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## Found 303 Documents (Results 1–100)

100
MathJax

### Efficient BBFM-collocation for weakly singular oscillatory Volterra integral equations of the second kind. (English)Zbl 07513123

MSC:  65D32 65D30
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### Convergence rates on spectral orthogonal projection approximation for functions of algebraic and logarithmatic regularities. (English)Zbl 1465.41003

MSC:  41A10 41A25 41A50
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### Hypergeometric forms of some composite functions containing arccosine$$(x)$$ using Maclaurin’s expansion. (English)Zbl 07400766

MSC:  33C05 33B10
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### Piece-wise analytic trajectory computation for polytopic switching between stable affine systems. (English)Zbl 07300846

Proceedings of the 23rd ACM international conference on hybrid systems: computation and control, HSCC 2020, Sydney, Australia and virtual, April 21–24, 2020. New York, NY: Association for Computing Machinery (ACM). Article No. 5, 11 p. (2020).
MSC:  68Q45 68Q60 93C30
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### Finite integration method via Chebyshev polynomial expansion for solving 2-D linear time-dependent and linear space-fractional differential equations. (English)Zbl 1463.65175

MSC:  65L05 65L10 65N30
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### A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable. (English. Ukrainian original)Zbl 1450.30015

J. Math. Sci., New York 249, No. 5, 786-803 (2020); translation from Ukr. Mat. Visn. 17, No. 2, 256-277 (2020).
MSC:  30C10 30B50
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### A unified framework for asymptotic analysis and computation of finite Hankel transform. (English)Zbl 1430.44001

MSC:  44A15 42B20 65R10
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### The faster methods for computing Bessel functions of the first kind of an integer order with application to graphic processors. (English)Zbl 07150899

MSC:  65-XX 41-XX
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### Dynamic computation for rigid-flexible multibody systems with hybrid uncertainty of randomness and interval. (English)Zbl 1420.70003

MSC:  70E55 60G60
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### Best polynomial approximation on the triangle. (English)Zbl 1414.41018

MSC:  41A50 33C50 42C10
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### Finite-part integration of the generalized Stieltjes transform and its dominant asymptotic behavior for small values of the parameter. II: Non-integer orders. (English)Zbl 1406.44004

MSC:  44A15 41A50
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### Complete asymptotics of the approximation of function from the Sobolev classes by the Poisson integrals. (English)Zbl 1400.42001

MSC:  42A05 41A50
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### On the optimal convergence rates of Chebyshev interpolations for functions of limited regularity. (English)Zbl 1471.41008

MSC:  41A25 41A10 41A58
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### A new hybrid uncertainty optimization method for structures using orthogonal series expansion. (English)Zbl 1446.74065

MSC:  74-10 74P10
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### Approximate solution of a singular integral equation using Chebyshev series. (Russian. English summary)Zbl 1474.65489

MSC:  65R20 45E05
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### Non-asymptotic results for Cornish-Fisher expansions. (English)Zbl 1353.62023

MSC:  62E17 62E20
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### On $${C}_{J}$$ and $${C}_{T}$$ in the Gross-Neveu and $$O(N)$$ models. (English)Zbl 1349.81167

MSC:  81T40 81T17 41A50
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### Series expansion method for weakly singular Volterra integral equations. (English)Zbl 1416.65535

MSC:  65R20 45D05
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### An improved error bound on Gauss quadrature. (English)Zbl 1336.41012

MSC:  41A55 65D30
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### Accurate solution and approximations of the linearized BGK equation for steady Couette flow. (English)Zbl 1410.76412

MSC:  76P05 65R20 82C40 82C80
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### On the coefficients of differentiated expansions and derivatives of Chebyshev polynomials of the third and fourth kinds. (English)Zbl 1340.42063

MSC:  42C05 33C45
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### A homotopy analysis solution to large deformation of beams under static arbitrary distributed load. (English)Zbl 1427.74180

MSC:  74S99 74K10 74B10
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### Efficient linear-scaling quantum transport calculations on graphics processing units and applications on electron transport in graphene. (English)Zbl 1344.82043

MSC:  82C80 82C70 82C10
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### Method of normalized systems of functions. (Метод нормированных систем функций.) (Russian)Zbl 1297.35005

Chelyabinsk: Izd. Tsentr Yuzhno-Ural’skiĭ Gosudarstvennyĭ Universitet (ISBN 978-5-696-04562-7/hbk). 452 p. (2014).

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### Some new Ostrowski-type bounds for the Chebyshev functional and applications. (Some new Ostrowski-type bounds for the Čebyšev functional and applications.) (English)Zbl 1294.26021

MSC:  26D15 41A55
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### Solutions of hypersingular integral equations over circular domains by a spectral method. (English)Zbl 1340.65316

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, May 15–17, 2013. In honor of the 70th birthday of Karel Segeth. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-61-5). 52-66 (2013).
MSC:  65R20 76B15 45E10
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### A note on an error bound of Gauss-Turán quadrature with the Chebyshev weight. (English)Zbl 1340.65034

MSC:  65D32 41A55 41A80
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### Chebyshev polynomial solution of the system of Cauchy-type singular integral equations of the first kind. (English)Zbl 1278.65204

MSC:  65R20 45E05
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### Asymptotic expansions for distributions of sums of independent random vectors. (English)Zbl 1287.60032

Shiryaev, Albert N. (ed.) et al., Prokhorov and contemporary probability theory. In honor of Yuri V. Prokhorov on the occasion of his 80th birthday. Berlin: Springer (ISBN 978-3-642-33548-8/hbk; 978-3-642-33549-5/ebook). Springer Proceedings in Mathematics & Statistics 33, 107-125 (2013).
MSC:  60F05
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### Computation of integrals with oscillatory and singular integrands using Chebyshev expansions. (English)Zbl 1255.65073

MSC:  65D32 65D30
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MSC:  65D20
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### Partial fraction expansions for Newton’s and Halley’s iterations for square roots. (English)Zbl 1292.65044

MSC:  65H04 65E05 30C15
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### On the convergence rates of Gauss and Clenshaw-Curtis quadrature for functions of limited regularity. (English)Zbl 1259.65059

MSC:  65D32 41A25 41A55
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### On the exact analytical and numerical solutions of nano boundary-layer fluid flows. (English)Zbl 1253.76089

