical Investigation
Investigation of Transient Behaviors of Flat Plate Heat Pipes
An Experimental Investigation of the Transient Characteristics on a Flat-Plate Heat Pipe During Startup and Shutdown Operations
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Posterior contraction and credible regions for level sets
2021 Posterior contraction and credible regions for level sets
Wei Li, Subhashis Ghosal
Wei Li,1 Subhashis Ghosal2
1Department of Mathematics, Syracuse University, Syracuse, NY 13244-1150, U.S.A.
2Department of Statistics, North Carolina State University, Raleigh, NC 27695-8203, U.S.A.
For a given function f on a multivariate domain, the level sets, given by
\left\{x:f\left(x\right)=c\right\}
for different values of c, provide important geometrical insights about the underlying function of interest. The distance on level sets of two functions may be measured by the Hausdorff metric or a metric based on the Lebesgue measure of a discrepancy, both of which can be linked with the
{L}^{\mathrm{\infty }}
-distance on the underlying functions. In a Bayesian framework, we derive posterior contraction rates and optimal sized credible sets with assured frequentist coverage for level sets in some nonparametric settings by extending some univariate
{L}^{\mathrm{\infty }}
-posterior contraction rates to the corresponding multivariate settings. For the multivariate Gaussian white noise model, adaptive Hausdorff and Lebesgue contraction rates for levels sets of the signal function and its mixed order partial derivatives are derived using a wavelet series prior on the function. Assuming a known smoothness level of the signal function, an optimal sized credible region for a level set with assured frequentist coverage is derived based on a multidimensional trigonometric series prior. For the nonparametric regression problem, adaptive rates for level sets of the function and its mixed partial derivatives are obtained using a multidimensional wavelet series prior. When the smoothness level is given, optimal sized credible regions with assured frequentist coverage are obtained using a finite random series prior based on tensor products of B-splines. We also derive Hausdorff and Lebesgue contraction rates of a multivariate density function under a known smoothness setting.
Wei Li. Subhashis Ghosal. "Posterior contraction and credible regions for level sets." Electron. J. Statist. 15 (1) 2647 - 2689, 2021. https://doi.org/10.1214/21-EJS1846
Keywords: coverage , credible region , Level sets , posterior contraction
Wei Li, Subhashis Ghosal "Posterior contraction and credible regions for level sets," Electronic Journal of Statistics, Electron. J. Statist. 15(1), 2647-2689, (2021)
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Ideal insulated-gate bipolar transistor for switching applications - MATLAB - MathWorks Deutschland
IGBT (Ideal, Switching)
Integral Protection Diode Option
On-state voltage, Vds(Tj,Ice)
Collector-emitter current vector, Ice
Collector-emitter current vector for switching losses, Ice
Switch-on loss, Eon(Tj,Ice)
Switch-off loss, Eoff(Tj,Ice)
Ideal insulated-gate bipolar transistor for switching applications
The IGBT (Ideal, Switching) block models an ideal insulated-gate bipolar transistor (IGBT) for switching applications. The switching characteristic of an IGBT is such that if the gate-emitter voltage exceeds the specified threshold voltage, Vth, the IGBT is in the on state. Otherwise, the device is in the off state. This figure shows a typical i-v characteristic:
To define the I-V characteristic of the IGBT, set the On-state behaviour and switching losses parameter to either Specify constant values or Tabulate with temperature and current. The Tabulate with temperature and current option is available only if you expose the thermal port of the block.
In the on state, the collector-emitter path behaves like a linear diode with forward-voltage drop, Vf, and on-resistance, Ron. However, if you expose the thermal port of the block and parameterize the device using tabulated I-V data, the tabulated resistance is a function of the temperature and current.
In the off state, the collector-emitter path behaves like a linear resistor with a low off-state conductance value, Goff.
if (v>Vf)&&(G>Vth)
v is the collector-emitter voltage.
G is the gate-emitter voltage.
i is the collector-emitter current.
Using the Integral Diode parameters, you can include an integral emitter-collector diode. An integral diode protects the semiconductor device by providing a conduction path for reverse current. An inductive load can produce a high reverse-voltage spike when the semiconductor device suddenly switches off the voltage supply to the load.
Switching losses are one of the main sources of thermal loss in semiconductors. During each on-off switching transition, the IGBT parasitics store and then dissipate energy.
Switching losses depend on the off-state voltage and the on-state current. When a switching device is turned on, the power losses depend on the initial off-state voltage across the device and the final on-state current once the device is fully in its on state. Similarly, when a switching device is turned off, the power losses depend on the initial on-state current through the device and the final off-state voltage once the device is fully in its off state.
In this block, switching losses are applied by stepping up the junction temperature with a value equal to the switching loss divided by the total thermal mass at the junction. The Switch-on loss, Eon(Tj,Ice) and Switch-on loss, Eoff(Tj,Ice) parameter values set the sizes of the switching losses and they are either fixed or dependent on junction temperature and drain-source current. In both cases, losses are scaled by the off-state voltage prior to the latest device turn-on event.
Port associated with the gate terminal. You can set the port to either a physical signal or electrical port
Electrical conserving port associated with the collector terminal
Electrical conserving port associated with the emitter terminal
Forward voltage, Vf Threshold voltage, Vth
On-state resistance On-state behaviour and switching losses
Off-state conductance Forward voltage, Vf On-state voltage, Vds(Tj,Ice)
Threshold voltage, Vth On-state resistance Temperature vector, Tj
Off-state conductance Collector-emitter current vector, Ice
On-state resistance — On-state collector-emitter resistance
Off-state conductance — Off-state collector-emitter conductance
On-state voltage, Vds(Tj,Ice) — On-state voltage
Collector-emitter current vector, Ice — Collector-emitter current vector
Collector-emitter currents for the on-state voltage is defined. The first element must be zero. Specify this parameter using a vector quantity.
Collector-emitter current vector for switching losses, Ice — Collector-emitter current vector for switching losses
Collector-emitter currents for which the switch-on loss and switch-off-loss are defined. The first element must be zero. Specify this parameter using a vector quantity.
Switch-on loss, Eon(Tj,Ice) — Switch-on loss
Switch-off loss, Eoff(Tj,Ice) — Switch-off loss
Block integral protection diode.
-\frac{{i}^{2}{}_{RM}}{2a},
From R2021a forward, the Energy dissipation time constant parameter of the IGBT (Ideal, Switching) block is no longer used. A step in junction temperature now reflects the switching losses. If your model contains a thermal mass directly connected to this block thermal port, remove it and model the thermal mass inside the component itself.
From R2020b forward, the IGBT (Ideal, Switching) block has improved losses and thermal modelling options.
If you selected Voltage, current, and temperature for Thermal loss dependent on, then the thermal on-state losses are unchanged and the On-state voltage, Vds(Tj,Ice) parameter sets their values. However, the electrical on-state losses are now equal to the thermal on-state losses. Prior to R2020b, the electrical on-state losses were defined by the value of the on-state resistance.
Diode | GTO | Ideal Semiconductor Switch | MOSFET (Ideal, Switching) | Thyristor (Piecewise Linear)
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HankelMatrix - Maple Help
Home : Support : Online Help : Mathematics : Linear Algebra : LinearAlgebra Package : Constructors : HankelMatrix
construct a Hankel Matrix
HankelMatrix(L, r, cpt, options)
Vector or list of values
The HankelMatrix(L) function returns a Hankel Matrix.
If H := HankelMatrix(L), then H is a symmetric r x r Matrix with H[i, j] = L[i+j-1]. It is an error if L has an even number of elements. By default, H is built with the symmetric shape.
This function is part of the LinearAlgebra package, and so it can be used in the form HankelMatrix(..) only after executing the command with(LinearAlgebra). However, it can always be accessed through the long form of the command by using LinearAlgebra[HankelMatrix](..).
\mathrm{with}\left(\mathrm{LinearAlgebra}\right):
\mathrm{H1}≔\mathrm{HankelMatrix}\left([\frac{1}{11},\frac{3}{11},\frac{5}{11}],\mathrm{compact}\right)
\textcolor[rgb]{0,0,1}{\mathrm{H1}}\textcolor[rgb]{0,0,1}{≔}[\begin{array}{cc}\frac{\textcolor[rgb]{0,0,1}{1}}{\textcolor[rgb]{0,0,1}{11}}& \frac{\textcolor[rgb]{0,0,1}{3}}{\textcolor[rgb]{0,0,1}{11}}\\ \frac{\textcolor[rgb]{0,0,1}{3}}{\textcolor[rgb]{0,0,1}{11}}& \frac{\textcolor[rgb]{0,0,1}{5}}{\textcolor[rgb]{0,0,1}{11}}\end{array}]
\mathrm{MatrixOptions}\left(\mathrm{H1},\mathrm{shape}\right)
[{\textcolor[rgb]{0,0,1}{\mathrm{Hankel}}}_{[\frac{\textcolor[rgb]{0,0,1}{1}}{\textcolor[rgb]{0,0,1}{11}}\textcolor[rgb]{0,0,1}{,}\frac{\textcolor[rgb]{0,0,1}{3}}{\textcolor[rgb]{0,0,1}{11}}\textcolor[rgb]{0,0,1}{,}\frac{\textcolor[rgb]{0,0,1}{5}}{\textcolor[rgb]{0,0,1}{11}}]}]
L≔〈f,g,h,i,j,k,l,m,n〉:
\mathrm{H2}≔\mathrm{HankelMatrix}\left(L,4\right)
\textcolor[rgb]{0,0,1}{\mathrm{H2}}\textcolor[rgb]{0,0,1}{≔}[\begin{array}{cccc}\textcolor[rgb]{0,0,1}{f}& \textcolor[rgb]{0,0,1}{g}& \textcolor[rgb]{0,0,1}{h}& \textcolor[rgb]{0,0,1}{i}\\ \textcolor[rgb]{0,0,1}{g}& \textcolor[rgb]{0,0,1}{h}& \textcolor[rgb]{0,0,1}{i}& \textcolor[rgb]{0,0,1}{j}\\ \textcolor[rgb]{0,0,1}{h}& \textcolor[rgb]{0,0,1}{i}& \textcolor[rgb]{0,0,1}{j}& \textcolor[rgb]{0,0,1}{k}\\ \textcolor[rgb]{0,0,1}{i}& \textcolor[rgb]{0,0,1}{j}& \textcolor[rgb]{0,0,1}{k}& \textcolor[rgb]{0,0,1}{l}\end{array}]
\mathrm{MatrixOptions}\left(\mathrm{H2},\mathrm{shape}\right)
[\textcolor[rgb]{0,0,1}{\mathrm{symmetric}}]
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Compute value of x in Ax = B for complex-valued matrices using QR decomposition - Simulink - MathWorks Italia
X(i, :)
Compute value of x in Ax = B for complex-valued matrices using QR decomposition
The Complex Partial-Systolic Matrix Solve Using QR Decomposition block solves the system of linear equations Ax = B using QR decomposition, where A and B are complex-valued matrices. To compute x = A-1, set B to be the identity matrix.
When Regularization parameter is nonzero, the Complex Partial-Systolic Matrix Solve Using QR Decomposition block computes the matrix solution of complex-valued
\left[\begin{array}{c}\lambda {I}_{n}\\ A\end{array}\right]X=\left[\begin{array}{c}{0}_{n,p}\\ B\end{array}\right]
X(i, :) — Rows of matrix X
Rows of matrix X, returned as a scalar or vector.
Use the Complex Partial-Systolic Matrix Solve Using QR Decomposition block to solve the regularized least-squares matrix equation
Real Partial-Systolic Matrix Solve Using QR Decomposition | Complex Partial-Systolic Matrix Solve Using Q-less QR Decomposition | Complex Burst Matrix Solve Using QR Decomposition
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Moresby's vessel mixed freely with them. They practise several useful arts, such as pottery, and possess extensive well-fenced plantations.
{\displaystyle =}
{\displaystyle =}
128 millimetres. The walls of the skull were thick and heavy; the dura mater exceedingly adherent to the bone and remarkably thick. The pia mater moderately transparent. Along the arachnoid veins were white lines indicating chronic thickening; the veins themselves rather more injected than usual. The cerebral sulci were deep and wide. On each side of the median line, near the anterior ascending convolution on the left, and the posterior ascending convolution on the right, was a depression which might have held a prune-stone or a little more. The brain-tissue around was diminished without evidence of disease. The arteries at the base of the brain showed evidence of extensive chronic disease of their lining membrane, with narrowing of the calibre of the carotids. The basilar artery was apparently a continuation of the left vertebral alone, the right vertebral being represented by an exceedingly small vessel which united the basilar with the inferior cerebellar, the latter being merely the prolongation of the exceedingly small right vertebral. The left vertebral was larger
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EUDML | Spaces making continous convergence and locally uniform convergence coincide, their very weak P-property, and their topological behaviour. EuDML | Spaces making continous convergence and locally uniform convergence coincide, their very weak P-property, and their topological behaviour.
Spaces making continous convergence and locally uniform convergence coincide, their very weak P-property, and their topological behaviour.
H.-P. Butzmann; M. Schroder
Butzmann, H.-P., and Schroder, M.. "Spaces making continous convergence and locally uniform convergence coincide, their very weak P-property, and their topological behaviour.." Mathematica Scandinavica 67.2 (1990): 227-254. <http://eudml.org/doc/167136>.
@article{Butzmann1990,
author = {Butzmann, H.-P., Schroder, M.},
keywords = {convergence space; pretopological space; P-space; minimal limit; continuous convergence; locally uniform convergence; -space; topological modification},
title = {Spaces making continous convergence and locally uniform convergence coincide, their very weak P-property, and their topological behaviour.},
AU - Butzmann, H.-P.
TI - Spaces making continous convergence and locally uniform convergence coincide, their very weak P-property, and their topological behaviour.
KW - convergence space; pretopological space; P-space; minimal limit; continuous convergence; locally uniform convergence; -space; topological modification
convergence space, pretopological space, P-space, minimal limit, continuous convergence, locally uniform convergence,
c=lu
-space, topological modification
Articles by H.-P. Butzmann
Articles by M. Schroder
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EUDML | Norm attaining bilinear forms on . EuDML | Norm attaining bilinear forms on .
Norm attaining bilinear forms on
{L}_{1}\left(\mu \right)
Saleh, Yousef
Saleh, Yousef. "Norm attaining bilinear forms on .." International Journal of Mathematics and Mathematical Sciences 23.12 (2000): 833-837. <http://eudml.org/doc/48808>.
@article{Saleh2000,
author = {Saleh, Yousef},
keywords = {norm attaining multilinear forms; -spaces; denseness; purely atomic; -spaces},
title = {Norm attaining bilinear forms on .},
AU - Saleh, Yousef
TI - Norm attaining bilinear forms on .
KW - norm attaining multilinear forms; -spaces; denseness; purely atomic; -spaces
norm attaining multilinear forms,
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-spaces, denseness, purely atomic,
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Radon-Nikodým, Kreĭn-Milman and related properties
Articles by Saleh
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In this article we discuss the process through which a compiler checks for correct syntactic and semantic conversions for a source language.
Design spaces for types.
Environments for type checking.
Type checking expressions.
Type checking of function declarations.
Type checking a program.
Other type checking aspects.
Type checking is the process of verifying and enforcing constraints of types in values.
Lexical analysis and parsing phases in the compiler filter out many texts however many programing languages with well-formed requirements cannot be handled by the techniques used in these two phases because more often than not, they are not context free and thus cannot be able check by membership of a context-free grammar.
The type checking phase in compiler design is interleaved with the syntax analysis phase therefore it is done before execution or translation of a program(static typing) and thus the information is gathered for use by subsequent phases, for example, the translator will exploit type information for it to naturally combine calculation of types with the actual translation.
Syntax of a simple programming language.
Program → Funs
Funs → Fun
Funs → Fun Funs
Fun → TypeId(TypeIds) = Exp
TypeId → int id
TypeId → bool id
TypeIds → TypeId
TypeIds → TypeId, TypeIds
Exp → num
Exp → Exp + Exp
Exp → Exp = Exp
Exp → if Exp then Exp else Exp
Exp → id(Exps)
Exp → let id = Exp in Exp
Exps → Exp
Exps → Exp, Exps
It is a first-order functional programming language with recursive definitions.
A program is a list of function declarations.
Functions are mutually exclusive and no function can be declared more than once.
Each function declares its result type and the types and names of its arguments.
Functions and variables have separate name spaces.
Parameters should not be repeated.
The body of a function is an expression either an integer constant, variable names, sum expression, comparison, a function call or a locally declared expression.
Comparison is defined for booleans and integers.
Addition is defined for integers.
A program must contain main with an integer as its argument.
main returns an integer when called for execution.
Design space for types.
Statically typed languages are those programming languages which perform type checking at compile-time, these include C, C++, java.
Dynamically types languages are those whereby type checking is performed during run-time, they include Javascript, python, php.
Strongly typed languages are language implementations whereby whenever an operation is performed, arguments to the operation are of the specified type defined by the operation.
e.g You cannot concatenate a string type and a floating point number.
Weakly typed languages are implementations whereby there is no explicit specification of types of objects or variables.
These are mainly used for systems programming whereby you manipulate data(moving, encrypting, compressing) without regard to what the data represents.
Some programming languages such as C will combine both static and dynamic typing i.e, some types are checked before execution while others during execution.
The design space for static verses dynamic, and weak verse strong typing
Type-checking operates on the abstract syntax tree(AST) and can make several recursive passes on this tree each time gathering information or using information gathered from previous phases.
This information is what we call attributes.
Attributes can be Synthesized, (attributes passed up the AST) or Inherited, (attributes passed down the AST).
Attributes synthesized on one subtree can be inherited in another subtree for example a symbol table that is synthesized by a declaration and inherited by the declaration's scope.
A syntactic category represents a type in the data structure for the AST or a group of related non-terminal in a grammar.
Syntactic categories will have their own set of attributes.
Writing a type checker as a set of mutually recursive functions will result in one or more such functions for each syntactic category.
We use the simple language in the previous section for static type checking.
A symbol table is needed to bind variables and functions to their types.
We use two symbol tables, one for variables and the other for functions.
A variable can be bound to either int or bool types.