MSC:  76M25 76D10 76D05
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### Accelerating the secure distributed computation of the mean by a Chebyshev expansion. (English)Zbl 1292.68055

Susilo, Willy (ed.) et al., Information security and privacy. 17th Australasian conference, ACISP 2012, Wollongong, NSW, Australia, July 9–11, 2012. Proceedings. Berlin: Springer (ISBN 978-3-642-31447-6/pbk). Lecture Notes in Computer Science 7372, 57-70 (2012).
MSC:  68P25 94A62
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### Numerical methods based on rational variable substitution for Wiener-Hopf equations of the second kind. (English)Zbl 1247.65175

MSC:  65R20 45E10
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MSC:  41A25
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MSC:  97U40

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MSC:  33C45
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### Multidimensional $$q$$-normal and related distributions – Markov case. (English)Zbl 1222.62061

MSC:  62H10 60E05 33C90
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MSC:  65L05
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### The expansions approach for solving Cauchy integral equation of the first kind. (English)Zbl 1218.65152

MSC:  65R20 45E05
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### Series expansion on integral of normal function and normality approximate to some discrete distributions. (English)Zbl 1195.60035

MSC:  60F05 60E05
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### Applications of a numerical spectral expansion method to problems in physics; a retrospective. (English)Zbl 1191.65187

Ball, Joseph A. (ed.) et al., Topics in operator theory. Volume 2: Systems and mathematical physics. Proceedings of the 19th international workshop on operator theory and applications (IWOTA), College of William and Mary, Williamsburg, VA, USA, July 22–26, 2008. A tribute to Israel Gohberg on the occasion of his 80th birthday. Basel: Birkhäuser (ISBN 978-3-0346-0160-3/hbk; 978-3-0346-0163-4/set; 978-3-0346-0161-0/ebook). Operator Theory: Advances and Applications 203, 409-426 (2010).
MSC:  65R20 45B05

### Magnus expansion for time-periodic systems: parameter-dependent approximations. (English)Zbl 1221.34024

MSC:  34A25 34A30 65L99
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MSC:  82C10
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### Linearization of conservative nonlinear oscillators. (English)Zbl 1159.70016

MSC:  70K99 70-08
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### Discretized fractional calculus with a series of Chebyshev polynomial. (English)Zbl 1337.26013

Seda, Anthony (ed.) et al., Proceedings of the Irish conference on the mathematical foundations of computer science and information technology (MFCSIT 2006), National University of Ireland, Cork, Ireland, August 1–5, 2006. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 225, 239-244 (2009).
MSC:  26A33 41A50 65D32
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### Expansion method for linear Fredholm integral equations of second kind by Chebyshev, Legendre and Shannon wavelats and the comparison of their numerical results. (English)Zbl 1206.65261

MSC:  65R20 45B05 65T60
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### Chebyshev expansion techniques. (English)Zbl 1140.41006

Fehske, Holger (ed.) et al., Computational many-particle physics. Papers presented at the summer school, Greifswald, Germany, September 2006. Berlin: Springer (ISBN 978-3-540-74685-0/hbk). Lecture Notes in Physics 739, 545-577 (2008).
MSC:  41A50

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### Spectral solutions of the MHD equations in cylindrical geometry. (English)Zbl 1141.76046

MSC:  76M22 76W05

### A Chebyshev approximation for solving nonlinear integral equations of Hammerstein type. (English)Zbl 1122.65409

MSC:  65R20 45G10
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### The kernel polynomial method. (English)Zbl 1205.81090

MSC:  81Q15 65D15 65Z05 82-08
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### Zonal current formation in two-dimensional turbulence on a rotating hemisphere and its dependence on boundary conditions. (English)Zbl 1135.76053

MSC:  76U05 76F99 76M25 86A05
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### Approximation of multivariate functions and evaluation of particular solutions using Chebyshev polynomial and trigonometric basis functions. (English)Zbl 1130.65115

MSC:  65N38 35J05 35J25
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### Asymptotic expression of the linear discrete best $$\ell_{p}$$-approximation. (English)Zbl 1108.41021

MSC:  41A60 41A50
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### $$D$$-optimal designs for weighted polynomial regression – a functional approach. (English)Zbl 1092.62072

MSC:  62K05 65C60 62J02
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MSC:  65R20
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### Adaptive bivariate Chebyshev approximation. (English)Zbl 1065.41016

MSC:  41A10 65D10 65R10
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### A fast Nyström-Broyden solver by Chebyshev compression. (English)Zbl 1076.65125

MSC:  65R20 45G10
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### On the harmonic analysis of functions of a real variable on a sphere. (Russian, English)Zbl 1121.42008

Zh. Vychisl. Mat. Mat. Fiz. 44, No. 11, 1964-1971 (2004); translation in Comput. Math. Math. Phys. 44, No. 11, 1867-1974 (2004).
MSC:  42B05 42C10 12E10

### On instability characteristics of isolated vortices and models of trailing-vortex systems. (English)Zbl 1069.76013

MSC:  76D17 76E99 76M25
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### Taylor expansion of best $$l_{p}$$-approximations about $$p$$ = 1. (English)Zbl 1056.41018

MSC:  41A58 41A50
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### Brittle detachment of a stiffener bonded to an elastic plate. (English)Zbl 1052.74049

MSC:  74R10 74G10
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### $$p$$-adic analysis and the calculus of finite differences. (English)Zbl 1038.11077

Schikhof, W. H. (ed.) et al., Ultrametric functional analysis. Proceedings of the seventh international conference on $$p$$-adic functional analysis, Nijmegen, The Netherlands, June 17–21, 2002. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-2889-4/pbk). Contemp. Math. 319, 413-422 (2003).

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# incrpcorr

Compute a sample Pearson product-moment correlation coefficient incrementally.

The Pearson product-moment correlation coefficient between random variables X and Y is defined as

where the numerator is the covariance and the denominator is the product of the respective standard deviations.