A function is bound to its type(types of its arguments and result).
We write function types as a parenthesized list of argument types.
(int, bool) → int
This represents a function taking two parameters of types int and bool and a result type int which will be the return type for the function separated by an arrow.
We assume a stack-like behavior, that is, we don't preserve symbol tables for inner scopes once they are exited but preserve them for outer scopes so as no action is required to restore them.
Symbol tables for variables and functions become inherited attributes when expressions are type checked.
int and bool expressions will re returned ad synthesized attributes.
The type checker function will use a concrete syntax for pattern matching purposes so that the presentation is independent of any specific data structure for the abstract syntax.
We assume that for terminals(variable names and numeric constants) with attributes there are predefined functions for extracting them.
Therefore id will have a function getname that extracts the name of the identifier and num has a function getvalue that extracts the value of the number.
For non-terminals we define functions which take an AST subtree and inherited attributes as arguments and return the synthesized attributes.
Type checking function for expressions
Chec{k}_{Exp}
is the function responsible for type checking.
vtable is the symbol table for variables.
ftable is the symbol table for functions.
error function is responsible for reporting errors, if we let this function return, then the type-checker will continue reporting errors.
Cases handled by
Chec{k}_{Exp}
A number has type int.
A variable type is found be a lookup in the variables symbol table. If not found, the lookup function returns unbound special value then an error is reported and the type checker guesses that the type is an int otherwise a type is returned.
Plus(+) expression requires that both arguments have the same type(integer) and that the result is also an integer.
Comparison requires both arguments to have the same type and in either case the result is of boolean type.
Conditional expression must be of boolean type and both branches should have same types. The result of the condition is one of its branches. If branches have different types, an error is reported and a type is arbitrarily chosen for the whole expression which will be the type for then branch.
When a function is called, the function name is looked up in the function environment to find the number of arguments, types of arguments and the return type. Number of arguments must correspond with the expected number and types must match declared types. The resulting type is the function's return type. If function name is absent in the symbol table for functions ftable an error is reported and the type checker guesses an int type for the result.
Let-expression declares a new variable with the type of which is that of the expression defining the value of the variable. Bind function is used to extend the symbol table which is then used for checking the body of the expression and finding its type which is the type for the whole expression. Type errors cannot be caused by let-expression therefore no testing is done.
Chec{k}_{Exp}
mentions non-terminal Exps and its related type-checking function
Chec{k}_{Exps}
Chec{k}_{Exp}
builds a list of types in the expression list.
A list is written in [ ] with commas between elements.
The :: operator is used to add elements to the front of the list.
Type checking function declarations.
A function declaration explicitly declares the types of its arguments and this information is used to build a symbol table for variables used when type checking the body of a function.
The declared result type must match the function body type.
type checking funcion declarations
Chec{k}_{Fun}
has an inherited attribute in the symbol table for functions which is passed down to the type check function for expressions.
Chec{k}_{Fun}
uses TypeId and TypeIds functions to check for internal errors and returns no information.
Ge{t}_{TypeId}
returns a pair(name, type) of the declared type.
Chec{k}_{TypeIds}
will build a symbol table from the (name, type) pair and also check if parameters have different names.
A program is said to be correct if all functions are type correct and there are no two definitions defining the same function name.
In addition, the function main should have one integer argument and one integer result.
Functions are type checked by use of the symbol table where they will be bound to their types.
Two passes are required for this, the first to construct the symbol table and the second to check function definitions from the constructed table, therefore there will be two functions operating over Fun and two functions operating over Funs.
One of the functions for Funs can be seen from image in the previous section.
The other
Ge{t}_{Fun}
returns the pair(name, type) of the declared function which consists of type arguments and result type and are obtained by the
Ge{t}_{Types}
auxilliary function.
Functions for the syntactic category Funs are
Ge{t}_{Funs}
which builds the symbol table and checks for duplicate definitions while the
Chec{k}_{Funs}
functions calls the
Chec{k}_{Fun}
function for all functions.
The is
Chec{k}_{program}
function is the main function.
The language we defined at the begining of this article does not cover all aspects of type checking therefore in this section we consider other features and how they are handled.
When a variable is assigned a value, the type checker ensures that this value is the same type with the declared type of the variable.
A data structure might define a value with several components e.g struct or a value with different type at different times.
A type checker will need the data structure to describe complex types so as to be able to represent them.
This data structure is similar to the data structure used in an AST of declarations.
Overloading is whereby a similar name is used for several operations with several different types.
We can see this in the sample language defined in previous sections whereby the = operator is used for comparisons for both integers and boolean values, similarly + and - operators are used for both boolean an integer operations in most programming languages.
When these operators are predefined they only cover a finite number of cases and therefore all cases are tried however this requires disjoint argument types for different instances.
e.g if there is a function read that is defined to read either integers or booleans values from a text stream, the type checker must pass the expected type of each expression as an inherited attribute so as to pick the correct instance of the overloaded operator.
A language might have operators which are used for converting a type to another type, e.g converting an integer into a floating type.
To handle type checking in such cases, if the type checker discovers that arguments don't have the correct type, it will try to convert one or both of the arguments.
Polymorphism/generic types.
In some languages polymorphism(definition of a function over a large class of similar types) is allowed.
For type checking a function will explicitly declare generic parts and the type checker will insert the actual types at every use of the generic/polymorphic function so as to create instances of this type.
Implicit types.
Some languages e.g Haskell require that programs are well typed but don't require explicit variable or function type declarations, therefore a type inference algorithm is used to gather information about the uses of functions and variables which is used for inference of these types.
A type error is reported when there exists inconsistent inferences.
By now we know differences between static, dynamic, strongly and weakly typed languages each with their properties and advantages.
Lexing and parsing also perform type checking however some languages have weel-formed requirements which cannot be handled by the techniques used in these two phases.
Compilers, Principles,Techniques and Tools Alfred V. Aho, Ravi Sethi, and Jeffrey D. Ullman.
Basics of Compiler Design Torben Ægidius Mogensen Chapter 6.
Parallel programming models in Compiler Design
Parallel systems solve solves given problems as fast as possible by utilizing multiple processors. In this article we discuss five models for parallel programming and how they are expressed in parallel programming languages.
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Ada Programming/Subprograms - Wikibooks, open books for an open world
In Ada the subprograms are classified into two categories: procedures and functions. A procedures call is a statement and does not return any value, whereas a function returns a value and must therefore be a part of an expression.
Subprogram parameters may have three modes.
The actual parameter value goes into the call and is not changed there. The formal parameter is a constant and allows only reading. This is the default when no mode is given. The actual parameter is an expression.
The actual parameter goes into the call and may be redefined. The formal parameter is a variable and can be read and written.
The actual parameter's value before the call is irrelevant, it will get a value in the call. The formal parameter can be read and written. (In Ada 83 out parameters were write-only.)
A parameter of any mode may also be explicitly aliased.
The formal parameter is an access (a pointer) to some variable. (This is not a parameter mode from the reference manual point of view.)
Note that parameter modes do not specify the parameter passing method. Their purpose is to document the data flow.
The parameter passing method depends on the type of the parameter. A rule of thumb is that parameters fitting into a register are passed by copy, others are passed by reference. For certain types, there are special rules, for others the parameter passing mode is left to the compiler (which you can assume to do what is most sensible). Tagged types are always passed by reference.
Explicitly aliased parameters and access parameters specify pass by reference.
Unlike in the C class of programming languages, Ada subprogram calls cannot have empty parameters parentheses ( ) when there are no parameters.
A procedure call in Ada constitutes a statement by itself.
When the procedure is called with the statement
A_Test (5 + P, 48, Q);
the expressions 5 + P and 48 are evaluated (expressions are only allowed for in parameters), and then assigned to the formal parameters A and B, which behave like constants. Then, the value A + B is assigned to formal variable C, whose value will be assigned to the actual parameter Q when the procedure finishes.
C, being an out parameter, is an uninitialized variable before the first assignment. (Therefore in Ada 83, there existed the restriction that out parameters are write-only. If you wanted to read the value written, you had to declare a local variable, do all calculations with it, and finally assign it to C before return. This was awkward and error prone so the restriction was removed in Ada 95.)
Within a procedure, the return statement can be used without arguments to exit the procedure and return the control to the caller.
For example, to solve an equation of the kind
{\displaystyle ax^{2}+bx+c=0}
procedure Quadratic_Equation
(A, B, C : Float; -- By default it is "in".
Valid : out Boolean)
Z : Float;
Z := B**2 - 4.0 * A * C;
Valid := False; -- Being out parameter, it should be modified at least once.
R1 := 0.0;
R1 := (-B + Sqrt (Z)) / (2.0 * A);
R2 := (-B - Sqrt (Z)) / (2.0 * A);
end Quadratic_Equation;
The function SQRT calculates the square root of non-negative values. If the roots are real, they are given back in R1 and R2, but if they are complex or the equation degenerates (A = 0), the execution of the procedure finishes after assigning to the Valid variable the False value, so that it is controlled after the call to the procedure. Notice that the out parameters should be modified at least once, and that if a mode is not specified, it is implied in.
A function is a subprogram that can be invoked as part of an expression. Until Ada 2005, functions can only take in (the default) or access parameters; the latter can be used as a work-around for the restriction that functions may not have out parameters. Ada 2012 has removed this restriction.
Here is an example of a function body:
function Minimum (A, B: Integer) return Integer is
end Minimum;
(There is, by the way, also the attribute Integer'Min, see RM 3.5.) Or in Ada2012:
return (if A <= B then A else B);
or even shorter as an expression function
function Minimum (A, B: Integer) return Integer is (if A <= B then A else B);
The formal parameters with mode in behave as local constants whose values are provided by the corresponding actual parameters. The statement return is used to indicate the value returned by the function call and to give back the control to the expression that called the function. The expression of the return statement may be of arbitrary complexity and must be of the same type declared in the specification. If an incompatible type is used, the compiler gives an error. If the restrictions of a subtype are not fulfilled, e.g. a range, it raises a Constraint_Error exception.
The body of the function can contain several return statements and the execution of any of them will finish the function, returning control to the caller. If the flow of control within the function branches in several ways, it is necessary to make sure that each one of them is finished with a return statement. If at run time the end of a function is reached without encountering a return statement, the exception Program_Error is raised. Therefore, the body of a function must have at least one such return statement.
Every call to a function produces a new copy of any object declared within it. When the function finalizes, its objects disappear. Therefore, it is possible to call the function recursively. For example, consider this implementation of the factorial function:
When evaluating the expression Factorial (4); the function will be called with parameter 4 and within the function it will try to evaluate the expression Factorial (3), calling itself as a function, but in this case parameter N would be 3 (each call copies the parameters) and so on until N = 1 is evaluated which will finalize the recursion and then the expression will begin to be completed in the reverse order.
A formal parameter of a function can be of any type, including vectors or records. Nevertheless, it cannot be an anonymous type, that is, its type must be declared before, for example:
type Float_Vector is array (Positive range <>) of Float;
function Add_Components (V: Float_Vector) return Float is
Result : Float := 0.0;
Result := Result + V(I);
end Add_Components;
In this example, the function can be used on a vector of arbitrary dimension. Therefore, there are no static bounds in the parameters passed to the functions. For example, it is possible to be used in the following way:
V4 : Float_Vector (1 .. 4) := (1.2, 3.4, 5.6, 7.8);
Sum : Float;
Sum := Add_Components (V4);
In the same way, a function can also return a type whose bounds are not known a priori. For example:
function Invert_Components (V : Float_Vector) return Float_Vector is
Result : Float_Vector(V'Range); -- Fix the bounds of the vector to be returned.
Result(I) := V (V'First + V'Last - I);
end Invert_Components;
The variable Result has the same bounds as V, so the returned vector will always have the same dimension as the one passed as parameter.
A value returned by a function can be used without assigning it to a variable, it can be referenced as an expression. For example, Invert_Components (V4) (1), where the first element of the vector returned by the function would be obtained (in this case, the last element of V4, i.e. 7.8).
Named parametersEdit
In subprogram calls, named parameter notation (i.e. the name of the formal parameter followed of the symbol => and then the actual parameter) allows the rearrangement of the parameters in the call. For example:
Quadratic_Equation (Valid => OK, A => 1.0, B => 2.0, C => 3.0, R1 => P, R2 => Q);
This is especially useful to make clear which parameter is which.
Phi := Arctan (A, B);
Phi := Arctan (Y => A, X => B);
The first call (from Ada.Numerics.Elementary_Functions) is not very clear. One might easily confuse the parameters. The second call makes the meaning clear without any ambiguity.
Another use is for calls with numeric literals:
Ada.Float_Text_IO.Put_Line (X, 3, 2, 0); -- ?
Ada.Float_Text_IO.Put_Line (X, Fore => 3, Aft => 2, Exp => 0); -- OK
Default parametersEdit
On the other hand, formal parameters may have default values. They can, therefore, be omitted in the subprogram call. For example:
procedure By_Default_Example (A, B: in Integer := 0);
can be called in these ways:
By_Default_Example (5, 7); -- A = 5, B = 7
By_Default_Example (5); -- A = 5, B = 0
By_Default_Example; -- A = 0, B = 0
By_Default_Example (B => 3); -- A = 0, B = 3
By_Default_Example (1, B => 2); -- A = 1, B = 2
In the first statement, a "regular call" is used (with positional association); the second also uses positional association but omits the second parameter to use the default; in the third statement, all parameters are by default; the fourth statement uses named association to omit the first parameter; finally, the fifth statement uses mixed association, here the positional parameters have to precede the named ones.
Note that the default expression is evaluated once for each formal parameter that has no actual parameter. Thus, if in the above example a function would be used as defaults for A and B, the function would be evaluated once in case 2 and 4; twice in case 3, so A and B could have different values; in the others cases, it would not be evaluated.
Subprograms may be renamed. The parameter and result profile for a renaming-as-declaration must be mode conformant.
procedure Solve
(A, B, C: in Float;
R1, R2 : out Float;
Valid : out Boolean) renames Quadratic_Equation;
This may be especially comfortable for tagged types.
package Some_Package is
type Message_Type is tagged null record;
procedure Print (Message: in Message_Type);
end Some_Package;
with Some_Package;
Message: Some_Package.Message_Type;
procedure Print renames Message.Print; -- this has convention intrinsic, see RM 6.3.1(10.1/2)
Method_Ref: access procedure := Print'Access; -- thus taking 'Access should be illegal; GNAT GPL 2012 allows this
begin -- All these calls are equivalent:
Some_Package.Print (Message); -- traditional call without use clause
Message.Print; -- Ada 2005 method.object call - note: no use clause necessary
Print; -- Message.Print is a parameterless procedure and can be renamed as such
Method_Ref.all; -- GNAT GPL 2012 allows illegal call via an access to the renamed procedure Print
-- This has been corrected in the current version (as of Nov 22, 2012)
But note that Message.Print'Access; is illegal, you have to use a renaming declaration as above.
Since only mode conformance is required (and not full conformance as between specification and body), parameter names and default values may be changed with renamings:
procedure P (X: in Integer := 0);
procedure R (A: in Integer := -1) renames P;
Section 6: Subprograms (Annotated)
4.1.3 Subprograms
Retrieved from "https://en.wikibooks.org/w/index.php?title=Ada_Programming/Subprograms&oldid=3371737"
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Class 10- Physics Magnetic Effects of Electric Current
Class 10- Physics Magnetic Effects of Electric CurrentContact Number: 9667591930 / 8527521718
The direction of magnetic field around a straight conductor carrying can be determined by
1. Fleming's left hand rule
4. Flemin's right hand rule
Magnetic field is produced by the flow of current in a staright wire. This phenomenon was discovered by
The magnetic field produced due to a circular wire at its centre is
1. at
{45}^{°}
to the plane of the wire
{60}^{°}
3. in the plane of the wire
4. perpendicular to the plane of the wire
A magnetic field exerts no force on
1. a stationary electric charge
3. an electric charge moving perpendicular to its direction
4. an unmagnetised
At the centre of a magnet, the magnetism is
2. same as the pole
Which of the following instruments works by electromagnetic induction?
2. moving coil galvanometer
3. telephone receiver
4. simple motor
A DC generator is based on the principal of
2. heating effect of current
3. energy dessipation
The use of fuses in electric power line is
1. just to show an indication where there is an over load
2. as a switch to use in an emergency
3. to keep main vaoltage constant
4. to open the lines permanently when there is an overload
When the main switch of the house circuit is put off, it disconnects the
1. earth wire
2. live and neutral wires
For making a strong electromagnet, the material of the core should be
2. laminated steel strips
A soft iron bar is introduced inside a current carrying solenoid. The magnetic field inside the solenoid
2. will remain unaffected
3. will become zero
The magnetic field lines inside a current carrying solenoid are
1. circular and they do not intersect each other
2. circular at the ends but they are parallel to the axis inside the sloenoid
3. along the axis and parallel to each other
4. perpendicular to the axis and eqiudistant from each other
Which of the following describes the common domestic power supplied in India?
1. 220 V, 100 Hz
Potential difference between a live wire and the neutral wire is
A device for producing electric current is called
2. electrical energy into mechanical enrgy
3. mechanical energy into electrial energy
4. mechanical energy iinto heat energy
An electrical generator converts
1. electrical enrgy into chemical energy
2. mehanical energy into electrical energy
3. electrical energy into mechanical energy
The ring system of wiring is better than the tree system because
2. all appliances can be joined in series
3. less power is consumed in the ring system
4. it can work even at low voltage supply
Four students plotted the sketch of the patterens of magnetic field lines representing the magnetic field around a current carrying straight wire as shown in figures A, B, C and D. Which of the sketches is correct?
A soft iron bar is enclosed by a coil of insulated copper wire as shown in figure. When the plug of the key is closed, the face B of the iron bar marked as
1. N-pole
2. S-pole
3. N-pole if current is large
4. S-pole if current is small
Magnetic field lines determine
1. the space of the magnetic field
2. only the direction of the magnetic field
3. only the relative strength of the magnetic field
4. both the direction and the relative strength of the magnetic field
1. straight field lines parallel to the wire
2. straight field lines perpendicular to the wire
3. concentric circles centred on the wire
4. radial field lines starting from the wire
1. an electromagnet to rotate the armature
2. a permanent magnet to rotate the armature
3. a soft iron core on which the coil is wound
4. effectively large number of turns of conducting wires in the current-carrying coil
At the time of short circuit,the current in the circuit
1. vary continously
2. reduces considerably
3. increases heavily
1. always exerts a force on a charged particle
2. never exerts a force on a charged particle
3. exerts a force, if the charged particle is moving across the magnetic field lines
4. exerts a force, if the charged particle is moving along the magnetic field lines
If a copper rod carrioes a direct current, the mahnetic field associated with the current will be
1. only inside the rod
2. only outside the rod
3. both inside and outside the rod
4. neither inside nor outside the rod
An electric charge in uniform motion produces
1. an electric field only
2. a magnetic field only
3. both electric and magnetic fields
4. no such field at all
In a safety fuse, the temperature to which the wire gets heated does not depend upon
1. the radius of the wire
2. the type of alloy used
3. the magnitude of the current
An electron is travelling horizontally towards east. A magnetic field in vertically downward direction exerts a force on the electron along
Induced current flows through a coil
1. more than the period duriing which flux changes through it
2. lass than the period during which flux changes through it
3. only for the period during which flux changes through it
When a fuse is rated at 8A, it means
1. it will work only if current is 8 A
2. it will burn if current exceeds 8 A
3. it will not work if current is less than 8 A
4. it has a resistance of 8 ohm
Power is transmitted from a power-house on high voltage AC as
1. power cannot be generated at low voltages
2. a precaution against theft of transmission lines.
3. the rate of transmission is faster at high voltage
4. it is more economical due to the less power wasted
A circular loop is suspended in air as shown in figure. When the loop is seen from above, current flows anticlockwise and when seen from below, current flows clockwise. This loop behaves as a magnet. The N-pole of this magnet is one
1. the upper face
3. the lower face if current is large
4. upper face if current is large
A student connects a coil of wire with a sensitive galvanometer as shown in figure. He will observe the deflection in the galvanometer if bar magnet is
1. placed near one of the faces of the coil and parallel to the axis of the coil.
2. placed near one of the faces of the coil and perpendicular to the axis of the coil
3. placed inside the coil
4. moves towards or away from the coil parallel to the axis of the coil
Electric supply of a house is through a 15 A fuse. When a 2000 W heater is used in this house, how many 100 W bulbs can be used simultaneously? The supply is at 220 V, and the heater and the bulbs are rated for 220 V.
2. towards south
3. towards east
4. towards west
A compass needle placed just above a wire in which electrons are towards west, will point
A positively charged particle moving due east enters a region of uniform magnetic field directed vertically upwards. The particle will
1. get deflected in vertically upward direction
2. move in circular path with an increased speed
3. move in circular path with a decreased speed
4. move in circular path with a uniform speed
When a magnetic compass needle is carried nearby to a straight wire carrying current, then
I. the straight wire causes a noticeable deflection in the compass needle
II. the aligment of the needle is tangential to an imaginary circle with straight wire as its centre and has a plane perpendicular to the wire
1. (I) is correct
2. (II) is correct
3. both (I) and (II) are correct
4. neither (I) nor (II) is correct
If an electron is moving with velocity
\stackrel{\to }{v}
\stackrel{\to }{B}
1. the direction of field
\stackrel{\to }{B}
will be same as the direction of velocity
\stackrel{\to }{v}
\stackrel{\to }{B}
will be opposite to the direction of velocity
\stackrel{\to }{v}
\stackrel{\to }{B}
will be perpendicular to the direction of velocity
\stackrel{\to }{v}
\stackrel{\to }{B}
does not depend upon the direction of velocity
\stackrel{\to }{v}
Which of the following is correct regarding the nature of parallel and anti-parallel currents?
1. Parallel currents repel an dantiparallel currents attract.
2. Parallel currents attracts and antiparallel currents repel.
3. No force exist due to both currents.
The magnetism of a magnet due to
3. the spin motion of electrons
4. pressure of big magnet inside the earth
The magnetic field lines due to a bar magnet are correctly shown in figure
A charged particle is moving along a magnetic field line. The magnetic force on the particle is
1. along its velocity
2. opposite to its velocity
3. perpendicular to its velocity
Choose the incorrect statement from the following regarding magnetic lines of field:
1. the direction of magnetic field at a point is taken to be the directionin which the north pole of a magnetic compass needle points.
2. Magnetic field lines are closed curves
3. If magnetic field lines are parallel and equidistant, they represent zero field strength.
4. Relative strength of magnetic field is shown by the degree of closeness of the field lines.
If the key in the arrangements, in the given figure is taken out (the circuit is made open) and magnetic field lines are drwn over the horizontal plane ABCD, the lines are:
2. elliptial in shape
3. straight lines parallel to each other
4. concentric circles near the point O but of elliptical shapes as we go away from it.
A circular loop placed perpendicular to the plane of paper carries a current when the key is ON. The current as seen fro points A and B (in the plane of paper and on the axis of the coil) is aniclockwise and clockwise respectively. The magnetic field lines point from B to A. The N-pole of the resulstant magnet is on the face close to:
3. A if the current is small, and B if the current is large
4. B if the current is small, and A if the current is large
For a current in a long straight solenoid, N and S-pole are created at the two ends. Amoong the following statements, the incorrect statement is:
1. the field lines inside the solenoid are in the form of straight lines which indicate that the magnetic field is the same at all points inside the solenoid
2. the strong magnetic field produced inside the solenoid can be used to magnetise a piece of magnetic material like soft iron, when placed inside the coil
3. the pattern of the magnetic field associated with the solenoid is different from the patteren of the mahnetic field around a bar magnet
4. the N- and S-poles exchange positions when the direction of current through the solenoid is reversed
A uniform magnetic field exists in the plane of paper point from left to right as shown in figure. In th field, an electron and a proton move a shown. The electron and the proton experience forces.
1. both pointin into the plane of paper
2. both pointing out of the plane of paper
3. pointing into the plane of paper and out of the plane of paper, respectively
4. pointing opposite and along the direction of the uniform magnetic field respectively
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Current Electricity, Popular Questions: CBSE Class 12-science SCIENCE, Science - Meritnation
{A}_{1}, {A}_{2} and {A}_{3}
1. 10\Omega 2. 5\Omega 3. 40\Omega 4. 15\Omega
\left(1\right) \frac{12\mathrm{R}}{13} \left(2\right) \frac{\mathrm{R}}{13}\phantom{\rule{0ex}{0ex}}\left(3\right) \frac{5\mathrm{R}}{13} \left(4\right) \frac{15\mathrm{R}}{13}
20\Omega
{r}_{1}=6\Omega and {r}_{2}=4\Omega .
\left(A\right) 2\phantom{\rule{0ex}{0ex}}\left(B\right) 2.4\phantom{\rule{0ex}{0ex}}\left(C\right) 10\phantom{\rule{0ex}{0ex}}\left(D\right) 24
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Do all figure have at least one rotational symmetry and all figures have centre of rotation - Maths - Symmetry - 16911027 | Meritnation.com
Do all figure have at least one rotational symmetry and all figures have centre of rotation
Yes , All figure have at least one rotational symmetry and all figures have centre of rotation.
The centre of a shape or object with rotational symmetry is the point around which the rotation occurs. Hence all figures have centre of rotation.
As in a complete turn of 360
°
, every object looks exactly the same as the original at least once , i.e., after one complete turn. So every object has 1 rotational symmetry.
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EUDML | On the Ritt order and type of a certain class of functions defined by -Dirichletian elements. EuDML | On the Ritt order and type of a certain class of functions defined by -Dirichletian elements.
On the Ritt order and type of a certain class of functions defined by
BE
-Dirichletian elements.
Berland, Marcel
Berland, Marcel. "On the Ritt order and type of a certain class of functions defined by -Dirichletian elements.." International Journal of Mathematics and Mathematical Sciences 22.3 (1999): 445-458. <http://eudml.org/doc/48765>.
@article{Berland1999,
author = {Berland, Marcel},
keywords = {Ritt order; -Dirichletian elements; -Dirichletian elements},
title = {On the Ritt order and type of a certain class of functions defined by -Dirichletian elements.},
AU - Berland, Marcel
TI - On the Ritt order and type of a certain class of functions defined by -Dirichletian elements.
KW - Ritt order; -Dirichletian elements; -Dirichletian elements
Ritt order,
BE
-Dirichletian elements,
BE
-Dirichletian elements
Articles by Berland
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Strong Convergence Theorems for Modifying Halpern Iterations for Quasi-ϕ-Asymptotically Nonexpansive Multivalued Mapping in Banach Spaces with Applications
2012 Strong Convergence Theorems for Modifying Halpern Iterations for Quasi-
\mathbf{\varphi }
-Asymptotically Nonexpansive Multivalued Mapping in Banach Spaces with Applications
An iterative sequence for quasi-
\varphi
-asymptotically nonexpansive multivalued mapping for modifying Halpern's iterations is introduced. Under suitable conditions, some strong convergence theorems are proved. The results presented in the paper improve and extend the corresponding results in the work by Chang et al. 2011.
Li Yi. "Strong Convergence Theorems for Modifying Halpern Iterations for Quasi-
\mathbf{\varphi }
-Asymptotically Nonexpansive Multivalued Mapping in Banach Spaces with Applications." J. Appl. Math. 2012 (SI15) 1 - 11, 2012. https://doi.org/10.1155/2012/912545
Li Yi "Strong Convergence Theorems for Modifying Halpern Iterations for Quasi-
\mathbf{\varphi }
-Asymptotically Nonexpansive Multivalued Mapping in Banach Spaces with Applications," Journal of Applied Mathematics, J. Appl. Math. 2012(SI15), 1-11, (2012)
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Global asymptotics for the damped wave equation with absorption in higher dimensional space
July, 2006 Global asymptotics for the damped wave equation with absorption in higher dimensional space
We consider the Cauchy problem for the damped wave equation with absorption
{u}_{tt}-\mathrm{\Delta }u+{u}_{t}+|u{|}^{\rho -1}u=0,\phantom{\rule{1em}{0ex}}\left(t,x\right)\in {\mathbf{R}}_{+}×{\mathbf{R}}^{N},\phantom{\rule{2em}{0ex}}\left(*\right)
N=3,4
. The behavior of
u
t\to \mathrm{\infty }
is expected to be the Gauss kernel in the supercritical case
\rho >{\rho }_{c}\left(N\right):=1+2/N
. In fact, this has been shown by Karch [12] (Studia Math., 143 (2000), 175--197) for
\rho >1+\frac{4}{N}\left(N=1,2,3\right)
, Hayashi, Kaikina and Naumkin [8] (preprint (2004)) for
\rho >{\rho }_{c}\left(N\right)\left(N=1\right)
and by Ikehata, Nishihara and Zhao [11] (J. Math. Anal. Appl., 313 (2006), 598--610) for
{\rho }_{c}\left(N\right)<\rho \le 1+\frac{4}{N}\left(N=1,2\right)
{\rho }_{c}\left(N\right)<\rho <1+\frac{3}{N}\left(N=3\right)
. Developing their result, we will show the behavior of solutions for
{\rho }_{c}\left(N\right)<\rho \le 1+\frac{4}{N}\left(N=3\right)
{\rho }_{c}\left(N\right)<\rho <1+\frac{4}{N}\left(N=4\right)
. For the proof, both the weighted
{L}^{2}
-energy method with an improved weight developed in Todorova and Yordanov [22] (J. Differential Equations, 174 (2001), 464--489) and the explicit formula of solutions are still usefully used. This method seems to be not applicable for
N=5
, because the semilinear term is not in
{C}^{2}
and the second derivatives are necessary when the explicit formula of solutions is estimated.
Kenji NISHIHARA. "Global asymptotics for the damped wave equation with absorption in higher dimensional space." J. Math. Soc. Japan 58 (3) 805 - 836, July, 2006. https://doi.org/10.2969/jmsj/1156342039
Keywords: Critical exponent , Explicit formula , global asymptotics , semilinear damped wave equation , weighted energy method
Kenji NISHIHARA "Global asymptotics for the damped wave equation with absorption in higher dimensional space," Journal of the Mathematical Society of Japan, J. Math. Soc. Japan 58(3), 805-836, (July, 2006)
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Home > Course Outline > Lesson 4 - Measurement and Estimations of the Solar Resource > 4.6 Using Components for a Tilted Aperture
J.R. Brownson, Solar Energy Conversion Systems (SECS), Chapter 8: Measure & Estimation of the Solar Resource (Isotropic and Anisotropic Sky Models.)
[repeated] C. A. Gueymard (2008) From Global Horizontal to Global Tilted Irradiance: How accurate are solar energy engineering predictions in practice? [1] Solar 2008 Conference, San Diego, CA, American Solar Energy Society
Please make sure you read all of Ch 8 in SECS for this lesson, still related to "Empirical Correlation for Components," but paying attention to the isotropic and anisotropic sky models and this page content. This is the third page for which we have included review of the Gueymard paper, so you should be familiar with the findings by now. The Perez et al. paper will be useful to you in Learning Activity 4.2 and for your Lesson Quiz.
Earlier, we discussed the different components of light, beam and diffuse on a horizontal surface. Now, we will discuss how these components can be estimated for tilted surfaces through isotropic or anisotropic diffuse sky/ground models of light source components.
Estimating the Plane of Array (tilted surfaces)
We shall see that we do not need to measure every component of light (scattered and unscattered) to make estimations on the contributions of each component to the total irradiation incident on the aperture of interest. We can rely somewhat on decades of historical observation and empirical correlation by solar scientists and engineers for hourly, daily, and monthly average day data.
The main tools we need are the equations for hourly and daily extraterrestrial irradiance (Air Mass Zero, or AM0) and the integrated energy density (irradiation: $MJ/m^2$) gathered from a horizontally mounted pyranometer, which you learned of in the last section. We shall also find that we can infer more than just the components of light from the ratios of measured irradiation to AM0 calculated irradiation--we can describe the fractions of days in a given month where lighting conditions will be clear or overcast/cloudy.
Following our step to break apart the beam horizontal component from the diffuse horizontal components, we then estimate the components on a tilted surface.
Procedure for Components
For a tilted plane of array,
Total Radiation = beam + diffuse, sky + diffuse, ground
{G}_{t}={G}_{b,t}+{G}_{b,d}+{G}_{g,t}
A simple calculation of the beam component can be achieved using
{G}_{b,t}={G}_{b,n}.cos\theta
Radiation on a sloped surface can be calculated for the beam component of irradiation by the geometric scaling factor of
{R}_{b}=\frac{cos\left(\theta \right)}{cos\left({\theta }_{z}\right)}
In order to estimate the diffuse component, we use alternate models that become increasingly better fits with the empirical data. We can integrate any of these equations over an hour or a day (irradiation). I prefer to offer the irradiance version as a bit easier to read. Note: all of these estimation models use irradiation values that were measured from a pyranometer mounted along the horizontal plane, and then estimated for beam and diffuse components from data correlation or directly measured using a shadow band measurement and energy balance equations.
Isotropic Diffuse Model: Liu & Jordan (1960)
The isotropic sky model was developed in the 1960s to estimate the diffuse sky on a tilted surface, complemented by an estimate for diffuse light from the ground. This model assumes that the sky is uniform in composition across the sky dome.
The following expression gives the total solar irradiance incident on a tilted surface as
\[ G=\quad {\text{beam+diffuse}}_{\text{sky}}{\text{+diffuse}}_{\text{ground}} \]
{G}_{total}={G}_{b}{R}_{b}+{G}_{d}\left({F}_{surface-sky}\right)+G\rho \left({F}_{surface-ground}\right)
\[ {F}_{surface-sky}=\quad \frac{1+cos\beta }{2} \]
\[ {F}_{surface-ground}=\quad \frac{1-cos\beta }{2} \]
\[ {G}_{d,t}\quad ={G}_{d}.\quad \frac{1+cos\beta }{2} \]
\[ {G}_{g,t}={\rho }_{g}({G}_{b}+{G}_{d}).\quad \frac{1-cos\beta }{2} \]
The fraction proportional to the collector tilt is called the diffuse sky irradiance tilt factor for an isotropic sky model, and the reflectance of the ground is called the albedo (a fraction between 0 and 1), and is multiplied by the GHI and the diffuse ground irradiance tilt factor for an isotropic sky model.
Note: "Surface": the aperture.
\rho
: is the collective reflectivity of the ground (the albedo).
\rho
reduces the irradiance G by a value between 0--1. On an inclined surface, Gd,ground increases, relative to a horizontal collector.
HDKR Model:
This model incorporates isotropic diffuse, circumsolar radiation and horizontal brightening. It also employs an anisotropic index A defined mathematically as
A=\frac{{G}_{N,I}}{G}
The total irradiance on a tilted surface is then calculated by using
{G}_{T}=\left({G}_{b}+{G}_{d}A\right){R}_{B}+{G}_{d}\left(1-A\right)\frac{1+\mathrm{cos}\beta }{2}×\left[1+\sqrt{\frac{{G}_{b}}{G}}{\mathrm{sin}}^{3}\frac{\beta }{2}\right]+G\rho \frac{1-\mathrm{cos}\beta }{2}
Go to Kalogirou (Solar Energy Engineering) Ch 2 (pdf from Library) this will be labeled the "Reindl model"
Perez Diffuse Model: Richard Perez (1990)
This is an anisotropic diffuse sky model that takes into consideration the real observations of subcomponents of diffuse light. The Perez model adds the circumsolar diffuse component and the horizon diffuse component to the diffuse$_{sky}$ component of the isotropic model. Notice how the beam component is not mentioned here--it doesn't change.
Sidenote: Richard Perez is a Senior Research Associate in the Atmospheric Sciences Research Center in SUNY Albany. He has a great website [2].
\[ {G}_{d}={G}_{iso}+{G}_{cir}+{G}_{hor}\quad +diffus{e}_{ground} \]
{G}_{d}=\left[{G}_{d}\left(1-{F}_{1}\right)\frac{1+cos\beta }{2}\right]+\left[{G}_{d}\left({F}_{1}\right)\frac{cos\theta }{cos{\theta }_{z}}\right]+\left[Gd\left({F}_{2}\right)sin\beta \right]+\left[{G}_{d}\rho \frac{1-cos\beta }{2}\right]
The shape factors (F) in this model can be reviewed in the original article by Perez et. al (1990). However, we can inspect the equations and observe in the equation that $F_{surface-sky}$ is reduced by a proportion of $F_1$ (circumsolar radiance), and $F_2$ can either increase or decrease the contribution of horizon radiance.