For a sample of size n, the sample Pearson product-moment correlation coefficient is defined as

## Usage

var incrpcorr = require( '@stdlib/stats/incr/pcorr' );

#### incrpcorr( [mx, my] )

Returns an accumulator function which incrementally computes a sample Pearson product-moment correlation coefficient.

var accumulator = incrpcorr();

If the means are already known, provide mx and my arguments.

var accumulator = incrpcorr( 3.0, -5.5 );

#### accumulator( [x, y] )

If provided input value x and y, the accumulator function returns an updated sample correlation coefficient. If not provided input values x and y, the accumulator function returns the current sample correlation coefficient.

var accumulator = incrpcorr();

var v = accumulator( 2.0, 1.0 );
// returns 0.0

v = accumulator( 1.0, -5.0 );
// returns 1.0

v = accumulator( 3.0, 3.14 );
// returns ~0.965

v = accumulator();
// returns ~0.965

## Notes

• Input values are not type checked. If provided NaN or a value which, when used in computations, results in NaN, the accumulated value is NaN for all future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly before passing the value to the accumulator function.

## Examples

var randu = require( '@stdlib/random/base/randu' );
var incrpcorr = require( '@stdlib/stats/incr/pcorr' );

var accumulator;
var x;
var y;
var i;

// Initialize an accumulator:
accumulator = incrpcorr();

// For each simulated datum, update the sample correlation coefficient...
for ( i = 0; i < 100; i++ ) {
x = randu() * 100.0;
y = randu() * 100.0;
accumulator( x, y );
}
console.log( accumulator() );

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# Calling All Duke Fall 2010 Applicants! (MERGED)

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TAGS:
Intern
Joined: 08 Jun 2009
Posts: 22
Location: California
Schools: Ross, Fuqua
Followers: 1

Kudos [?]: 4 [1] , given: 0

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  02 Nov 2009, 20:12
1
KUDOS
Here you go:

* What do you consider the applicant's primary talents or strengths?
* In what areas does the applicant need improvement or growth? How would you describe the applicant's insight into these areas?
* How would you describe the applicant's leadership skills/career potential?
* Comment on the applicant's interpersonal skills (effectiveness in establishing and maintaining relationships;working with supervisors, peers, and subordinates; willingness to work in a team environment).
* If applicable, describe the applicant's experience working on international projects or with international teams. If you do not know of any international experience, describe any interest in international management expressed by the applicant?
* For non-native English speakers, please comment on the applicant's verbal and written English ability.
VP
Joined: 07 Apr 2009
Posts: 1172
Concentration: General Management, Strategy
Schools: Duke (Fuqua) - Class of 2012
Followers: 35

Kudos [?]: 392 [1] , given: 19

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  09 Nov 2009, 21:17
1
KUDOS
Expert's post
ElleBee wrote:
I'm an EA applicant and now I'm getting even more nervous for the 24th. Sigh.

Only two more weeks!!!
I think it's good that Duke doesn't roll out the decisions slowly. With single decision, at least it'll be relatively painless.
Current Student
Joined: 16 Jul 2008
Posts: 92
Schools: Duke
Followers: 3

Kudos [?]: 17 [1] , given: 2

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  20 Nov 2009, 07:18
1
KUDOS
I can't believe decisions are out! I'm IN!!!!!! This was my one and only app and I got the fee waived (alumni recommendation) and I'm so happy (and really, really stunned that decisions came out so early)!

Profile: 710 GMAT/F/26/3.5 GPA at top U.S. private undergrad/unique consulting and management position/very strong extracurriculars
_________________

Current Student
Joined: 26 Oct 2009
Posts: 45
Schools: Fuqua Class of 2012
Followers: 0

Kudos [?]: 10 [1] , given: 9

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  20 Nov 2009, 07:28
1
KUDOS
Just got my decision. I'm in!!!!!!!!! Fuqua FTW!

Now the tough part comes...figuring out how to afford it.
Current Student
Joined: 16 Jul 2008
Posts: 92
Schools: Duke
Followers: 3

Kudos [?]: 17 [1] , given: 2

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  20 Nov 2009, 07:57
1
KUDOS
ACNguy wrote:
CONGRATS TO EVERYONE THAT GOT IN!!! I'm really proud that this community seems to be so beneficial to so many applicants. Now go out and celebrate this weekend, your hard work has paid off.

Hoping to join you guys in R2.

Quick question, Duke seems to point out that its beneficial to apply early. Does that mean R2 is siginificantly frowned upon?

I don't think R2 is frowned upon though I heard that supposedly there were no acceptances in R3 last year (just waitlists and few, if any, got off). I mean, if your application is at its strongest in R2 then it's to your benefit to apply when it's at its strongest as opposed to applying earlier if it isn't as strong. If it makes you feel better, I know several people accepted R2 last year for Fuqua. Good luck to you! Hope you'll join us soon!
_________________

Current Student
Joined: 18 Nov 2009
Posts: 13
Followers: 0

Kudos [?]: 2 [1] , given: 0

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  01 Dec 2009, 15:00
1
KUDOS
mjjking wrote:
Hi,

any R1 applicant has received his/her interview invite yet? Do they release them on Dec. 8th only or also before?

thanks!

I cannot speak for R1, but for EA I got my invitation to interview on 21 October, which is the date advertised on the website. Of course it came late...about 3pm PST.
Although I have been admitted and accepted, my application still reads submitted...so don't stress over that. However, once I got an invite to interview another bullet will appear under submission status that reads "Interview Status: Invited". A third bullet will appear once a decision is rendered "Decision Status" that will have a link directing you to your acceptance or denial letter. I hope this helps...don't expect your "submission status" to change anytime soon, if ever.
Current Student
Joined: 09 Jun 2009
Posts: 182
Schools: Fuqua Class of 2012
Followers: 4

Kudos [?]: 54 [1] , given: 21

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  04 Dec 2009, 07:20
1
KUDOS
xpiano1978 wrote:
Ditto on the email.

Think it's a generic one sent to all R1 apps? If not, it'd be a bad sign if our apps are "complete"...