Try This! Tilted Surface Radiation Model
Software: SAM from NREL
You can open up SAM [3] at this point and click the button "Create a New File."
At the bottom of the screen on the right is a large "+" sign labeled "PV Albedo and Radiation". Please expand the section. I want to draw your attention to the little section called "Diffuse Sky Model (Advanced)." Yep, it's so advanced that you don't even realize this is where a powerful data transformation sits!
You can see that one may select "Irradiance Components used for Calculation": this is specifying the type of horizontal irradiation components that you will use in your tilted model. In a data set called the Typical Meteorological Year, the data for the beam is often not actually a measured value.
You can also see that one may select three diffuse sky/ground transposition models to transform the "Irradiance Components" (horizontal) to tilted values. The default is the Perez model that we describe below (and in your supplemental reading). The isotropic model is not used in practice, but it contains the basis for the other anisotropic models of Hay-Davies-Klutcher-Reindl (HDKR) and Perez et al. 1990.
Diffuse Sky Model (Advanced)
Tiny box hidden within a plus sign, whole lotta power. Keep that in mind.
Also, when in doubt: Read the Fine Manual. SAM has a detailed Help manual with links to the literature for every aspect of the program.
Perez, Ineichen, and Seals (1990) Modeling Daylight Availability and Irradiance Components from Direct and Global Irradiance [4]. Solar Energy J. 44(5), 271-289.
Liu, B.Y.H., Jordan, R.C., 1960. The interrelationship and characteristic distribution of direct, diffuse, and total solar radiation. Solar Energy 4(3),1-19
Perez, R., Ineichen, P., Seals, R., Michalsky, J., Stewart, R., 1990. Modeling daylight and Irradiance components from direct and global irradiance. Solar Energy 44(5), 271-289
[1] https://www.researchgate.net/publication/236314649_From_global_horizontal_to_global_tilted_irradiance_How_accurate_are_solar_energy_engineering_predictions_in_practice
[2] http://www.asrc.cestm.albany.edu/perez/
[4] http://www.sciencedirect.com/science/article/pii/0038092X9090055H
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Classification of Elements & Periodicity - Live Session - NEET & AIIMS 2019Contact Number: 9667591930 / 8527521718
Which of the following arrangements shows the correct order of decreasing paramagnetism?
1. N > Al > O > Ca
2. N > O > Al > Ca
3. O > N > Al > Ca
4. O > N > Ca > Al
The outer electronic structure of lawrencium (atomic number 103) is:
\mathrm{Rn} 5 {\mathrm{f}}^{13}7{s}^{2}7{p}^{2}
\mathrm{Rn} 5 {\mathrm{f}}^{13}6{d}^{2}7{s}^{1}7{p}^{2}
\mathrm{Rn} 5 {\mathrm{f}}^{14}7{s}^{1}7{p}^{2}
\mathrm{Rn} 5 {\mathrm{f}}^{14}6{d}^{1}7{s}^{2}
Which of the following pairs of molecules have the almost identical bond dissociation energy?
1. F2 and H2
2. N2 and CO
3. F2 and I2
4. HF and O2
Zn and Cd metals do not show variable valency because:
1. They have only two electrons in the outermost subshells
2. Their d-subshells are completely filled
3. Their d-subshells are partially filled
4. They are relatively soft metals
An element whose IUPAC name is ununtrium (Uut) belongs to:
1. s-block element
2. p-block element
3. d-block element
4. Transition element
Which of the following anion has the smallest radius?
The correct order of increasing atomic radius of the following elements is:
1. S < O < Se < C
2. O < C < S < Se
3. O < S < Se < C
4. C < O < S < Se
The correct order of atomic/ionic radii is:
1. Sc > Ti > V > Cr
2. Co > Ni > Cu > Zn
3. S2- > Cl- > O2- > N3-
The first, second and third ionisation energies (E1, E2 and E3) for an element are 7 eV, 12.5 eV and 42.5 eV respectively. The most stable oxidation state of the element will be:
The order of ionisation potential between He+ ion and H-atom (both species are in gaseous state) is:
1. I.P. (He+) = I.P. (H)
2. I.P. (He+) < I.P. (H)
3. I.P. (He+) > I.P. (H)
4. cannot be compared
Second ionization potential of Li, Be and B is in the order:
1. Li > Be > B
2. Li > B > Be
3. Be > Li > B
4. B > Be > Li
Which of the following atomic species has maximum electron affinity?
The correct order of I.E.2. is:
1. Na > F > O > N
2. O > F > Ne > N
3. Ne > O > F > N
4. O > Ne > F > N
Which of the following processes involves absorption of energy?
\mathrm{S}\left(\mathrm{g}\right)+{\mathrm{e}}^{-}\to {\mathrm{S}}^{-}\left(\mathrm{g}\right)
{\mathrm{S}}^{-}+{\mathrm{e}}^{-}\to {\mathrm{S}}^{2-}\left(\mathrm{g}\right)
\mathrm{Cl}\left(\mathrm{g}\right)+{\mathrm{e}}^{-}\to {\mathrm{Cl}}^{-}\left(\mathrm{g}\right)
Arrange N, O and S in order of decreasing electron affinity:
1. S > O > N
2. O > S > N
3. N > O > S
4. S > N > O
Which of the following order is incorrect?
1. Electronegativity of central atom :
{\mathrm{CF}}_{4}>{\mathrm{CH}}_{4}>{\mathrm{SiH}}_{4}
2. Hydration energy :
{\mathrm{Al}}^{3+}>{\mathrm{Be}}^{2+}>{\mathrm{Mg}}^{2+}>{\mathrm{Na}}^{+}
3. Electrical conductance :
{\mathrm{F}}_{\left(\mathrm{aq}.\right)}^{-}>{\mathrm{Cl}}_{\left(\mathrm{aq}.\right)}^{-}>{\mathrm{S}}_{\left(\mathrm{aq}.\right)}^{2-}
4. Magnetic moment :
{\mathrm{Ni}}^{4+}>{\mathrm{V}}^{3+}>{\mathrm{Sr}}^{2+}
A compound contains three elements A, B and C, if the oxidation number of A = +2, B = +5 and C = -2, the possible formula of the compound is:
{\mathrm{A}}_{3}{\left(\mathrm{B}}_{}
4C)2
{\mathrm{A}}_{3}{\left(\mathrm{BC}}_{}
{\mathrm{A}}_{2}{\left(\mathrm{BC}}_{}
{\mathrm{ABC}}_{2}
Cosider the following four elements, which are represented according to long form of periodic table.
Here W, Y and Z are left, up and right elements with respect to the element 'X' and 'X' belongs to 16th group and 3rd period. Then according to given information the incorrect statement regarding given elements is:
1. Maximum electronegativity : Y
2. Maximum catenation property : X
3. Maximum electron affinity : Z
4. Y exhibits variable covalency
What is the atomic number of the element with the maximum number of unpaired 4p electrons?
The electronic configuration of four elements are:
\left[\mathrm{Kr}\right]5{\mathrm{s}}^{1}
\left[\mathrm{Rn}\right]5{\mathcal{f}}^{14}6{\mathrm{d}}^{1}7{\mathrm{s}}^{2}
\left[\mathrm{Ar}\right]3{\mathrm{d}}^{10}4{\mathrm{s}}^{2}4{\mathrm{p}}^{5}
\left[\mathrm{Ar}\right]3{\mathrm{d}}^{6}4{\mathrm{s}}^{2}
i. I shows variable oxidation state
ii. II is a d-block element
iii. The compound formed between I and III is covalent
iv. IV shows single oxidation state
Which statement is True (T) or Flase (F)?
1. FTFF
2. FTFT
3. FFTF
The set representing the correct order of ionic radius is:
{\mathrm{Na}}^{+}>{\mathrm{Mg}}^{2+}>{\mathrm{Al}}^{3+}>{\mathrm{Li}}^{+}>{\mathrm{Be}}^{2+}
{\mathrm{Na}}^{+}>{\mathrm{Li}}^{+}>{\mathrm{Mg}}^{2+}>{\mathrm{Al}}^{3+}>{\mathrm{Be}}^{2+}
{\mathrm{Na}}^{+}>{\mathrm{Mg}}^{2+}>{\mathrm{Li}}^{+}>{\mathrm{Al}}^{3+}>{\mathrm{Be}}^{2+}
{\mathrm{Na}}^{+}>{\mathrm{Mg}}^{2+}>{\mathrm{Li}}^{+}>{\mathrm{Be}}^{2+}
If the ionic radii of K+ and F- are nearly the same (i.e., 1.34 Å), then the atomic radii of of K and F respectively are:
1. 1.34 Å, 1.34 Å
Incorrect order of ionic size is:
{\mathrm{La}}^{3+}>{\mathrm{Gd}}^{3+}>{\mathrm{Eu}}^{3+}>{\mathrm{Lu}}^{3+}
{\mathrm{V}}^{2+}>{\mathrm{V}}^{3+}>{\mathrm{V}}^{4+}>{\mathrm{V}}^{5+}
{\mathrm{Tl}}^{+}>{\mathrm{In}}^{+}>{\mathrm{Sn}}^{2+}>{\mathrm{Sb}}^{3+}
{\mathrm{K}}^{+}>{\mathrm{Sc}}^{3+}>{\mathrm{V}}^{5+}>{\mathrm{Mn}}^{7+}
{\mathrm{X}}_{\left(\mathrm{g}\right)}\to {{\mathrm{X}}^{+}}_{\left(\mathrm{g}\right)}+{\mathrm{e}}^{-}, △\mathrm{H}=+720 \mathrm{kJ} {\mathrm{mol}}^{-1}
Calculate the amount of energy required to convert 110 mg of 'X' atom in gaseous state into X+ ion. (Atomic wt. for X=7 g/mol)
1. 10.4 kJ
The third ionization energy is maximum for:
1. Q: Alkaline earth metal
2. P: Alkali metals
3. R: s-block element
4. They belong to same period
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LMIs in Control/Matrix and LMI Properties and Tools/D-Stability Settling Time Poles - Wikibooks, open books for an open world
LMIs in Control/Matrix and LMI Properties and Tools/D-Stability Settling Time Poles
LMI for Settling Time Poles
The following LMI allows for the verification that poles of a system will fall within a settling time constraint. This can also be used to place poles for settling time when the system matrix includes a controller, such as in the form A+BK.
4 The LMI: LMI for Settling Time Poles
{\displaystyle {\begin{aligned}{\dot {x}}(t)&=Ax\end{aligned}}}
{\displaystyle A\in \mathbb {R} ^{n\times n}}
The data required is the matrix A and the settling time
{\displaystyle t_{s}}
{\displaystyle {(z+z^{*}) \over 2}+{4.6 \over t_{s}}{\leq }0}
{\displaystyle 2Re(z){\leq }-\alpha }
The LMI: LMI for Settling Time PolesEdit
The LMI problem is to find a matrix P > 0 satisfying:
{\displaystyle {\begin{aligned}AP+(AP)^{T}+\alpha P&<0\\\end{aligned}}}
If the LMI is found to be feasible, then the pole locations of A, represented as z, will meet the settling time specification of
{\displaystyle {(z+z^{*}) \over 2}+{4.6 \over t_{s}}{\leq }0}
Retrieved from "https://en.wikibooks.org/w/index.php?title=LMIs_in_Control/Matrix_and_LMI_Properties_and_Tools/D-Stability_Settling_Time_Poles&oldid=4011184"
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Classical Mechanics Problem: Binary Black Hole Inspiral - Matt DeCross | Brilliant
Two black holes in a mutually orbiting binary system both have mass
M
and orbit at radius
R
to their center of rotation.
What is the magnitude of the rate of change of their radius (the rate at which they inspiral due to energy loss to gravitational radiation)?
The power radiated in gravitational waves by an inspiraling binary is
P = -\dfrac25 \dfrac{G^4 M^5}{c^5 R^5}.
Apart from the expression for gravitational wave radiation, assume Newtonian mechanics applies.
\frac{2}{5} \frac{G^3 M^3}{c^5 R^3}
\frac{8}{5} \frac{G^3 M^3}{c^5 R^3}
\frac{16}{5} \frac{G^3 M^3}{c^5 R^3}
\frac{128}{5} \frac{G^3 M^3}{c^5 R^3}
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Bifurcation Analysis of a Coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-Type Model
2013 Bifurcation Analysis of a Coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-Type Model
We study the bifurcation and stability of trivial stationary solution
\left(\mathrm{0},\mathrm{0}\right)
of coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-type equations (KS-GL) on a bounded domain
\left(\mathrm{0},L\right)
with Neumann's boundary conditions. The asymptotic behavior of the trivial solution of the equations is considered. With the length
L
of the domain regarded as bifurcation parameter, branches of nontrivial solutions are shown by using the perturbation method. Moreover, local behavior of these branches is studied, and the stability of the bifurcated solutions is analyzed as well.
Lei Shi. "Bifurcation Analysis of a Coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-Type Model." J. Appl. Math. 2013 1 - 8, 2013. https://doi.org/10.1155/2013/926512
Lei Shi "Bifurcation Analysis of a Coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-Type Model," Journal of Applied Mathematics, J. Appl. Math. 2013(none), 1-8, (2013)
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EUDML | Max-min representation of piecewise linear functions. EuDML | Max-min representation of piecewise linear functions.
Max-min representation of piecewise linear functions.
Ovchinnikov, Sergei. "Max-min representation of piecewise linear functions.." Beiträge zur Algebra und Geometrie 43.1 (2002): 297-302. <http://eudml.org/doc/225460>.
@article{Ovchinnikov2002,
author = {Ovchinnikov, Sergei},
keywords = {piecewise linear functions on convex domains in Euclidean -space; min-max representation; polyhedral complexes; piecewise linear functions on convex domains in Euclidean -space},
title = {Max-min representation of piecewise linear functions.},
AU - Ovchinnikov, Sergei
TI - Max-min representation of piecewise linear functions.
KW - piecewise linear functions on convex domains in Euclidean -space; min-max representation; polyhedral complexes; piecewise linear functions on convex domains in Euclidean -space
Yasuo Narukawa, Vicenç Torra, Twofold integral and multi-step Choquet integral
piecewise linear functions on convex domains in Euclidean
-space, min-max representation, polyhedral complexes, piecewise linear functions on convex domains in Euclidean
Articles by Ovchinnikov
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Right array division - MATLAB rdivide ./ - MathWorks India
Divide Scalar by Array
x = A./B divides each element of A by the corresponding element of B. The sizes of A and B must be the same or be compatible.
x = rdivide(A,B) is an alternative way to divide A by B, but is rarely used. It enables operator overloading for classes.
Divide an int16 scalar value by each element of an int16 vector.
a = int16(10);
b = int16([3 4 6]);
MATLAB® rounds the results when dividing integer data types.
Create an array and divide it into a scalar.
x = C./D
When you specify a scalar value to be divided by an array, the scalar value expands into an array of the same size, then element-by-element division is performed.
The result is a 3-by-2 matrix, where each (i,j) element in the matrix is equal to a(j) ./ b(i):
\mathit{a}=\left[{\mathit{a}}_{1}\text{\hspace{0.17em}}{\mathit{a}}_{2}\right],\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathit{b}=\left[\begin{array}{c}{\mathit{b}}_{1}\\ {\mathit{b}}_{2}\\ {\mathit{b}}_{3}\end{array}\right],\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\text{\hspace{0.17em}}\mathit{a}\text{\hspace{0.17em}}./\text{\hspace{0.17em}}\mathit{b}=\left[\begin{array}{cc}{\mathit{a}}_{1}\text{\hspace{0.17em}}./\text{\hspace{0.17em}}{\mathit{b}}_{1}& {\mathit{a}}_{2}\text{\hspace{0.17em}}./\text{\hspace{0.17em}}{\mathit{b}}_{1}\\ {\mathit{a}}_{1}\text{\hspace{0.17em}}./\text{\hspace{0.17em}}{\mathit{b}}_{2}& {\mathit{a}}_{2}\text{\hspace{0.17em}}./\text{\hspace{0.17em}}{\mathit{b}}_{2}\\ {\mathit{a}}_{1}\text{\hspace{0.17em}}./\text{\hspace{0.17em}}{\mathit{b}}_{3}& {\mathit{a}}_{2}\text{\hspace{0.17em}}./\text{\hspace{0.17em}}{\mathit{b}}_{3}\end{array}\right].
If you use rdivide with single type and double type operands, the generated code might not produce the same result as MATLAB. See Binary Element-Wise Operations with Single and Double Operands (MATLAB Coder).
Starting in R2020b, rdivide supports implicit expansion when the arguments are duration arrays. Between R2020a and R2016b, implicit expansion was supported only for numeric data types.
ldivide | mldivide | mrdivide | idivide
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Q-less QR decomposition for complex-valued matrices - Simulink - MathWorks Italia
The Complex Burst Q-less QR Decomposition block uses QR decomposition to compute the economy size upper-triangular R factor of the QR decomposition A = QR, where A is a complex-valued matrix, without computing Q. The solution to A'Ax = B is x = R\R'\b.
When Regularization parameter is nonzero, the Complex Burst Q-less QR Decomposition block computes the upper-triangular factor R of the economy size QR decomposition of
\left[\begin{array}{c}\lambda {I}_{n}\\ A\end{array}\right]
A(i,:) — Rows of complex matrix A
Rows of complex matrix A, specified as a vector. A is a m-by-n matrix where m ≥ 2 and n ≥ 2. If A is a fixed-point data type, A must be signed and use binary-point scaling. Slope-bias representation is not supported for fixed-point data types.
R(i,:) — Rows of upper-triangular matrix R
Rows of the economy size QR decomposition matrix R, returned as a scalar or vector. R is an upper-triangular matrix. The output at R(i,:) has the same data type as the input at A(i,:).
Whether the output data is valid, specified as a Boolean scalar. This control signal indicates when the data at output port R(i,:) is valid. When this value is 1 (true), the block has successfully computed the matrix R. When this value is 0 (false), the output data is not valid.
Use fixed.getQlessQRDecompositionModel(A) to generate a template model containing a Complex Burst Q-less QR Decomposition block for complex-valued input matrix A.
Real Burst Q-less QR Decomposition | Complex Partial-Systolic Q-less QR Decomposition | Complex Burst QR Decomposition
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Anisotropic L 2 -estimates of weak solutions to the stationary Oseen-type equations in 3D-exterior domain for a rotating body
January, 2010 Anisotropic
{L}^{2}
-estimates of weak solutions to the stationary Oseen-type equations in 3D-exterior domain for a rotating body
Stanislav KRAČMAR, Šárka NEČASOVÁ, Patrick PENEL
We study the Oseen problem with rotational effect in exterior three-dimensional domains. Using a variational approach we prove existence and uniqueness theorems in anisotropically weighted Sobolev spaces in the whole three-dimensional space. As the main tool we derive and apply an inequality of the Friedrichs-Poincaré type and the theory of Calderon-Zygmund kernels in weighted spaces. For the extension of results to the case of exterior domains we use a localization procedure.
Stanislav KRAČMAR. Šárka NEČASOVÁ. Patrick PENEL. "Anisotropic
{L}^{2}
-estimates of weak solutions to the stationary Oseen-type equations in 3D-exterior domain for a rotating body." J. Math. Soc. Japan 62 (1) 239 - 268, January, 2010. https://doi.org/10.2969/jmsj/06210239
Keywords: anisotropically weighted $L^{2}$ spaces , Oseen problem , rotating body
Stanislav KRAČMAR, Šárka NEČASOVÁ, Patrick PENEL "Anisotropic
{L}^{2}
-estimates of weak solutions to the stationary Oseen-type equations in 3D-exterior domain for a rotating body," Journal of the Mathematical Society of Japan, J. Math. Soc. Japan 62(1), 239-268, (January, 2010)
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Mathematics | Free Full-Text | Semi-Local Integration Measure of Node Importance
Improving Facial Emotion Recognition Using Residual Autoencoder Coupled Affinity Based Overlapping Reduction
Multicriteria Optimization Problem on Prefractal Graph
Temporal Artificial Stress Diffusion for Numerical Simulations of Oldroyd-B Fluid Flow
Ban Kirigin, T.
Bujačić Babić, S.
Perak, B.
Tajana Ban Kirigin
Sanda Bujačić Babić
Department of Mathematics, University of Rijeka, R. Matejčić 2, 51000 Rijeka, Croatia
Faculty of Humanities and Social Sciences, University of Rijeka, Sveučilišna Avenija 4, 51000 Rijeka, Croatia
Academic Editors: Jonatan Lerga, Ljubisa Stankovic, Nicoletta Saulig and Cornel Ioana
Numerous centrality measures have been introduced as tools to determine the importance of nodes in complex networks, reflecting various network properties, including connectivity, survivability, and robustness. In this paper, we introduce Semi-Local Integration (
SLI
), a node centrality measure for undirected and weighted graphs that takes into account the coherence of the locally connected subnetwork and evaluates the integration of nodes within their neighbourhood. We illustrate
SLI
node importance differentiation among nodes in lexical networks and demonstrate its potential in natural language processing (NLP). In the NLP task of sense identification and sense structure analysis, the
SLI\phantom{\rule{0.166667em}{0ex}}
centrality measure evaluates node integration and provides the necessary local resolution by differentiating the importance of nodes to a greater extent than standard centrality measures. This provides the relevant topological information about different subnetworks based on relatively local information, revealing the more complex sense structure. In addition, we show how the
SLI\phantom{\rule{0.166667em}{0ex}}
measure can improve the results of sentiment analysis. The
SLI
measure has the potential to be used in various types of complex networks in different research areas. View Full-Text
Keywords: centrality measure; node importance; complex networks; applications of graph data processing; lexical graph analysis; sentiment analysis centrality measure; node importance; complex networks; applications of graph data processing; lexical graph analysis; sentiment analysis
Link: https://github.com/sbujacic/SLI-Node-Importance-Measure
Description: This is the Python implementation of the Semi-Local Intregation (SLI) measure, a node centrality measure for undirected and weighted graphs that takes into account the coherence of the locally connected subnetwork and evaluates the integration of nodes within their neighbourhood.
Ban Kirigin, T.; Bujačić Babić, S.; Perak, B. Semi-Local Integration Measure of Node Importance. Mathematics 2022, 10, 405. https://doi.org/10.3390/math10030405
Ban Kirigin T, Bujačić Babić S, Perak B. Semi-Local Integration Measure of Node Importance. Mathematics. 2022; 10(3):405. https://doi.org/10.3390/math10030405
Ban Kirigin, Tajana, Sanda Bujačić Babić, and Benedikt Perak. 2022. "Semi-Local Integration Measure of Node Importance" Mathematics 10, no. 3: 405. https://doi.org/10.3390/math10030405
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On the Formalization of MEV | Flashbots
On the Formalization of MEV
04.12.21 · 13 min read
Thanks to Phil Daian, Alex Obadia, and Mahimna Kelkar for plenty of discussions on the topic.
Since its introduction in the Flashboys 2.0 paper of 2019 by Daian et al., a lot has been said about Miner (now Maximal) Extractable Value, or MEV. In particular, the launch of the Flashbots Auction propelled what is today a billion dollar economy across various blockchains and centralized exchanges. From thrilling Twitter threads to academic research papers, the MEV phenomenon has captured a central spot in the cryptocurrency discourse. Oddly, however, there is no agreed upon formal definition of MEV.
While some may argue that the widely shared, intuitive notion of MEV will be sufficient in most scenarios, we believe that proper formalization is critical to establishing a foundation upon which complex theorizing can take place. As Tim Roughgarden put it in a recent talk on building a theory of DeFi, the first step before "easy" and later "difficult" theorems is to have definitions and basic vocabulary. Further, as was evidenced by a recent public discussion where some claimed that arbitrage is not MEV, it might even be the case that we don't share an intuitive notion of MEV after all! A unifying formal definition of MEV would certainly help.
As it turns out, however, formalizing MEV in a robust, general way is no easy task. In this post, we explore some of the difficulties we encounter when trying to come up with such a definition. We start by reviewing some of the existing formalizations, point out some of their problems, and go on a quest trying to amend some of them. While we present new definitions that improve on some of these issues, our main contribution rests in highlighting many of the subtleties involved, paving the way for a more systematic approach in future work around MEV.
Current MEV definitions#
The original Flashboys paper defines MEV as "the total amount of Ether miners can extract from manipulation of transactions within a given timeframe, which may include multiple blocks’ worth of transactions", but stays short of attempting a formal definition. Most recently, the widely adopted working definition rings something like:
Perhaps the definition that comes closest to formalizing this is the one given in the recent Clockwork Finance paper via the following two expressions:
\mathsf{EV}(p,B,s)=\max_{(B_1, \ldots, B_k)\in B} \left\{ b(p, s_k)-b(p,s)\right\} \tag{1}
k\mathsf{-MEV}(p,s)=\mathsf{EV}(p, \mathsf{validBlocks}_k(p,s), s). \tag{2}
Here, EV is the extractable value by player
p
s
given a set of valid block sequences
B
(B_1, \ldots, B_n)
is one such sequence, and
b(p, s_k)
is the balance of player
p
in the state resulting of applying blocks
(B_1, \ldots, B_k)
s
. k-MEV is the k-maximal extractable value by a player
p
s
acting as block proposer, where
\mathsf{validBlocks}_k
is the set of all valid block sequences of
k
blocks that
p
can create, and single-block MEV is just 1-MEV.
These expressions were slightly tweaked from those in the paper for notational simplicity, but are otherwise equivalent. In particular, we consider balances of players as opposed to accounts (omitting a sum over accounts controlled by a player), and remove the explicit reference to the chain's native asset; we will return to this point later.
We will use this definition of MEV as a starting point, noting that most other papers provide similar definitions that face the same limitations, or do not provide formal definitions at all.
Existing limitations#
We start by noting a fatal flaw in the above expressions: the maximal extractable value depends on the player
p
! This means that if
p
has, say, some pending airdrop claim, their MEV will be larger than for a player who doesn't. While this might make sense for the extractable value, it is certainly at odds with the idea of a "permissionlessly extracted" value.
Upon closer inspection, it is not entirely clear what the notion of "player" is actually referring to. We can identify at least three intertwined meanings: i) a player as a transaction signer, having balances and controlling accounts, ii) a player as an actor in the protocol game, having (or lacking) block proposing rights, and iii) a player in the networking sense, a node operator affected by latencies and having a unique mempool view.
While the latter meaning does probably not apply in this formulation (although we will come back to it later), meanings i) and ii) are somewhat conflated:
p
certainly refers to i) when talking about balances in (1), but in going from (1) to (2) we also ascribe
p
block proposing rights, in line with meaning ii). We argue that a proper definition of MEV should be independent of the player in the sense of i), that is, it should not depend on particular signing rights. With respect to ii), we will define MEV given block proposing privileges. This effectively decouples the problem into value extraction on one hand, and obtaining sequencing rights on the other, which might prove useful when thinking about extraction costs, network security, etc.
Other caveats with the above definitions are the treatment of multi-block MEV (related to the tangling of meanings i) and ii) above), the omission of fees arising from reverted transactions, and the inadequacy of the notion of blocks when attempting to generalize MEV to the cross-domain setting. In what follows, we attempt to patch the definitions to solve some of these issues when possible, and discuss some other difficulties we find along the way.
Patching MEV#
As mentioned above, the first task is to come up with a truly permissionless MEV definition. We will keep the player dependency in the definition of extractable value, but get rid of it when moving to MEV. We note here that we use player in sense i) above, giving it, for both EV and MEV, full block sequencing rights. We propose the following:
\mathsf{EV}(p, s)=\max_{B \in \mathsf{validBlocks}(p)} \left\{ b(p, B(s))-b(p,s)\right\} \tag{3}
\mathsf{MEV}(s)=\min_{p\in P}\{\mathsf{EV}(p, s)\}. \tag{4}
The first expression here closely resembles (1), but we removed the dependency on the set of valid block sequences, which is implicit, and we're only considering a single block (more on this later). Here
\mathsf{validBlocks}(p)
is the set of valid blocks that can be proposed by
p
\mathsf{validBlocks}_1(p,s)
before, omitting the amount of blocks and state dependency for succinctness).
B(s)
, in turn, denotes the state obtained by applying block
B
on top of state
s
In expression (4), we obtained a definition for MEV that, as desired, is independent of the player (denoting
P
the set of players). While it might perhaps be counterintuitive to find a minimum in the definition of maximal extractable value, this minimum simply encodes the idea that extraction should be permissionless. EV already takes care of maximizing, the value extractable permissionlessly is the one the least privileged actor can take from the network (again, assuming they have block proposing rights).
This definition begs the question, however, what happens when extraction requires upfront capital? Definition (2) did not have this problem since it had an explicit dependency on the player, but having now removed it, we need to take into account that some MEV might only be extractable at certain levels of initial capital. We note however that gas fees are not part of the requirement here, since a proposer can sequence "free" transactions at will, so that in general MEV might be greater than zero even with no initial capital.
Still, we want to make the dependency on capital explicit, since many MEV opportunities depend on it. We write (using EV from (3)):
\mathsf{MEV}(s;K)=\min_{\{p\in P | b(p,s)\geq K\}}\{\mathsf{EV}(p, s)\}. \tag{5}
This definition tells us that the maximal extractable value in state
s
for initial capital
K
is the value that can be extracted by any player that possesses at least that amount of initial capital.
The next step we consider is what happens with transactions in the mempool. In the above we were considering "valid blocks", but crucially these can contain reverted transactions, that pay fee, but do not modify the state. This is a tricky point, as it involves meaning iii) above for the player due to the fact that different views of the mempool yield different sets of valid blocks. While in practice searchers extracting MEV are constantly looking at the mempool for opportunities, transactions will eventually need to be included in a block to modify the state and give rise to the opportunity, so there is no loss of generality in terms of valid transactions if we only consider state changes as opposed to the more general notion of valid blocks. We do lose reverted transactions as a source of MEV in this case, so we could try to modify our formulas to include a view of the mempool dependent on the player, but this would conflate meanings i) and iii), and we would run into trouble when minimizing over players. Considering that the mempool architecture is particular only to some domains, this would also limit the generalizability of the expressions. We thus explicitly leave out reverted transactions as a source of MEV, but note that they are part of the revenue that sequencers take home, and contribute to the negative externalities of MEV extraction, as quantified by the extractable value cost.
Leaving out reverted transactions enables us to go even further, beyond the notion of blocks, which will enable us to consider MEV in more general domains, like centralized exchanges. We rewrite our definition for extractable value as:
\mathsf{EV}(p, s)=\max_{\left\{s'\in S|s\xrightarrow{a_p} s'\right\}} \left\{ b(p, s')-b(p,s)\right\}. \tag{6}
S
is the set of all states, and the notation
s\xrightarrow{a_p} s'
means that state
s'
is reachable from state
s
by some action or sequence of actions
a_p
by player
p
. Together with equation (5) above, we achieved defintions that will allow us to easily generalize to the cross-domain case (see below), and solves most of the issues we encountered with definitions (1) and (2).
Outstanding issues and extensions#
In patching the MEV definition, we moved to single blocks, sweeping under the rug the issue of multi-block MEV. In fact, this is automatically taken into account by our latest expressions (5) and (6), since by expressing EV in terms of state as opposed to blocks, the formulas apply to whatever period the proposer has ordering rights in. The question now becomes one of how to get those ordering rights. In order to do this cleanly we need to ascribe probabilities for the different events (say producing a single block, two consecutive blocks, etc.), so we can come up with an expected value for the total MEV. This, however, is beyond the scope of the MEV formalization, since expression (5) can be simply plugged in once the adequate ensemble is defined.
Another topic we touched upon in passing is that of cross-domain MEV. In a world where different chains (or more generally domains) have their own mechanisms for state updates, but are effectively linked by dependencies in their states (think an L1 deposit affecting L2 balances when processed), we expect to find MEV that can be only extracted by sequencing state changes jointly in more than one domain. Our formulation in terms of states is amenable to this extension, with the caveat that different domains have different native assets, which we need to take into account. We won't go into the details here, but this can be tackled introducing pricing functions for translating from one domain to the next. At first approximation, we can take a pricing function
p_{i\rightarrow j}
to go from the native asset in domain
i
to the one of domain
j
, and ask that
p_{j\rightarrow i}=1/p_{i \rightarrow j}
. More realistically, we expect price to be a player-dependent function of many factors as the different volumes of the assets in the different domains, the trust assumptions of the domains, etc.
We note that, throughout, we considered EV and MEV as revenue to the player, never taking into account the costs. This bodes well with our definitions in terms of players with given ordering rights, since getting those rights is arguably the costliest component of MEV extraction (although compute cost might be non-trivial considering the ordering problem is an NP-complete knapsack problem). In any case, it seems cleaner to think of MEV as only a revenue component, and consider the extraction costs separately. Like in the multi-block setting, we can define a probabilistic ensemble for obtaining the ordering rights, and consider the costs associated to each probability distribution. It is trickier, however, in that ordering rights are typically granted in units that are characteristic of each domain (e.g. propose one block), while costs are typically expressed as rates (per unit of time). So while MEV will usually come in, say, blocks, the cost of producing those blocks will be expressed in units of time, and the specifics of their relation will be particular to each domain. How each domain achieves finality will also be critical to establishing this relation (perhaps there was a great MEV opportunity 1 year ago, but the cost of re-orging the chain to get it would be prohibitive), so we don't expect a general formulation of MEV to accommodate it.
Finally, we have only considered "sure-thing" MEV by expressing it in terms of balances that increase after a state change (for the MEV to be positive). This falls short of describing the more general notion of "probabilistic MEV", where actors are comfortable taking risk in expectation of later rewards. Examples of this are buyouts of new token listings in expectation of rising prices, or more esoterically front-running of NFT bids. It is likely that most of these opportunities can be described by incorporating pricing functions, and we look forward to seeing work in this direction.
The burgeoning phenomenon of MEV begs for a consistent formal approach to unlock proper theory to emerge (think automated auditing of MEV exposure of smart contract systems for an example, in line with the work presented in the Clockwork Finance paper cited above). Formalizing MEV, however, involves droves of technicalities that usually trade off generality for completeness (like the case of whether to include reverted transactions). Here, we provided a clear meaning to the notion of players, which led us to separate the problem of achieving sequencing rights from that of value extraction, allowing us to go to great generality in defining MEV. Our formulas (5) and (6) provide a consistent, easily generalizable definition that can be taken to the multi-domain world. We also highlighted many of the issues faced in achieving formal definitions of MEV, which we hope will allow for a more systematic treatment of the subject.
« Speeding up the EVM (part 1)
Unity is Strength - A Formalization of Cross-Domain Maximal Extractable Value »
Current MEV definitions
Patching MEV
Outstanding issues and extensions
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Home : Support : Online Help : Connectivity : MTM Package : floor
greatest integer smaller than or equal to a number
floor(M)
floor(x) is the greatest integer less than or equal to x.
The floor(M) function computes the element-wise floor of M. The result, R, is formed as R[i,j] = floor(M[i,j]).