Well I did an open interview, so I'm fine with "complete" as long as it means "accepted" and of course the aforementioned gold bars.
Manager
Joined: 08 Nov 2009
Posts: 112
Schools: Cornell (R1),
WE 1: E-Payments (3 years)
WE 2: Semiconductors (3 years)
WE 3: Aerospace & Defense (2 years)
Followers: 1

Kudos [?]: 11 [1] , given: 6

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  04 Dec 2009, 07:26
1
KUDOS
Or we get a mob mentality and all have a collective super-freak out...
Current Student
Joined: 09 Jun 2009
Posts: 182
Schools: Fuqua Class of 2012
Followers: 4

Kudos [?]: 54 [1] , given: 21

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  04 Dec 2009, 07:36
1
KUDOS
The GMATClub admins should create a few graphs that match forum posts/volume with certain events. Any little thing happens and these forums explode!
Manager
Joined: 08 Nov 2009
Posts: 112
Schools: Cornell (R1),
WE 1: E-Payments (3 years)
WE 2: Semiconductors (3 years)
WE 3: Aerospace & Defense (2 years)
Followers: 1

Kudos [?]: 11 [1] , given: 6

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  07 Dec 2009, 11:36
1
KUDOS
Got an email telling me to go to the app site. It indicated I got an interview.

Email said follow up email will occur w/in 36 hours... Good luck all!

(Check your apps maybe? I dunno)
Manager
Joined: 28 Aug 2009
Posts: 150
Followers: 1

Kudos [?]: 9 [1] , given: 3

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  07 Dec 2009, 11:40
1
KUDOS
xpiano1978 wrote:
Got an email telling me to go to the app site. It indicated I got an interview.

Email said follow up email will occur w/in 36 hours... Good luck all!

(Check your apps maybe? I dunno)

Just got the same email and got an interview invite as well. Good luck everyone!!!!
Intern
Joined: 01 Dec 2009
Posts: 22
Followers: 0

Kudos [?]: 6 [1] , given: 1

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  07 Dec 2009, 12:31
1
KUDOS
Got the email as well, invited.
Current Student
Joined: 29 Sep 2008
Posts: 94
Schools: Duke R1, Cornell R2, Columbia RD, Darden R2 (withdrawn), Ross R2
Followers: 2

Kudos [?]: 8 [1] , given: 0

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  07 Dec 2009, 12:44
1
KUDOS
Got an email about 45 minutes ago, invited!! Good luck everyone and congratulations to all the invited people!!
Current Student
Joined: 26 Oct 2009
Posts: 45
Schools: Fuqua Class of 2012
Followers: 0

Kudos [?]: 10 [1] , given: 9

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  08 Dec 2009, 08:38
1
KUDOS
A lot of people went full professional, but I went business casual (clean pressed shirt w/a tie) and my interviewer actually jokingly commented that I had read the letter. With that said, she followed up by saying that suits were absolutely fine, they were just looking for us to be comfortable.

xpiano1978 wrote:
BTW, Email said business casual, and I think I'll wear business casual... Anyone have an opinion on this?
Current Student
Joined: 29 Sep 2008
Posts: 94
Schools: Duke R1, Cornell R2, Columbia RD, Darden R2 (withdrawn), Ross R2
Followers: 2

Kudos [?]: 8 [1] , given: 0

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  21 Dec 2009, 06:45
1
KUDOS
bhy wrote:
Applied Fuqua R1, recieved an interview invite around Dec 8th and interviewed on Sun Dec 20th.

Does anyone know what the ratio of "invited to interview at Fuqua" applicants to those who are accepted. I know that something like 75% of applicants are interviewed, but how many of those are invited?

Thanks!

Unfortunately, there's no way to know. But we could assume that more or less 50-60% of people are invited (excluding those who went to the open interview), so that - given a 30% acceptance rate, makes about 50% your chances of getting in. it's a very rough estimate though. But of course, getting an invite is better than not getting one
Manager
Joined: 05 Nov 2009
Posts: 137
Location: United States
Concentration: Real Estate, Finance
GMAT 1: 680 Q46 V37
GRE 1: 680 Q46 V37
GPA: 3.14
WE: Architecture (Other)
Followers: 2

Kudos [?]: 9 [1] , given: 4

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  11 Jan 2010, 10:38
1
KUDOS
andromeda wrote:
Quote:
I don't mean to come off like an @, but the deadlines were released in July...if (potential) business students can't hit deadlines with that much lead time then there is a problem (there may be computer issues, but submitting a couple days early is always an option). These are only applications...so when you become a student are you going to do everything in your power to meet tighter time constraints on projects? Personally, I don't think I would want to be partners with people who can't submit an application in on time. It's not that difficult. There is a deadline. You either hit it or you don't.

I have to agree with you. Duke will evaluate all applications, regardless of the time they got in (few hours up or down doesn't make a difference). I bet the stress of you being late is also reflected in less than perfect essays and missed fields on 10 pages long application.

Well, considering I'm the one who first brought the deadline up, I figure I might add a few words.

One. Some deadlines are slightly ambiguous because 5:00pm is relative, not absolute, and some websites do a poor job of making that clear.

Two. All my essays were done in plenty of time. My problem was my transcript. I went to kinko's to scan my transcript where I quickly learned that the 500kb maximum file size would be difficult to hit and still be legible. I called the admissions office (3:30pm) worried about it and they informed me if I needed to scan it again, I still had plenty of time since I could actually submit until midnight. After playing with it some more, I finally remembered how to decrease the file size w/o hurting the legibility (6:30pm).

Honestly, I don't understand why Duke insists on having scanned copies of your official transcripts. I could have just as easily manipulated the scan as I could have manipulated an unofficial copy. Further, they require official copies to be sent upon granted admission regardless. Other schools allow unofficial/self-reported transcripts such as Columbia/Wharton, why can't they do the same? Of all the schools I've applied to, Duke is the only one that requires this, which to me makes their application slightly unconventional. As a result, I don't think anyone should be getting mad that I needed to use an extra hour or so to deal with technical difficulties that are unique to their application.

Three. Increased/decreased competition is a two-edged sword. If you get in, you obviously want to have the most competitive classmates surrounding you because your degree is only as good as the brand it represents, and so it's not such a bad thing that people were a little over the 5pm deadline. Conversely, I understand that there are those who are worried that they may be "on the bubble" relative to average statistics, and that these applications may further decrease your chances. Just think about that if you are accepted.

Four. Not everyone knows which schools they to plan to apply to in June, July, August, September, October, November, or in my case even December. As a result, I didn't start the Duke App until after Christmas - should I be penalized for that? I think people need to extract the "holyier than now" attitude from these forums. Things happen - and not everyone described their circumstances on a message board. Perhaps it might be better to not judge and keep a positive attitude.
VP
Joined: 07 Apr 2009
Posts: 1172
Concentration: General Management, Strategy
Schools: Duke (Fuqua) - Class of 2012
Followers: 35

Kudos [?]: 392 [1] , given: 19

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  11 Jan 2010, 12:41
1
KUDOS
Expert's post
I wonder if it's to boost rankings, since acceptance rate is part of the equation.
I know that Cal-Berkeley Law School is famous for giving out fee waiver to boost applications.