\mathrm{with}\left(\mathrm{MTM}\right):
M≔\mathrm{Matrix}\left(2,3,'\mathrm{fill}'=-3.6\right):
\mathrm{floor}\left(M\right)
[\begin{array}{ccc}\textcolor[rgb]{0,0,1}{-4}& \textcolor[rgb]{0,0,1}{-4}& \textcolor[rgb]{0,0,1}{-4}\\ \textcolor[rgb]{0,0,1}{-4}& \textcolor[rgb]{0,0,1}{-4}& \textcolor[rgb]{0,0,1}{-4}\end{array}]
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Systems of Particles and Rotational Motion - Live Session - NEET & AIIMS 2019
Systems of Particles and Rotational Motion - Live Session - NEET & AIIMS 2019Contact Number: 9667591930 / 8527521718
A cuboidal block of height a nad width b is placed on the horizontal surface with sufficient friction then for a given force
1. Probability of toppling is more of b > a
2. Probability of toppling is more of a > b
3. Probability of toppling is more of a = b
4. Block will not topple
Calculate the velocity of the center of mass of the system of two particles each of mass 2 kg as shown in figure
A rod of length 2l is bent as shown in figure. Coordinates of centre of mass are
\left(\frac{2l}{3}, \frac{l}{3}\right)
\left(\frac{l}{8}, \frac{l}{8}\right)
\left(\frac{l}{4} , \frac{3l}{4}\right)
\left(\frac{l}{3} , \frac{l}{6}\right)
A stick of length L mass M initially upright on a frictionless floor, starts falling, then
1. Center of mass will fall vertically down
2. Centre of mass will follow a circular path
3. Centre of mass will follow any curve path
A disc of radius R and mass M is under pure rolling when a force f is applied at the top most point (as shown in figure) and there is sufficient friction between the disc and the horizontal surface, then
{a}_{cm} = \frac{f}{M}
{a}_{cm} < \frac{f}{M}
{a}_{cm} > \frac{f}{M}
A shell following a parabolic path explodes somewhere in its fight. The centre of mass of fragments will move in
1. Tangential direction
2. Radial direction
3. Horizontal direction
4. Same parabolic path
A ring of mass m and radius R is acted upon by a force F as shown in the figure, there is sufficient friction between the ring and the ground then the force of friction necessary for pure rolling is
\frac{F}{2}
\frac{F}{3}
\frac{F}{4}
An elliptical disc shown in the figure is rotated turn about x-x', y-y' and z-z' axes passing through the centre of mass of the disc. Moment of inertia of the disc is
1. Same about all the three axes
2. Maximum about z-z' axes
3. Maximum about y-y' axis
4. Same about x-x' and y-y' axis
A particle of mass m = 3 kg is projected at an angle of
45°
with the horizontal with a speed of
20\sqrt{2}
m/s. The angular momentum of the particle at the highest point of trajectory about a horizontal axis passing through the origin and perpendicular to the plane of motion is
Moment of inertia of a rod of mass m and length/ about an axis at a distance
\frac{1}{4}
from oneof the ends of the rod and perpendicular to its length is
\frac{19}{48}M{l}^{{2}^{}}
\frac{7}{48}m{l}^{2}
\frac{7}{38}M{l}^{2}\phantom{\rule{0ex}{0ex}}
\frac{19}{38}m{l}^{2}
A rod of length L is hinged at one end. It is brought to a horizontal position and released. The angular velocity of the rod when it is in a vertical position is
\sqrt{3g/L}
\sqrt{2g/L}
\sqrt{g/2L}
\sqrt{g/L}
If a spherical ball is under pure rolling on a table, then the fraction of its total kinetic energy associated with rotation is
\frac{3}{5}
\frac{2}{7}
\frac{2}{5}
\frac{3}{7}
An automobile engine develops
{10}^{5}
W power when rotating at a speed of 1800 rad/minute. The average torque delivered by the engine is
\frac{1}{3}
×
{10}^{2}
\frac{1}{3}× {10}^{4}
\frac{1}{3} × {10}^{6}
\frac{1}{3} × {10}^{8}
A wheel starts from rest na attains an angular velocity of 20 rev/s after being uniformly accelerated for 20 s . The total angle is radian through which it has turned in 10 s is
\mathrm{\pi }
\mathrm{\pi }
\mathrm{\pi }
\mathrm{\pi }
A solid cylinder, a solid sphere, and a hollow sphere each of mass m and radius r are released from the top of a smooth inclined plane. Then which of the bodies has minimum acceleration down the plane?
1. Solid cylinder
2. Solid sphere
4. All have same acceleration
A solid cylinder of mass m and radius r is rolling with angular speed
\omega
on a horizontal plane. The magnitude of its angular momentum about origin O is
m{r}^{2}\omega
m{r}^{2}\omega
m{r}^{2}\omega
m{r}^{2}\omega
1. The centre of mass of a two-particle system lies on the line joining the two particles, being closer to the heavier particle
1. In rolling, the point of contact of the rolling body remains at rest relative to the surface on which it is rolling
3. Parallel axis theorem is applicable only for laminar bodies
4. A particle moving on a straight line may have non-zero angular momentum about a point
Two rigid bodies A and B rotate with angular momentum
{L}_{A}
{L}_{B}
{L}_{A }/ {L}_{B}
= 2. If their moment of inertia about axis of rotation are
{l}_{A}
{l}_{\mathbit{B}}
{l}_{A}
{l}_{\mathbit{B}}
= 4 , then the ratio of their kinetic energies is
{K}_{A}
{K}_{B}
John is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. Now, John stretches his arms so that moment of inertia of the system doubles. The kinetic energy of the system now is
A solid cylinder of mass m and radius r is rotating about its longitudinal axis (vertical with an angular speed
\text{'}\omega \text{'}
. If a disc of mass 2m and radius 2r is gently placed on it coaxially, then the new angular velocity of the system is
\omega
\frac{\omega }{4}
\frac{\omega }{8}
\frac{\omega }{9}
Calculate the torque acting on the disc in the given arrangement (Radius of disc 1m and mass m)
1. 2 mg/3
2. mg/3
4. 4 mg/s
The speed of the centre of mass of a homogenous sphere after rolling down an inclined plane of vertical height h from rest without sliding is
\sqrt{gh}
\sqrt{gh/5}
\sqrt{4gh/3}
\sqrt{10gh/7}
A rod of mass 4m and length l hinged at its centre is placed on a horizontal surface. A bullet of mass m moving with velocity v strikes the end A of the rod and gets embedded in it. The angular velocity with which the system rotates about its centre of mass after the bullet strikes the rod
\omega = \frac{6v}{7l}
\omega = \frac{5v}{4l}
\omega = \frac{2v}{3l}
\omega = \frac{v}{3l}
The magnitude of the angular momentum of a wheel change from 2L to 3L in 5 sec. by a constant torque acting opposite to the initial direction of rotation. What is the magnitude of the torque?
\frac{L}{5}
\frac{2L}{5}
\frac{3L}{5}
A solid cylinder is rolling without slipping with a velocity of its centre of mass v and angular velocity of its centre of mass
\omega
on a horizontal frictionless surface as shown in the figure. If it collides with a frictionless vertical wall X, then after collision its velocity and angular velocity respectively become
\frac{v}{2}, \frac{\omega }{2}
-v, -\omega
-v, \omega
v, -\omega
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Arihant - Class X - Life Processes : Transportation [ (Chapter - 6 (c) ]
Arihant - Class X - Life Processes : Transportation [ (Chapter - 6 (c) ]Contact Number: 9667591930 / 8527521718
2. transport of food
3. transport of amino acid
How is transportation of water in xylem tissue different from translocation of food in phloem tissue?
State the role and function of the following.
Why SA node is known as the pacemaker of heart?
\overline{ \mathrm{Organisms} \mathrm{Chambers} \mathrm{of} \mathrm{Heart} }\phantom{\rule{0ex}{0ex}}\overline{ Fishes ..............................}\phantom{\rule{0ex}{0ex}}\overline{ \mathrm{Amphibians} ..............................}\phantom{\rule{0ex}{0ex}}\overline{ \mathrm{Reptiles} ..............................}\phantom{\rule{0ex}{0ex}}\overline{ \mathrm{Human} \mathrm{beings} ..............................}\phantom{\rule{0ex}{0ex}}\overline{ }
Write the functions of two upper chambers of human heart.
What makes red blood corpuscles red?
Why are values present in heart and veins?
Why the walls of ventricles are thicker than the walls of atria?
What will happen according to you, of platelets are not present in the blood?
Which mechanism plays an important role in transport of water in plants?
(i) During daytime
(ii) At night
Draw a labelled diagram of the pumping machine in human beings.
In the given diagram that shows a vertical section through the human heart, which structure separates out the oxygenated blood from deoxygenated blood.
Explain why do multicellular organisms need a transportation system for carrying food and oxygen?
Enumerate the differences between lymphatic capillaries and blood capillaries.
What is the advantage of having four-chambered heart?
Write a function of (i) blood vessels (ii) blood platelets.
During one cycle, how many times does blood go to the heart of fish and why?
Mention the two main components of the transport system in plants. State one function of each one of these components?
From where do roots obtain water and minerals?
How are water and minerals absorbed by the plant?
State the role played by transpirational pull in transportation?
(ii) Pulmonary artery
(iii) Pulmonary vein
What are capillaries? State the function performed by them?
The body temperature of some organisms depends on the temperature of the environment. Comment.
Only deoxygenated blood is pumped through a fish's heart. Is it true? Justify your answer.
Which plant part needs the sugar stored in root or stem tissue in spring season?
Explain, why transportation of materials is necessary in animals?
List out various components of blood along with their functions.
In mammals and birds, why is it necessary to separate oxygenated and deoxygenated blood?
List the features of RBCs as the carrier of oxygen.
What is the differences between arteries, veins and capillaries?
List in tabular form, three differences between arteries and veins.
Write the function of each of the following components of the transport system in human beings:
(i) Blood vessels
(i) Arteries have thick and elastic walls
(ii) Arteries form capillaries
(i) Transport of food in plants requires living tissues and energy. Justify this statement.
(ii) Name the components of food that are transported by the living tissues.
What is 'translocation'? Why is it essential for plants? Where in plants are the following synthesised?
What is translocation? How does it take place in plants?
(i) Draw a schematic representation of transport and exchange of oxygen and carbon dioxide during transportation of blood in human
beings and label following parts on it.
Lung to capillaries, pulmonary artery to lungs, aorta to body, pulmonary veins from lungs.
(ii) What is the advantage of having separate channels of heart for oxygenated and deoxygenated blood in mammals and birds?
What is the functional difference between four-chambers of the heart?
(i) What do you understand by transpiration?
(ii) What is the role of transpiration in transportation? Explain with diagram.
(iii) Which plant part helps in unidirectional flow of water?
Draw the sectional view of human heart and label the following parts given below:
(i) Chamber where oxygenated blood from lungs is collected.
(ii) Largest blood vessel in our body.
(iii) Muscular wall separating right and left chambers.
(iv) Blood vessel that carries blood from heart to the lungs.
(i) Part which receives deoxygenated blood from vena cava.
(ii) Part which sends deoxygenated blood to lung through pulmonary artery.
(iii) Part which receives oxygenated blood from lungs.
(iv) Part which sends oxygenated blood to all parts of the body through aorta.
(i) The chamber of heart that pumps out deoxygenated blood.
(ii) The blood vessel that carries away oxygenated blood from the heart.
(iiii) The blood vessel that receives deoxygenated blood from the lower part of our body.
For observing transpiration in plants, a student prepared the setup and placed it in a cool and shady area and what will his observations be?
If a student has kept a plant to observe transpiration. How will he/she recognist that process is laking place?
Does evaporation play a role in the occurrence of transpiration? How?
If we want to observe the transpiration process in plants, what are the basic requirements?
Sunaina was travelling with her family by car. While moving on the way, they saw a biker on the road who was bleeding profusely. Her mother asked Sunaina's father to stop the car and help the person. Her father however, did not stopped as he feared that they would have to deal with the police enquiry, if they would stop.
(i) What happens, if a person bleeds profusely?
(ii) What will you do, if the hospital refuses to provide treatment unless the accident case is registered by police?
(iii) What values were shown by Sunaina's mother?
Prateek, an employee in MNC, planned to organise a blood donation camp in his office with support of red club society. He motivated everybody in his office to participate in the good cause by donating blood.
He also explained them that the donated blood will be stored in blood bank to be used whenever needed by patients.
(i) Why the camp was organised?
(ii) How the blood is prevented from clotting in the blood bank?
(iii) What values are shown by Prateek?
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Generalized lattice-point visibility in $\mathbb{N}^k$
2021 Generalized lattice-point visibility in $\mathbb{N}^k$
Carolina Benedetti, Santiago Estupiñan, Pamela E. Harris
A lattice point
\left(r,s\right)\in {ℕ}^{2}
is said to be visible from the origin if no other integer lattice point lies on the line segment joining the origin and
\left(r,s\right)
. It is a well-known result that the proportion of lattice points visible from the origin is given by
1∕\zeta \left(2\right)
\zeta \left(s\right)={\sum }_{n=1}^{\infty }1∕{n}^{s}
denotes the Riemann zeta function. Goins, Harris, Kubik and Mbirika generalized the notion of lattice-point visibility by saying that for a fixed
b\in ℕ
\left(r,s\right)\in {ℕ}^{2}
b
-visible from the origin if no other lattice point lies on the graph of a function
f\left(x\right)=m{x}^{b}
m\in ℚ
, between the origin and
\left(r,s\right)
. In their analysis they establish that for a fixed
b\in ℕ
the proportion of
b
-visible lattice points is
1∕\zeta \left(b+1\right)
, which generalizes the result in the classical lattice-point visibility setting. In this paper we give an
-dimensional notion of
b
-visibility that recovers the one presented by Goins et. al. in two dimensions, and the classical notion in
dimensions. We prove that for a fixed
b=\left({b}_{1},{b}_{2},\dots ,{b}_{n}\right)\in {ℕ}^{n}
b
-visible lattice points is given by
1∕\zeta \left({\sum }_{i=1}^{n}{b}_{i}\right)
Moreover, we give a new notion of
b
-visibility for vectors
b=\left({b}_{1}∕{a}_{1},{b}_{2}∕{a}_{2},\dots ,{b}_{n}∕{a}_{n}\right)\in {\left(ℚ\setminus \left\{0\right\}\right)}^{n},
with nonzero rational entries. In this case, our main result establishes that the proportion of
b
-visible points is
1∕\zeta \left({\sum }_{i\in J}|{b}_{i}|\right)
J
is the set of the indices
1\le i\le n
{b}_{i}∕{a}_{i}<0
. This result recovers a main theorem of Harris and Omar for
b\in ℚ\setminus \left\{0\right\}
in two dimensions, while showing that the proportion of
b
-visible points (in such cases) only depends on the negative entries of
b
Carolina Benedetti. Santiago Estupiñan. Pamela E. Harris. "Generalized lattice-point visibility in $\mathbb{N}^k$." Involve 14 (1) 103 - 118, 2021. https://doi.org/10.2140/involve.2021.14.103
Received: 28 January 2020; Revised: 13 September 2020; Accepted: 28 September 2020; Published: 2021
Keywords: generalized lattice-point visibility , lattice-point visibility , Riemann zeta function
Carolina Benedetti, Santiago Estupiñan, Pamela E. Harris "Generalized lattice-point visibility in $\mathbb{N}^k$," Involve: A Journal of Mathematics, Involve 14(1), 103-118, (2021)
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Home > Course Outline > Lesson 4 - Measurement and Estimations of the Solar Resource > 4.4 Empirical Correlation for Estimating Components of Light
Sengupta et al. (2015) Best Practices Handbook for the Collection and Use of Solar Resource Data for Solar Energy Applications [1]. NREL/TP-5D00-63112 p. 63-81 : Chapter 4. Modeling Solar Radiation--Current Practices
C. A. Gueymard (2008) From Global Horizontal to Global Tilted Irradiance: How accurate are solar energy engineering predictions in practice? [2] Solar 2008 Conference, San Diego, CA, American Solar Energy Society
Please make sure you read all of Ch 8 in SECS for this lesson, and focus on the section "Empirical Correlation for Components" and this page content. In the two additional readings, it is OK to scan the Stoffel Ch 4 and the Gueymard paper for key elements that are parallel with the lesson and the textbook. I included them also so that you could look back to them later as resources for your career development.
Which is better, direct measurements or making do with estimations from less data?
Now that we have our measurements, how do we make use of them to estimate irradiance on any given tilted surface? In the following section, we want to sort out the way that we measure light in comparison to the way that we use solar data for simulations of SECS in software like SAM (System Advisor Model). The SAM model will only have hourly Global Horizontal Irradiation metrics to use (I), but we will want to estimate the hourly irradiation for an oriented surface (POA, It).
As you move through this lesson, think about the Plane of Array (POA) for a Solar Energy Conversion System, and think about how we often measure irradiance using a horizontal pyranometer (and ONLY a horizontal pyranometer, unfortunately). What is the value of DNI in estimating the solar resource components for any given tilted (and maybe even moving) surface?
Estimating Light from Less Data (only GHI available)
As you have learned from reading Chapter 8, the main way that meteorologists have measured irradiation is from a horizontal surface. However, most of our SECSs are mounted on non-horizontal surfaces. This presents a challenge.
A component is a term for the groups of physical orientations and scattering of light (e.g., diffuse component, beam component).
We use the concept of components to break the sky dome and the ground into digestible chunks for receiving or reflective surfaces with common emission/absorption/scattering characteristics (e.g., direct, diffuse, circumsolar diffuse, ground reflected diffuse).
A solar collector with a non-horizontal orientation (tilt:
\beta \ne 0
)will receive solar irradiance from a multitude of reflecting and scattering surfaces, including the beam of the Sun, the refracted solar light from the broad sky, and the reflected light from the ground.
When a collector is oriented horizontally, it does not "see" the ground. In fact, per World Meteorological Organization requirements [3] (Ch. 7: Measurement of Radiation), a pyranometer measuring downwelling (light coming down from the Sun) irradiance must not measure the irradiance from the ground. This means we are missing a key piece of information with only a GHI measure from a single fixed, horizontal pyranometer.
When measuring the solar irradiation incident on a surface of interest, we measure the total or Global solar irradiance, which is a sum of the two components: Beam and Diffuse. Here, we present an equation for components of irradiance, G (we could have shown components of hourly irradiation in the same way) incident upon a horizontal surface.
G={G}_{b}+{G}_{d}
Solar radiation that reaches the earth from the sun is generally not constant. A number of factors can affect the amount of radiation we receive. These factors include time of day and year, state of the atmosphere, and presence of aerosols. As stated earlier, the total solar radiation incident on a surface comprises of different components, and there is a simple reason for this. Not all the light emitted by the sun reaches the surface of the earth without any interference. As the emitted light passes through the atmosphere, a number of things generally happen. Some of the light may be absorbed, scattered, or reflected by the air molecules, water vapor, and aerosols. This portion eventually reaches the earth but not with the full intensity it had when originally emitted by the sun. We call this diffuse irradiance (Gd).