I'm super broke, so fee waiver affected my decision in applying and not applying for some schools. Although with Fuqua, I was going to apply either way.
Current Student
Joined: 10 Nov 2009
Posts: 248
Schools: Emory 2012
WE 1: 1 yr proprietary trading
WE 2: 2 yrs global ibank in municipal derivatives
Followers: 6

Kudos [?]: 49 [1] , given: 11

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  14 Jan 2010, 15:27
1
KUDOS
Good luck to all you R1 applicants. Do you guys have some idea when interviews will be announced to R2 people?
_________________
Intern
Joined: 13 Jan 2010
Posts: 14
Schools: Fuqua, Darden, Tuck, Johnson, KF, Kelley
Followers: 0

Kudos [?]: 1 [1] , given: 0

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  15 Jan 2010, 07:09
1
KUDOS
I just called Fuqua. They said that email was an error and was not from one of their addresses. I'm sorry if that's bad news but I'd really take it for what it's worth. Maybe it means you guys have gotten in but they didn't want to release the decisions today.

Last edited by JoeKaneForHeisman on 15 Jan 2010, 07:11, edited 1 time in total.
GMAT Club Legend
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Posts: 5926
Schools: Chicago (Booth) - Class of 2009
GMAT 1: 730 Q45 V45
WE: Business Development (Consumer Products)
Followers: 288

Kudos [?]: 1838 [1] , given: 7

Re: Calling All Duke Fall 2010 Applicants! (MERGED) [#permalink]  15 Jan 2010, 07:29
1
KUDOS
This reminds me of how I found out about my Cornell admission ... an email with the subject "Scheduled Fedex Delivery Notice" with a "3.0lb" package from "Ithaca, NY".
Re: Calling All Duke Fall 2010 Applicants! (MERGED)   [#permalink] 15 Jan 2010, 07:29

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# Calling All Duke Fall 2010 Applicants! (MERGED)

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text:
Last edited by Shajar
Saturday, August 1, 2020 | History

2 edition of dictionary of chemical equations. found in the catalog.

dictionary of chemical equations.

Albert F. Gilman

# dictionary of chemical equations.

## by Albert F. Gilman

Written in English

Subjects:
• Chemical reactions,
• Chemistry -- Notation

• Edition Notes

Classifications The Physical Object Statement Editor: Albert F. Gilman, Jr.; associate editors: H. A. Ludwig [and others] LC Classifications QD65 .G5 1952 Pagination 543 p. Number of Pages 543 Open Library OL6108334M LC Control Number 52003518 OCLC/WorldCa 4926479

Beilstein German-to-English and English-to-German Dictionary, provided by the Swain Chemistry and Chemical Engineering Library at Stanford University. e.g. the word “mittelstandig” in a chemical text would almost invariably mean “in the middle or central position” and NOT “middle class” which is the everyday meaning of the word. This chapter begins with the development of a rate equation for chemical reaction with mass transfer involved in gas–liquid reactive absorption. Hatta number and enhancement factor are utilized to identify the reaction regime, viz., liquid film .

Chemical reaction definition is - a chemical change that occurs when two or more substances combine to form a new substance.   A chemical equation is a written symbolic representation of a chemical reaction (The symbols are the elemental letter or letters representing that element). The reactant chemical(s) are given on the left-hand side and the product chemical(s) on the right-hand side%().

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### Dictionary of chemical equations by Albert F. Gilman Download PDF EPUB FB2

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text:
# Difference expressed as integral of differential?

## Main Question or Discussion Point

Difference expressed as integral of differential??

Hi all, I came across an equation in this form while trying to understand a paper:

$$f(t+T) - f(t) = \int_t^\(t+T\$$$$\frac{d}{dt} f(t') \, dt'$$

but I was unable to see how it can be true. If I bring the term $$\frac{d}{dt}$$ outside of the definite integral, it seems to work, but I don't think that is allowed? Can anybody help? Thanks!

$$f(t+T) - f(t) = \int_t^\(t+T\$$$$\frac{d}{dt} f(t') \, dt'$$
I think it should be written with $$\frac{d}{dt'}$$ inside, not $$\frac{d}{dt}$$ .


text:
# geronimo-user mailing list archives

##### Site index · List index
Message view
Top
From "Ashwill, Steve (Facilities & Services)" <sashw...@uiuc.edu>
Subject Setting up CGI access
Date Fri, 18 Apr 2008 14:21:56 GMT
 I have a custom authentication system that uses Perl to do the
authenticating. Can anyone provide me information as to how I can
redirecting incoming requests to use the Perl scripts.  I will the
include the instructions given for IIS.

Configure <BluestemCGI> Directory for CGI Access and <ASPApplDir>
If the BluestemCGI directory in install-nt.conf is not already enabled
for CGI access, see your server's documentation for instructions on how
to do so.

If you are using IIS, you should be able to create a virtual directory
that is configured correctly using the following steps (or similar):

Right-click on "My Computer"
Select "Manage"
Expand "Services and Applications"
Expand "Internet Information Services (IIS) Manager"
Expand "Web Sites"
Right-click on the web site you want to configure (e.g., "Default Web
Site")
(if you have multiple web sites/virtual directories to configure, you
may need to repeat this and the following steps for each web
site/virtual directory)
Select "New", then "Virtual Directory". This will start the Virtual
Directory Creation Wizard
On the first screen of the wizard, fill in the "Alias". This should
match the value of BluestemPfx you set in install-nt.conf (e.g.,
"scripts" or "bluestem")
On the second screen, fill in the "Path". This should match the value of
BluestemCGI you set in install-nt.conf (e.g., "C:\InetPub\Scripts")
The third screen is for Access Permissions for the virtual directory.
Ensure that the one for "Execute (such as ISAPI applications or CGI)" is
enabled (i.e., checked).
If the virtual directory already exists, you should be able to modify
its configuration using the following steps (picking up from step 5
above):