When a collector is tilted: the diffuse component from the ground tends to increase in contribution.
{G}_{t}={G}_{b,t}+{G}_{d,t}+{G}_{g,t}
Air chemistry in the path of the beam will scatter the energy into a small cone of light, called the circumsolar component of the sky dome. Next, the scattering events that occur during the day produce a blue or white hue across the hemispherical surface. This is referred to as the sky diffuse component of irradiance. A horizon diffuse component is observed as the path length increases for scattering in the sky. Finally, the reflectance of the ground surfaces will contribute an extra component as long as the collection system is not mounted horizontally. Some light will be reflected from the ground back to the tilted surface. This component is appropriately called ground reflected component.
{G}_{d,t}={G}_{circ,t}+{G}_{sky,t}+{G}_{hor,t}
There also exist portions of the emitted light that reach the earth directly with no interference from the atmosphere. This is called the direct or beam irradiance (Gb). If we have a measurement of DNI (Direct Normal Irradiance), then we can quickly estimate beam irradiance for the horizontal surface via the cosine relation to the zenith angle (
{\theta }_{z}
). Atmospheric conditions, however, have a strong influence on the amount of beam radiation we receive. On clear, dry days, atmospheric condition can attenuate beam radiation by around 10% and by nearly 100% on very dark cloudy days.
Figure 4.4: Diagram of the multiple components of the clear sky.
Credit: Jeffrey R. S. Brownson © Penn State University is licensed under CC BY-NC-SA 4.0 [4]
The Flow of Data from GHI to components to POA
In the following flow chart of data processing, we see that measured irradiance (shortwave, from the Sun) is measured in four typical manners:
GHI (global horizontal irradiance), then integrated to the desired time step (1 min, 5 min, 1 hour)
DNI (direct normal irradiance), not the same as beam horizontal irradiance (Gb) or beam tilted irradiance (Gb,t)
DHI (diffuse horizontal irradiance), using a shadow band or similar device to obscure the beam component
POA (plane of array irradiance), then integrated to the desired time step
Figure 4.5: Flow chart of data processing
In the figure, we have integrated the time step to 1 hour of irradiation on a horizontal and tilted surface, respectively: I and It.
Measurement 1 (GHI) is the most common for a local site assessment in SECS design. Equipment for measuring DNI and DHI are atypical in an application site where the initial site assessment is beginning, and are absent from our satellite maps of the solar resource. Measurement 4 (POA) is becoming more and more popular, as it can potentially remove several steps of error propagation from empirical correlation on site.
Looking across the top line (Measurement 1), we see that we must perform "empirical correlations" using a metric called an "hourly clearness index" (kT) to arrive at "calculated horizontal components of Ib and Id (beam and diffuse hourly irradiation). Then, we must apply an "anisotropic diffuse sky/ground model" and sum the tilted components of irradiation, to finally arrive at a calculated POA irradiation estimate.
Paths 2 and 3 add to the level of precision by stepping past the clearness index correlations (which is error-prone) before applying an anisotropic diffuse sky/ground model and summing to a new calculated POA estimate.
Path 4 skips all of the empirical models and directly measures and integrates the irradiation on a POA surface. The one additional benefit would be to have a DNI measure along with a POA measure, for component decomposition if necessary (required for windows, for example).
[1] https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwjSipPcpsfWAhXF6iYKHYEbAzwQFggoMAA&url=https%3A%2F%2Fwww.nrel.gov%2Fdocs%2Ffy15osti%2F63112.pdf&usg=AFQjCNEo4XDcylSazI5c5DMOnDGcLqvcnA
[3] http://www.wmo.int/pages/prog/www/IMOP/CIMO-Guide.html
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For each equation below, solve for the given variable. If necessary, refer to the Math Notes box in Lesson 1.1.4 for guidance. Show the steps leading to your solution and check your answer.
75=14y+5
\begin{array} \; 75=14y+5\\ 70=14y\\ \; \; y=5 \end{array}
-7r+13=-71
\begin{array}{l} -7r+13=-71\\ \qquad \; -7r=-84\\ \qquad \quad \; \; r=12 \end{array}
3a+11=7a-13
Hint (c and d):
Refer to the process used for parts (a) and (b).
2m+m-8=7
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Alternating Current - Live Session - NEET & AIIMS 2019
Alternating Current - Live Session - NEET & AIIMS 2019Contact Number: 9667591930 / 8527521718
The potential difference V and the current i flowing through an instrument in an ac circuit of frequency f are given by V=5 cos
\omega
t volts and I =2 sin
\omega t amperes \left(where \omega =2\mathrm{\pi f}\right).\mathrm{The} \mathrm{power} \mathrm{dissipated} \mathrm{in} \mathrm{the} \mathrm{instrument} \mathrm{is} \phantom{\rule{0ex}{0ex}}
4. 2.5 W
In an ac circuit I= 100 sin 200
\mathrm{\pi }
t. The time required for the current to achieve its peak value will be:
\frac{1}{100}sec
\frac{1}{200}sec
\frac{1}{300}sec
\frac{1}{400}sec
An alternating current is given by the equation
i={i}_{1}\mathrm{cos} \omega t+{i}_{2} \mathrm{sin} \omega t.
The r.m.s. current is given by
\frac{1}{\sqrt{2}}\left({i}_{1}+{i}_{2}\right)
\frac{1}{\sqrt{2}}{\left({i}_{1}+{i}_{2}\right)}^{2}
\frac{1}{\sqrt{2}}{\left({i}_{1}^{2}+{i}_{2}^{2}\right)}^{1/2}
\frac{1}{\sqrt{2}}{\left(i+{i}_{1}^{2}+{i}_{2}^{2}\right)}^{1/2}
What will be the phase difference between virtual voltage and virtual current, when the current in the circuit is wattless
90°
45°
180°
60°
In a circuit L.C and R are connected in series with an alternating voltage source of
frequency f. The current leads the voltage by 45
°
. The value of C is
\frac{1}{2\mathrm{\pi }\left(2\mathrm{\pi fL}+\mathrm{R}\right)}
\frac{1}{\mathrm{\pi f}\left(2\mathrm{\pi fL}+\mathrm{R}\right)}
\frac{1}{2\mathrm{\pi f}\left(2\mathrm{\pi fL}-R\right)}
\frac{1}{\mathrm{\pi f}\left(2\mathrm{\pi fL}-R\right)}
One 10 V, 60 W bulb is to be connected to 100 V line. The required induction coil has self-inductance of value (f = 50 Hz)
1. 0.052 H
3. 16.2 mH
In the circuit given below, what will be the reading of hte voltmeter
In the circuit shown below, what will be the readings of the voltmeter and ammeter
1. 800 V, 2A
3. 220 V, 2.2 A
In the circuit shown in figure neglecting source resistance, the voltmeter and ammeter reading will respectively, will be
1. 0 V, 3A
2. 150 V, 3 A
A virtual current of 4A and 50 Hz flow in an ac circuit containing a coil. The power consumed in hte coil is 240 W. If the virtual voltage across te coil is 100 V its inductance will be
\frac{1}{3\pi }H
\frac{1}{5\pi }H
\frac{1}{7\pi }H
\frac{1}{9\pi }H
For a series RLC circuit R=X
{}_{L}
=2Xc. The impedance of the circuit and phase difference (between) V and i will be
\frac{\sqrt{5R}}{2}{\mathrm{tan}}^{-1}\left(2\right)
\frac{\sqrt{5R}}{2}{\mathrm{tan}}^{-1}\left(\frac{1}{2}\right)
\sqrt{5 X}{ }_{c} \mathrm{tan}{ }^{-1}\left(2\right)
\sqrt{5}R, {\mathrm{tan}}^{-1}\left(\frac{1}{2}\right)
In the adjoining ac circuit, the voltmeter whose reading will be zero at resonance is
{V}_{1}
{V}_{2}
{V}_{3}
{V}_{4}
In the adjoining figure, the impedance of the circuit will be
Which one of the following curves represents the variation of impedance (Z) with frequency f in series LCR circuit
The figure shows variation of R,
{X}_{L}
{X}_{C}
with frequency f in a series L, C, R circuit. Then for what frequency point, the circuit is inductive
An alternating emf is applied across a parallel combination of a resistance R, capacitance C and an inductance L. If
{I}_{R}
, Il,Ic are the currents through R, L and C respectively, then the diagram which correctly represents, the phase relationship among Tr, IL,Ic and source emf E, is given by
The output current versus time curve of a rectifier is shown in the figure. The average vale of output current in this case is
\frac{{I}_{0}}{2}
\frac{2{I}_{0}}{\mathrm{\pi }}
{I}_{0}
When an ac source of e.m.f. e is connected across a circuit, the phase difference between the e.m.f. e and the current
in the circuit is observed to be
\pi
/4 as shown in the diagram. If the circuit consists possibly only of or in series, find the relationship between the two elements
R=1k\Omega , C=1\mu F
Two sinusoidal voltages of the same frequency are shown in the diagram. What is the frequency are shown in the diagram. What is the frequency, and the phase relationship between the voltages
Frequency in Hz Phase lead of N
over M in radians
-\mathrm{\pi }/4
-\mathrm{\pi }/2
+\mathrm{\pi }/2
-\mathrm{\pi }/4
The voltage across a pure inductor is represented by the following diagram. Which one of the following diagrams will represent the current
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EUDML | A homotopy 2-groupoid from a fibration. EuDML | A homotopy 2-groupoid from a fibration.
A homotopy 2-groupoid from a fibration.
Kamps, K.H.; Porter, T.
Kamps, K.H., and Porter, T.. "A homotopy 2-groupoid from a fibration.." Homology, Homotopy and Applications 1 (1999): 79-93. <http://eudml.org/doc/232947>.
@article{Kamps1999,
author = {Kamps, K.H., Porter, T.},
keywords = {2-groupoid; -groupoid; crossed module; fibration; -groupoid},
title = {A homotopy 2-groupoid from a fibration.},
AU - Kamps, K.H.
TI - A homotopy 2-groupoid from a fibration.
KW - 2-groupoid; -groupoid; crossed module; fibration; -groupoid
2-groupoid,
{\text{cat}}^{1}
-groupoid, crossed module, fibration,
{\text{cat}}^{1}
-groupoid
2
Articles by Kamps
Articles by Porter
|
EUDML | On moduli of -convexity. EuDML | On moduli of -convexity.
k
-convexity.
Lim, Teck-Cheong. "On moduli of -convexity.." Abstract and Applied Analysis 4.4 (1999): 243-247. <http://eudml.org/doc/49181>.
@article{Lim1999,
author = {Lim, Teck-Cheong},
keywords = {modulus of convexity; modulus of -convexity; uniform convexity; uniform -convexity; continuity; modulus of -convexity; uniform -convexity},
title = {On moduli of -convexity.},
AU - Lim, Teck-Cheong
TI - On moduli of -convexity.
KW - modulus of convexity; modulus of -convexity; uniform convexity; uniform -convexity; continuity; modulus of -convexity; uniform -convexity
modulus of convexity, modulus of
k
-convexity, uniform convexity, uniform
k
-convexity, continuity, modulus of
k
-convexity, uniform
k
Articles by Lim
|
Moving Charges And Magnetism, Popular Questions: CBSE Class 12-science SCIENCE, Science - Meritnation
\underset{A}{\overset{B}{\int }}{\stackrel{\to }{B}}_{Q}·\stackrel{\to }{d\mathcal{l}}=2{µ}_{0}
\underset{D}{\overset{A}{\int }}{\stackrel{\to }{B}}_{P}·\stackrel{\to }{d\mathcal{l}}=-2{µ}_{0}
\underset{A}{\overset{B}{\int }}{\stackrel{\to }{B}}_{P}·\stackrel{\to }{d\mathcal{l}}=-{µ}_{0}
\mathrm{B}=\left(3\stackrel{^}{\mathrm{i}}+4\stackrel{^}{\mathrm{j}}+\stackrel{^}{\mathrm{k}}\right)
\left(\mathrm{A}\right) \sqrt{2}\left(\stackrel{^}{\mathrm{i}}+\stackrel{^}{\mathrm{j}}+\stackrel{^}{\mathrm{k}}\right) \left(\mathrm{B}\right) \sqrt{2}\left(\stackrel{^}{\mathrm{i}}-\stackrel{^}{\mathrm{j}}+\stackrel{^}{\mathrm{k}}\right)\phantom{\rule{0ex}{0ex}}\left(\mathrm{C}\right) \sqrt{2}\left(\stackrel{^}{\mathrm{i}}+\stackrel{^}{\mathrm{j}}-\mathrm{k}\right) \left(\mathrm{D}\right) \sqrt{2}\left(\stackrel{^}{-\mathrm{i}}+\stackrel{^}{\mathrm{j}}+\stackrel{^}{\mathrm{k}}\right)
a current carrying loop is free to turn is placed in a uniform magnetic field B.what will be its orientation relative to B in equilibrium state?
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Learn math and science with fun interactive courses, or create your own: it’s just blogging with buttons!
\def\A{\red{A}} \def\B{\blue{B}} \def\C{\green{C}} 2x^2 - 3x = 2
\def\A{\red{A}} \def\B{\blue{B}} \def\C{\green{C}} \sqrt{4ac - b^2}
\def\A{\red{A}} \def\B{\blue{B}} \def\C{\green{C}} +b^2
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The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures
15 August 2019 The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures
{g}_{0},\dots ,{g}_{k}:\mathbb{N}\to \mathbb{D}
1
-bounded multiplicative functions, and let
{h}_{0},\dots ,{h}_{k}\in \mathbb{Z}
be shifts. We consider correlation sequences
f:\mathbb{N}\to \mathbb{Z}
f\left(a\right):=\underset{m\to \infty }{}\frac{1}{log{\omega }_{m}}{\sum }_{{x}_{m}/{\omega }_{m}\le n\le {x}_{m}}\frac{{g}_{0}\left(n+a{h}_{0}\right)\cdots {g}_{k}\left(n+a{h}_{k}\right)}{n},
1\le {\omega }_{m}\le {x}_{m}
are numbers going to infinity as
m\to \infty
is a generalized limit functional extending the usual limit functional. We show a structural theorem for these sequences, namely, that these sequences
f
are the uniform limit of periodic sequences
{f}_{i}
. Furthermore, if the multiplicative function
{g}_{0}\cdots {g}_{k}
“weakly pretends” to be a Dirichlet character
\chi
, the periodic functions
{f}_{i}
can be chosen to be
\chi
-isotypic in the sense that
{f}_{i}\left(ab\right)={f}_{i}\left(a\right)\chi \left(b\right)
b
is coprime to the periods of
{f}_{i}
\chi
{g}_{0}\cdots {g}_{k}
does not weakly pretend to be any Dirichlet character, then
f
must vanish identically. As a consequence, we obtain several new cases of the logarithmically averaged Elliott conjecture, including the logarithmically averaged Chowla conjecture for odd order correlations. We give a number of applications of these special cases, including the conjectured logarithmic density of all sign patterns of the Liouville function of length up to three and of the Möbius function of length up to four.
Terence Tao. Joni Teräväinen. "The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures." Duke Math. J. 168 (11) 1977 - 2027, 15 August 2019. https://doi.org/10.1215/00127094-2019-0002
Received: 8 August 2017; Revised: 14 December 2018; Published: 15 August 2019
Keywords: Chowla conjecture , Elliott conjecture , multiple recurrence , multiplicative functions
Terence Tao, Joni Teräväinen "The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures," Duke Mathematical Journal, Duke Math. J. 168(11), 1977-2027, (15 August 2019)
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Ideal Semiconductor Switch - MATLAB - MathWorks Deutschland
The Ideal Semiconductor Switch block models an ideal semiconductor switching device.
The figure shows a typical i-v characteristic for an ideal semiconductor switch.
If the gate-cathode voltage exceeds the specified threshold voltage, the ideal semiconductor switch is in the on state. Otherwise the device is in the off state.
In the on state, the anode-cathode path behaves like a linear resistor with on-resistance Ron.
In the off state, the anode-cathode path behaves like a linear resistor with a low off-state conductance Goff.
Using the Integral Diode parameters, you can include an integral cathode-anode diode. An integral diode protects the semiconductor device by providing a conduction path for reverse current. An inductive load can produce a high reverse-voltage spike when the semiconductor device suddenly switches off the voltage supply to the load.
This figure shows the block port names.
Physical signal port associated with the gate terminal.
Electrical conserving port associated with the gate terminal.
To enable this port, set Modeling option to Electrical control port.
Modeling option — Whether to specify physical or electrical control port
PS control port (default) | Electrical control port
Whether to specify physical or electrical control port for the switch gate.
Specify whether the block includes an integral protection diode. The default value is None.
If you want to include an integral protection diode, there are two options:
To enable this parameter, set Integral protection diode to Protection diode with no dynamics or Protection diode with charge dynamics.
-\frac{{i}^{2}{}_{RM}}{2a},
Diode | GTO | Ideal Semiconductor Switch | IGBT (Ideal, Switching) | MOSFET (Ideal, Switching) | N-Channel MOSFET | P-Channel MOSFET | Thyristor (Piecewise Linear)
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Throughout this book, key problems have been selected as “checkpoints.” Each checkpoint problem is marked with an icon like the one at left. These checkpoint problems are provided so that you can check to be sure you are building skills at the expected level. When you have trouble with checkpoint problems, refer to the review materials and practice problems that are available in the Checkpoint Materials.
This problem is a checkpoint for finding the distance between two points and finding the equation of a line. It will be referred to as Checkpoint 2A.
For each pair of points, determine the distance between them. Then find the equation for a line through them.
(−2,4)
(4,7)
(3,4)
(3,−1)
(−7,20)
(3,−5)
(1,−2)
(5,−2)
Answers and extra practice for the Checkpoint problems are located in the back of your printed textbook or in the Reference Tab of your eBook. If you have an eBook for CCA2, login and then click the following link: Checkpoint 2A: Finding the Distance Between Two Points and the Equation of a Line
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Comments on tag 02HU—Kerodon
Subsection 5.6.6: Application: Corepresentable Functors (cite)
In the introduction, "
y \in \mathscr {F}(C)
" should read "
y \in \mathscr {F}(Y)
Comment #960 by Kerodon on April 28, 2021 at 18:26
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 02HU. The letter 'O' is never used.