Expand the web site containing the BluestemCGI directory (e.g., "Default
Web Site")
Right-click on the virtual directory corresponding to BluestemCGI (e.g.,
"scripts" or "bluestem")
Select "Properties"
Select the "Virtual Directory" or "Directory" tab
Click on the "Execute permissions" pulldown menu button
Choose the value "Scripts and Executables" (for CGI scripts; for ASP,
"Scripts only" should be sufficient)
If you are using Windows 2003 Server/IIS 6, you may also need to do the
following steps (again picking up from step 5 above):

Select "Web Service Extensions"
Select "Perl CGI Extension" (on the right-hand side pane). The default
is "Prohibited". Click on the "Allow" button to enable it.
[Note: If you need to fill in the value for a required file, as in step
3 above, it should look like '\path\to\perl.exe "%s" %s'; for example,
'C:\Perl\bin\perl.exe "%s" %s'.]
On Microsoft IIS, it is strongly recommended that you set the "Require
secure SSL channel" for the BluestemCGI directory and all others that
contain Bluestem applications. Otherwise, if a user mistakenly types
http:// instead of https:// in the URL they will get a Bluestem System
problem screen, because Bluestem can not be run without an SSL
connection to the browser.
You should be able to do this using the following steps (again picking
up from step 5 above):

Expand the web site containing the BluestemCGI directory (e.g., "Default
Web Site")
Right-click on the virtual directory corresponding to BluestemCGI (i.e.,
the directory alias you filled in in step 8 above, e.g., "scripts" or
"bluestem")
Select "Properties"
Select the "Directory Security" tab
Click on the "Edit ..." button in the "Secure Communications" section of
the tab (this will only be available if you have a server certificate)
Ensure that "Require secure channel (SSL)" is enabled

Can anyone translate this into geronimo?

Steven Ashwill

Mime
View raw message


text:
# getc

getc(__stream)

The macro getc used to be a "fast" macro implementation with a functionality identical to fgetc(). For space constraints, in avr-libc, it is just an alias for fgetc.


text:
# Math Help - Integrating a linear polynomial approx

1. ## Integrating a linear polynomial approx

hi,

thanks for reading.can anyone help me out?
see the attached file.i am working out for many hours how to integrate P1(t). does anyone know?
how do you get -1/2hf(..... ) + 3/2hf(....) ?
thats all i need to know!
i tried integrating MANY times. it looks easy.so what am i not understanding?

thanks all

2. Hi

The first integral is

$\left[\frac{t^2}{2}-t_it\right]_{t_i}^{t_{i+1}} = \frac{t_{i+1}^2}{2}- t_i t_{i+1}+\frac{t_i^2}{2}$

Substituting $t_{i+1} = t_i + h$

$\left[\frac{t^2}{2}-t_it\right]_{t_i}^{t_{i+1}} = \frac{t_{i}^2}{2} + h t_i + \frac{h^2}{2} - t_i^2 - h t_i + \frac{t_i^2}{2} = \frac{h^2}{2}$

3. Originally Posted by running-gag
Hi

The first integral is

$\left[\frac{t^2}{2}-t_it\right]_{t_i}^{t_{i+1}} = \frac{t_{i+1}^2}{2}- t_i t_{i+1}+\frac{t_i^2}{2}$

Substituting $t_{i+1} = t_i + h$

$\left[\frac{t^2}{2}-t_it\right]_{t_i}^{t_{i+1}} = \frac{t_{i}^2}{2} + h t_i + \frac{h^2}{2} - t_i^2 - h t_i + \frac{t_i^2}{2} = \frac{h^2}{2}$

aha...! thats where confusion happened... h can be anything =S
a difference between one point and another. thanks! =D


text:
Why do we need to write the noise as randn(2,1)./sqrt(2*SNR) instead of randn(1,1)/sqrt(2)?

I saw this code, about the error probability of on/off signal ,on the internet

Ts=10^4;
SNR_dB=[-3 0 3 6 9];
Ne=zeros(1,length(SNR_dB));

for i=1:length(SNR_dB)
SNR=10^(SNR_dB(i)/10);
for t=1:Ts
s=((sign(rand()-0.5))+1)/2; %create the "on"signal or "off" signal ."on"signal=1,"off" signal=0
r=randn(2,1)./sqrt(2.*SNR); %it seems that it is noise
if (s+r)>0.5
s_hat=1;
else
s_hat=0;
end
if abs(s_hat-s)>0
Ne(i)=Ne(i)+1;
end
y=Ne./Ts;
end
end
Pe=zeros(1,5);
for i=1:5
SNR=10^(SNR_dB(i)/10);
Pe(i)=erfc(sqrt(SNR/2)/(2^0.5))/2;
end
semilogy(SNR_dB,y,'-r',SNR_dB,Pe,'-k')

I don't understand why can the noise be written as

r=randn(2,1)./sqrt(2.*SNR)

,why do we need to write as randn(2,1)./sqrt(2*SNR) instead of randn(1,1)/sqrt(2)?Is anyone know about this?

• Because that's how the noise power is adjusted to give the desired SNR. – Marcus Müller Apr 21 '19 at 9:40
• @MarcusMüller Is there any formula can prove this? – shineele Apr 21 '19 at 9:40
• It's exactly the formula in that line of code: Power goes with the square of amplitude, and thus, you divide by the square root of the desired power factor. I honestly don't know what there is to explain about that... – Marcus Müller Apr 21 '19 at 9:43
• i mean,SNR=signal power/noise power.so r=randn(2,1)./sqrt(2.*SNR)=randn(2,1)./sqrt(2.*(signal power/noise power)).why?why doesn't the noise like SNR* randn(2,1)./sqrt(2)? – shineele Apr 21 '19 at 9:48
• I don't understand your criticism: you know that SNR is the ratio of signal power to noise power. Signal power is fixed in your code. You hence have to adjust the noise power. The higher the SNR gets, the lower the noise power hence must be. To scale the power linearly by a factor, you need to scale the amplitude by the square root of the factor. That's all there is! I recommend you don't get defensive towards people trying to help you. – Marcus Müller Apr 21 '19 at 10:18

Not sure if this will help, but let me show how to generate a noisy signal of a desired SNR, assuming additive white Gaussian noise (AWGN) model with fixed signal power.