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2016 Antinormal Weighted Composition Operators
Dilip Kumar, Harish Chandra
{l}^{\mathrm{2}}={L}^{\mathrm{2}}\left(\mathbb{N},\mu \right)
\mathbb{N}
is set of all positive integers and
\mu
is the counting measure whose
\sigma
-algebra is the power set of
\mathbb{N}
. In this paper, we obtain necessary and sufficient conditions for a weighted composition operator to be antinormal on the Hilbert space
{l}^{\mathrm{2}}
. We also determine a class of antinormal weighted composition operators on Hardy space
{H}^{\mathrm{2}}\left(\mathbb{D}\right)
Dilip Kumar. Harish Chandra. "Antinormal Weighted Composition Operators." Abstr. Appl. Anal. 2016 1 - 5, 2016. https://doi.org/10.1155/2016/5767426
Dilip Kumar, Harish Chandra "Antinormal Weighted Composition Operators," Abstract and Applied Analysis, Abstr. Appl. Anal. 2016(none), 1-5, (2016)
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Initial terminal voltage, Vt0 (pu)
Initial terminal current, It0 (pu)
Maximum voltage regulator output, V_PIDmax (pu)
Minimum voltage regulator output, V_PIDmin (pu)
Rectifier bridge gain, K_A (pu)
Rectifier bridge time constant, T_A (s)
Maximum exciter field current, V_FEmax (pu)
Minimum exciter voltage output limit, V_Emin (pu)
Rectifier loading factor proportional to commutating reactance, K_C1 (pu)
Maximum available exciter field voltage, V_Bmax (pu)
The Power Source models the dependency of the power source for the controlled rectifier from the terminal voltage.
SW1 is the user-selected power source switch for the controlled rectifier.
{V}_{C1}={V}_{T}+{I}_{T}\sqrt{{R}_{C}^{2}+{X}_{C}^{2}},
There are two Take-over Logic subsystems. They model the take-over point input location for the OEL, UEL, SCL and PSS voltages. For more information about using limiters with this block, see Field Current Limiters.
The PID_R subsystem models a PID controller that functions as a control structure for the automatic voltage regulator. The minimum and maximum anti-windup saturation limits for the block are VPIDmin and VPIDmax, respectively.
The Low-Pass Filter block models the major dynamics of the voltage regulator. Here, KA is the regulator gain and TA is the major time constant of the regulator. The minimum and maximum anti-windup saturation limits for the block are VRmin and VRmax, respectively.
The Logical switch 1 parameter controls the origin of the power source for the controlled rectifier. The voltage regulator command signal VR is multiplied by the exciter field voltage, VB. For more information about the user-selected logical switch for the power source of the controlled rectifier, see Power Source.
It is possible to use different power source representations for the controlled rectifier by selecting the relevant option in the Logical switch 1 parameter. The power source for the controlled rectifier can be either derived from the terminal voltage (Position A: power source derived from terminal voltage) or it can be independent of the terminal voltage (Position B: power source independent from the terminal conditions).
Initial terminal voltage, Vt0 (pu) — Initial terminal voltage
Initial per-unit voltage to apply to the terminal.
Initial terminal current, It0 (pu) — Initial terminal current
Maximum voltage regulator output, V_PIDmax (pu) — Maximum output of PID regulator
Maximum admissible per-unit output of the PID regulator.
Minimum voltage regulator output, V_PIDmin (pu) — Minimum output of the regulator
-99 (default) | positive number
Minimum admissible per-unit output of the PID regulator.
Rectifier bridge gain, K_A (pu) — Rectifier bridge gain
Gain associated with the rectifier.
Rectifier bridge time constant, T_A (s) — Rectifier bridge time constant
Time constant of the rectifier.
35 (default) | real number
Location of the overexcitation limiter input.
Location of the underexcitation limiter input.
Location of the stator current limiter input:
Maximum exciter field current, V_FEmax (pu) — Exciter upper limit
Minimum exciter voltage output limit, V_Emin (pu) — Exciter lower limit
To enable this parameter, set Logical switch 1 to Position A: power source derived from terminal voltage.
Rectifier loading factor proportional to commutating reactance, K_C1 (pu) — Rectifier loading factor proportional to commutating reactance
Per-unit loading factor of the rectifier that is proportional to the commutating reactance.
Logical switch 1 — Logical switch
Position A: power source derived from terminal voltage (default) | Position B: power source independent of the terminal conditions
Position of logical switch 1.
Maximum available exciter field voltage, V_Bmax (pu) — Maximum available exciter field voltage
Maximum per-unit available field voltage for the exciter.
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Capital_accumulation Knowpia
Measurement of accumulationEdit
Demand-led growth modelsEdit
In macroeconomics, following the Harrod–Domar model, the savings ratio (
{\displaystyle s}
) and the capital coefficient (
{\displaystyle k}
) are regarded as critical factors for accumulation and growth, assuming that all saving is used to finance fixed investment. The rate of growth of the real stock of fixed capital (
{\displaystyle K}
{\displaystyle {{\Delta K} \over K}={{{\Delta K} \over Y} \over {K \over Y}}={s \over k}}
{\displaystyle Y}
is the real national income. If the capital-output ratio or capital coefficient (
{\displaystyle k={K \over Y}}
) is constant, the rate of growth of
{\displaystyle Y}
is equal to the rate of growth of
{\displaystyle K}
. This is determined by
{\displaystyle s}
(the ratio of net fixed investment or saving to
{\displaystyle Y}
{\displaystyle k}
Marxist conceptEdit
Over-accumulation and crisisEdit
Concentration and centralizationEdit
Rate of accumulationEdit
Circuit of capital accumulation from productionEdit
Simple and expanded reproductionEdit
Capital accumulation as social relationEdit
"The relations of capital assume their most externalised and most fetish-like form in interest-bearing capital. We have here
{\displaystyle M-M'}
{\displaystyle M-C-M'}
, there is at least the general form of the capitalistic movement, although it confines itself solely to the sphere of circulation, so that profit appears merely as profit derived from alienation; but it is at least seen to be the product of a social relation, not the product of a mere thing. (...) This is obliterated in
{\displaystyle M-M'}
, the form of interest-bearing capital. (...) The thing (money, commodity, value) is now capital even as a mere thing, and capital appears as a mere thing. The result of the entire process of reproduction appears as a property inherent in the thing itself. It depends on the owner of the money, i.e., of the commodity in its continually exchangeable form, whether he wants to spend it as money or loan it out as capital. In interest-bearing capital, therefore, this automatic fetish, self-expanding value, money generating money, are brought out in their pure state and in this form it no longer bears the birth-marks of its origin. The social relation is consummated in the relation of a thing, of money, to itself.—Instead of the actual transformation of money into capital, we see here only form without content."
Markets with social influenceEdit
Wikiquote has quotations related to Capital accumulation.
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Arihant - Class X - Magnetic Effects Of Electric Current [ Chapter - 13 ]
Arihant - Class X - Magnetic Effects Of Electric Current [ Chapter - 13 ]Contact Number: 9667591930 / 8527521718
What is meant by magnetic field?
How is the direction of magnetic field at a point determined?
Draw a diagram to show magnetic field due to a bar magnet in a given region.
What does the degree of closeness of magnetic field lines near the poles signify?
State the conclusions that can be drawn from the observation that a current carrying wire deflects a magnetic needle placed near it.
The diagram given below represents the magnetic field caused by a current-carrying conductor. Identify the nature of the coil.
Identify the region, where the magnetic field around a current carrying solenoid is uniform.
State the direction of the magnetic field in the following case.
Name the rule which gives the direction of induced current in a conductor.
Under what orientation, the induced current produced in moving conductor in a magnetic field can be maximum?
How is induced current in a secondary coil related to current in a primary coil?
Why is an alternating current considered to be advantageous over direct current for long range transmission of electric energy?
An alternating current has frequency of 50 Hz. How many times does it change its direction in one second?
How is the type of current that we receive in domestic circuit different from one that runs a clock?
In a domestic electric circuit, mention the potential difference between live wire and neutral wire and frequency of AC?
How should the electric lamps in a building be connected, so that the switching on or off in a room has no effect on other lamps in the same building?
What is the advantage of third wire of the earth connection in domestic electrical application?
Which is the most important safety method used for protecting home appliances from short circuiting or overloading?
A region A has magnetic field lines relatively closer than another region B. Which region has stronger magnetic field? Give reason to support your answer.
A horizontal power line carries a current from East to West direction. What is the direction of the magnetic field due to the current in the power line at a point above and at a point below the power line?
How does the strength of magnetic field due to a current carrying conductor depend upon
(i) distance from the conductor?
State what would happen to the direction of rotation of a motor, if
(i) the current were reversed?
(ii) both current and magnetic field were reversed simultaneously?
(i) The diagram shows a bar magnet surrounded by four plotting compasses. Copy the diagram and mark the direction of the compass
needle for each of the cases B, C and D.
(ii) Which is the North pole, X or Y?
A plotting compass is placed inside a solenoid and the compass needle is pointing in the direction as shown.
(i) Complete the diagram by drawing arrowheads to indicate the direction of the current flow.
(ii) Describe the direction of the magnetic field inside the solenoid.
The wire in the figure below is being moved downwards through the magnetic field, so as to produce induced current.
What would be the effect of
(i) moving the wire at a higher speed?
(ii) moving the wire upwards rather than downwards?
(iii) using a stronger magnet?
(iv) holding the wire still in the magnetic field?
The given figure shows a DC motor model used by a student to study electromagnetism.
The two ends of the coil are fixed to a pair of curve elastic metal strips. The metal strips are connected to the power supply with a rheostat.
(i) State the direction of rotation of the coil when viewed from the front.
(ii) The student is still testing on the feasibility of using the metal strips in the model. What is he trying to achieve?
The figure shows the split ring commutator and the two carbon brushes in their respective positions.
What can you say about the carbon brush spilled ring commutator?
What are magnetic field lines? Justify the following statements.
(i) Two magnetic field lines never intersect each other.
(ii) Magnetic field lines are closed curves.
State the purpose for which the following rules are used
(i) Right hand thumb rule
Describe an activity with diagram to demonstrate the presence of magnetic field around a current carrying straight conductor.
The flow of current in a circular wire creates a magnetic held at its centre. How can existence of this field be detected? State the rule which helps to predict the direction of magnetic field.
Meena draws magnetic field lines of the field close to the axis of a current-carrying circular loop. As she mo s away from the centre of the circular loop she observes that the lines keep on diverging. How will you explain her observations?
Find the direction of magnetic field due to a current-carrying circular coil held:
(i) Vertically in the North-South plane and an observer looking it from East sees the current to flow in the anti-clockwise direction.
(ii) Vertically in East-West plane and an observer looking it from South sees the current to flow in the anti-clockwise direction.
(iii) Horizontally and an observer looking at it from below sees current to flow in the clockwise direction.
The diagram shows the lengthwise section of a current-carrying solenoid.
Indicates current entering into the page,
indicates current emerging out of the page.
Decide which end of the solenoid A or B, behave as North pole. Give a reason for our answer. Also, draw field lines inside the solenoid.
For the current-carrying solenoid as shown below, draw magnetic field lines and give reason to explain that out of the three points A, B, and C at which point the field strength is maximum and at which point it is minimum.
A circular metallic loop is kept above the wire AB as shown bélow:
What is the direction of induced current produced in the loop, if any when the current flowing in the straight wire
(i) is steady, i.e. does not vary?
(ii) is increasing in magnitude?
A copper coil is connected to a galvanometer. What would happen, if a bar magnet is
(i) pushed into the coil with it's North pole entering first?
Under what conditions permanent electromagnet is obtained, if a current-carrying solenoid is used? Support your answer with the help of a labelled circuit diagram.
A magnetic compass needle is placed in the plane of paper near point A as shown in the figure. In which plane should a straight current-carrying conductor be placed, so that it passes through A and there is no change in the deflection of the compass? Under what condition is the deflection maximum and why?
(i) Two circular coils P and Q are kept close to each other, of which coil P carries a current. If coil P is moved towards Q, then will some current be induced in coil Q? Give a reason for your answer and name the phenomenon involved.
(ii) What happens, if coil P is moved away from Q?
(iii) State a few methods of inducing a current in a coil.
List two distinguishing features between overloading and short-circuiting.
What is an electric fuse? What is its role in electric circuits? Should it be placed on neutral wire or on the live wire? Justify your answer.
(i) Describe an activity to obtain a magnetic field line around the current-carrying straight conductor.
(ii) State the rule used to find the direction of this magnetic field.
(iii) How does the magnitude of the magnetic field depend on the current through a conductor?
(i) Draw the magnetic field lines through and around a single loop of wire carrying electric current.
(ii) State whether an
\mathrm{\alpha }
-particle Will experience any force in a magnetic field, if (a-particles are positively charged
(c) It is the magnetic field perpendicular to field lines. Justify yours in each case.
Explain with the help of a labelled diagram, the distribution of the magnetic field due to a current through a circular loop. Why is it that, if a current-carrying coil has n turns the field produced at any point is n times as large as that produced by a single turn?
Explain the meanings . of words "electromagnetic" and "induction" in the term electromagnetic induction. List three factors on which the value of induced current produced in a circuit depends.
Name and state the rule used to determine the direction of the induced current. State one practical application of this phenomenon in everyday life.
Draw a labeled circuit diagram Of a simple electric motor and explain its working. In what way these simple electric motors are different from commercial motors?
(i) What is meant by electromagnetic induction? Name one device which works on electromagnetic induction.
(ii) Describe three different ways to produce induced current in a coil of wire.
Differentiate between AC and DC. Name one source of each. write any two advantages of alternating current over direct current.
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ISAAC (cipher) - Wikipedia
ISAAC (cipher)
Crytographic number generator
ISAAC (indirection, shift, accumulate, add, and count) is a cryptographically secure pseudorandom number generator and a stream cipher designed by Robert J. Jenkins Jr. in 1993.[1] The reference implementation source code was dedicated to the public domain.[2]
3 Usage outside cryptography
The ISAAC algorithm has similarities with RC4. It uses an array of 256 four-octet integers as the internal state, writing the results to another 256 four-octet integer array, from which they are read one at a time until empty, at which point they are recomputed. The computation consists of altering i-element with (i⊕128)-element, two elements of the state array found by indirection, an accumulator, and a counter, for all values of i from 0 to 255. Since it only takes about 19 32-bit operations for each 32-bit output word, it is very fast on 32-bit computers.
Cryptanalysis has been undertaken by Marina Pudovkina (2001).[3] Her attack can recover the initial state with a complexity that is approximated to be less than the time needed for searching through the square root of all possible initial states. In practice this means that the attack needs
{\displaystyle 4.67\times 10^{1240}}
{\displaystyle 10^{2466}}
. This result has had no practical impact on the security of ISAAC.[4]
In 2006 Jean-Philippe Aumasson discovered several sets of weak states.[5] The fourth presented (and smallest) set of weak states leads to a highly biased output for the first round of ISAAC and allows the derivation of the internal state, similar to a weakness in RC4. It is not clear if an attacker can tell from just the output whether the generator is in one of these weak states or not. He also shows that a previous attack[6] is flawed, since the Paul-Preneel attack is based on an erroneous algorithm rather than the real ISAAC. An improved version of ISAAC is proposed, called ISAAC+.[4]
Usage outside cryptography[edit]
Many implementations of ISAAC are so fast that they can compete with other high speed PRNGs, even with those designed primarily for speed not for security. Only a few other generators of such high quality and speed exist in usage. ISAAC is used in the Unix tool shred to securely overwrite data.[7] Also ISAAC algorithm is implemented in Java Apache Commons Math library. [8]
^ Robert J. Jenkins Jr., ISAAC. Fast Software Encryption 1996, pp. 41–49.
^ The ISAAC Cipher
^ Marina Pudovkina, A known plaintext attack on the ISAAC keystream generator, 2001, Cryptology ePrint Archive: Report 2001/049, [1].
^ a b "On the pseudo-random generator ISAAC" (PDF). Cryptology ePrint Archive. Retrieved 21 August 2016.
^ Jean-Philippe Aumasson, On the pseudo-random generator ISAAC. Cryptology ePrint archive, report 2006/438, 2006.
^ Souradyuti Paul, Bart Preneel, On the (In)security of Stream Ciphers Based on Arrays and Modular Addition.Asiacrypt 2006.
^ GNU coreutils git
^ Apache Commons Math reference
Official ISAAC website
Multiple ISAAC implementations at Rosetta Code
Pascal/Delphi port
Math::Random::ISAAC, a Perl module implementation of the algorithm
isaac.js, a JavaScript implementation
Retrieved from "https://en.wikipedia.org/w/index.php?title=ISAAC_(cipher)&oldid=1084911331"
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EUDML | The real rank of inductive limit C*-algebras. EuDML | The real rank of inductive limit C*-algebras.
The real rank of inductive limit C*-algebras.
B. Blackadar; M. Dadarlat; M. Rordam
Blackadar, B., Dadarlat, M., and Rordam, M.. "The real rank of inductive limit C*-algebras.." Mathematica Scandinavica 69.2 (1991): 211-216. <http://eudml.org/doc/167180>.
@article{Blackadar1991,
author = {Blackadar, B., Dadarlat, M., Rordam, M.},
keywords = {inductive limits of direct sums of -algebras; reak rank zero; stable rank one},
title = {The real rank of inductive limit C*-algebras.},
AU - Blackadar, B.
AU - Dadarlat, M.
AU - Rordam, M.
TI - The real rank of inductive limit C*-algebras.
KW - inductive limits of direct sums of -algebras; reak rank zero; stable rank one
inductive limits of direct sums of
{C}^{*}
-algebras, reak rank zero, stable rank one
{C}^{*}
{W}^{*}
{C}^{*}
Articles by B. Blackadar
Articles by M. Dadarlat
Articles by M. Rordam
|
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