First the basic definition of SNR (signal to noise ratio) is : $$\text{SNR} = \frac{\sigma_x^2}{\sigma_v^2}$$

where $${\sigma_x^2}$$ is the signal power based on a WSS random signal model, and $${\sigma_v^2}$$ is therefore the noise power (which I take here as white Gaussian noise).

SNR can also be defined in decibells: $$\text{SNR}_{dB} = 10 \log_{10} \left( \frac{\sigma_x^2}{\sigma_v^2} \right) = 10 \log_{10}( \text{SNR})$$

Assuming your signal power $$\sigma_x^2$$ is fixed, then you can adjust the noise power $$\sigma_v^2$$ to achieve a desired SNR with your AWGN signal model. The necessary noise power is found from required SNR as:

$$\sigma_v^2 = \frac{ \sigma_x^2 }{ SNR }$$

Now, Matlab's built in Gaussian function randn() generates standard normal with zero mean and unit variance. Then to get a desired variance (hence noise power) you should scale it with the square root of the target power as shown:

sigx2  = 5.1;          % signal variance (power)
SNR    = 23 ;          % SNR = sigx^2 / sigv^2
sigv2  = sigx2 / SNR;  % noise variance (power)
N      = 1024;         % number of noise samples
v = sqrt( sigv2 ) * randn(N,1); % White Gaussian noise

The reason why you multiply with the square root of the power (or variance) is based on the following property of the variance operator:

$$\text{Var}(X) = \sigma_x^2 \implies \text{Var}(aX) = a^2 \sigma_x^2$$

• because the randn() will produce the unit variance,that is ,$\sigma^2_{n}=1$,and now i know the SNR and the signal power,$\sigma^2_{x}$, is fixed.So actually,in this case,we have to let the $1$ become $\sigma^2_{n}$,and $\sigma^2_{n}= \frac{\sigma^2_{x}}{SNR}$ ,so we have to $1 \times \sqrt{\frac{\sigma^2_{x}}{SNR}}$,that's why we will write sqrt( sigv2 ) * randn(N,1) ,is my thinking right? – shineele Apr 22 '19 at 2:10
• yes that's exactly what I did ;-) – Fat32 Apr 22 '19 at 10:51
• How would you adjust this for a signal represented in complex form? – BigBrownBear00 Jul 23 '20 at 12:19
• Discrete-Random Signals and Statistical Signal Processing_THERRIEN gives quite detailed answers to complex random processing. – Fat32 Jul 24 '20 at 10:13


text:
# Para Magnetism

## Para Magnetism

Paramagnetism refers to a property of materials that are weakly attracted to a magnetic field. When exposed to a magnetic field, internal induced magnetic fields form in the material that are ordered in the same direction as the applied filed. Once the applied field is removed, the material loses its magnetism as thermal motion randomizes the electron spin orientation.

It is a kind of magnetism where several objects are attracted through an externally applied magnetic field. Whereas the diamagnetic materials are repelled by magnetic fields and develop induced magnetic fields in the direction which is opposite to that of the applied magnetic fields.

The paramagnetic material becomes good magnetic material when placed in the strong magnetic material. It acts as a magnet which attracts and repel other magnetic and ferromagnetic materials. When the magnetic field is removes, the total magnetic alignment of the magnetic dipoles is lost and the dipole returned to their normal random motion. This condition is known as Paramagentism.

The Super Paramagnetism is described as the property as some materials magnetic moments change their direction at the nanoscale and behaves like a paramagnet event. According to Curie law, if there is no magnetic field applied, Curie temperature is applied at the same time as they show high magnetic susceptibility.

Curie’s Law: According to Curie’s law, the magnetization in the paramagnetic material is inversely proportional to the temperature which means the more the temperature of the paramagnetic material increases, its magnetization decreases.

$$M\,\,=\,\,\frac{C}{BT}$$.

Where,

C = Curie constant,

T = Temperature in Kelvin and,

B = Applied the magnetic field.


text:
# ``cite'' the steady state level in the model block

In the model block, can we ``cite’’ the steady state level computed in the steady_state_ model block?
for example:

model;
log(M)-log(Mbar)=rho*(log(M(-1))-log(Mbar));
end;

where Mbar is the steady state of M

Thanks!

```model; log(M)-log(steady_state(Mbar))=rho*(log(M(-1))-log(steady_state(M))); end;```


text:
## Easings Library

monolifed
Party member
Posts: 189
Joined: Sat Feb 06, 2016 9:42 pm

### Easings Library

I am writing yet another easings library

smoothstep 1 to 6
polynomial 2 to 6
circle, sine, expo
back, elastic, bounce

https://github.com/monolifed/lua-modules -> easings
Last edited by monolifed on Sat Sep 18, 2021 9:51 am, edited 5 times in total.
pgimeno
Party member
Posts: 2775
Joined: Sun Oct 18, 2015 2:58 pm

### Re: Easings Preview

Nice! But I miss the smoothstep function, 3x² - 2x³.

I'm not a big fan of piecewise defined functions for easing, because their lack of smoothness is sometimes perceptible.

monolifed
Party member
Posts: 189
Joined: Sat Feb 06, 2016 9:42 pm

### Re: Easings Preview

Which ones are not smooth?
bounce is clearly not
elasticOutIn, expoOutIn also not
Anything else?

I think its out version can be

Code: Select all

f(x) = sqrt(x * (x - 1) / 3) for x < 0.5
1 - f(x - 2) for x >= 0.5

Thinking again, smoothstep is more like an InOut function
pgimeno
Party member
Posts: 2775
Joined: Sun Oct 18, 2015 2:58 pm

### Re: Easings Preview

I mean smooth as in infinitely derivable. Any polynomial function, like smoothstep, has this property. Note however that just having the first derivative continuous makes the function have no angles, but that's not what I meant. Many if not all of the first derivatives of your piecewise InOut and OutIn functions have angles, and that may cause visible effects.

Consider for example the quadInOut function. It's equivalent to the following scenario: imagine you're in a car; starting from 0 speed, you accelerate with constant acceleration for the first 50 m and then brake for another 50 m with constant deceleration until you're stopped again. In the car, it means you go from having your back against the back of the seat, to suddenly having your chest against the seatbelt, rather than having a smooth transition between these two cases. The abrupt change from accelerating to decelerating means the second derivative is not continuous, and it's noticeable for someone observing the car's movement.

It's even worse in the case of cubicInOut, for example, because it means that the acceleration grows constantly for the first half of the trajectory and suddenly changes its sign during the second half.
monolifed
Party member
Posts: 189
Joined: Sat Feb 06, 2016 9:42 pm

### Re: Easings Preview

Yes they (InOut ones) don't seem to have continuous second derivatives.
Interestingly leap from acceleration to deceleration doesn't seem to affect smoothness of the transition noticeably
Last edited by monolifed on Tue Sep 14, 2021 5:12 pm, edited 1 time in total.
milon
Party member
Posts: 182
Joined: Thu Jan 18, 2018 9:14 pm

### Re: Easings Preview

As pgimeno as pointed out in both posts, it can/will affect the smoothness of transitions. Whether or not it's noticed will depend on the hardware, framerate, user, etc. If you want to guarantee a smooth transition then the second derivative function must be continuous.
monolifed
Party member
Posts: 189
Joined: Sat Feb 06, 2016 9:42 pm

### Re: Easings Preview

I understand that they are not mathematically smooth but I am yet to see visual artifacts caused by it, Feel free to provide an example

That said I am not inventing new functions here. They are some standard functions and some other functions from easings.net
If they are not smooth there is nothing I can do.

Also you can provide functions if you want, I will add them

pgimeno
Party member
Posts: 2775
Joined: Sun Oct 18, 2015 2:58 pm

### Re: Easings Preview

Here's an example.

Code: Select all

local smooth = 0

love.graphics.setNewFont(30)

local function lerp(a, b, t)
return t < 0.5 and a + (b - a) * t or b + (a - b) * (1.0 - t)
end

local function smootherstep(t)
return t*t*t*(t*(6*t-15)+10)
end

return t < 0.5 and 2*t*t or 1-2*(1-t)^2
end

local T = 0
function love.update(dt)
T = (T + dt) % 2
end

function love.draw()
local w, h = love.graphics.getDimensions()
local t = T < 1 and T or 2 - T
if smooth == 0 or smooth == 2 then
love.graphics.print("quadInOut", 0, h * 0.4 - love.graphics.getFont():getHeight() - 8)
love.graphics.circle("fill", lerp(w * 0.2, w * 0.8, quadInOut(t)), h*(smooth == 2 and 0.4 or 0.5), 4)
end
if smooth == 1 or smooth == 2 then
love.graphics.print("Smooth", 0, h * 0.6 + 8)
love.graphics.circle("fill", lerp(w * 0.2, w * 0.8, smootherstep(t)), h*(smooth == 2 and 0.6 or 0.5), 4)
end
end

function love.keypressed(k)
if k == "escape" then return love.event.quit() end
if k == "space" then smooth = (smooth + 1) % 3 end
end

I see a visible jerk in the middle of the quadInOut function compared to the approximately equivalent smootherstep function. The jerk is best observed in isolation, and the approximate equivalence can be observed side by side. The jerk is more obvious the steeper the slope in the middle point is; with circInOut it's maximum because the slope is infinite.

I didn't include your code because I've realized that you haven't included a license, so the default copyright applies, which doesn't give me any rights to reproduce it.

BTW, there's a typo in the latest version (missing a separating comma; easily fixable).
monolifed
Party member
Posts: 189
Joined: Sat Feb 06, 2016 9:42 pm

### Re: Easings Preview

Thanks
Yes very slight but there and compared to smootherstep it becomes very noticeable.
polynomial outin functions seem to be smooth but all inout ones have that problem
One solution is adding a higher degree polynomial that resembles the piecewise inout function
(Like the smootherstep you provided)

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text:
# Vigorous actions on the Cantor set

This is related to my previous question here:

Antichains and measure-preserving actions on Boolean algebras

This time I will ask something more precise.

Let $G$ be a group acting by homeomorphisms on the standard Cantor set $X$ (or if you prefer, $G$ is acting on the countable atomless Boolean algebra, which can be realised as the clopen subsets of $X$). Say a non-empty clopen subset $\alpha$ of $X$ is minorising (for $G$) if the following holds:

For every non-empty clopen subset $\beta$ of $X$, there is some $g \in G$ such that $g\beta$ contains $\alpha$.

Now suppose that there is a minorising subset $\alpha$, and that $G\alpha$ (that is the set of $g\alpha$ for $g \in G$) covers $X$. Let $n$ be the smallest size of a subcover of $G\alpha$, that is the smallest number of $G$-translates of $\alpha$ needed to cover $X$. It is clear that $n$ is finite (by compactness) and at least $2$, and that $n$ does not depend on the choice of $\alpha$ (beyond ensuring that $\alpha$ is minorising), so it is an invariant of the action.

The condition $n=2$ is equivalent to the condition that every proper non-empty clopen subset is minorising. (This occurs for instance if $G$ consists of every homeomorphism of $X$.)

Questions: Can $n$ be greater than $2$? What if $G$ is simple, and/or every orbit of $G$ on $X$ is dense?

If $n=2$, can $G$ still have infinitely many orbits on the clopen subsets of $X$?

NB: The existence of a minorising subset means that $G$ destroys most of the extra structure I can think of putting on $X$, such as non-trivial metrics and measures. (Can $G$ act by quasi-isometries?) Effectively $\alpha$ is `as small as possible' up to the action of $G$.

-
If $\alpha$ is minorising (which by the way is equivalent to saying that $G\alpha$ is a $\pi$-base for $X$) and $G\alpha$ covers $X$ then necessarily every orbit of $G$ on $X$ is dense. –  Ramiro de la Vega Dec 16 '11 at 16:34
Ah yes, good point. This is a space in which every nonempty open set contains a nonempty clopen set. –  Colin Reid Dec 16 '11 at 17:21

The answer to your last question is YES. Maybe there is a simpler way to see this, but here is a way:

If $G$ acts freely on $X$ and $\alpha$ is minorising (with $n=2$ if you wish), then there is a zero-dimensional compact space $Z$ of uncountable weight, a suryective map $\pi:Z \to X$ and an action of $G$ on $Z$ commuting with $\pi$ such that $\pi^{-1}\alpha$ is minorising. If $G$ was countable then necessarily $G$ has infinitely many (in fact uncountably many) orbits on the clopen subsets of $Z$. Now you can just consider a suitable countable subalgebra of clopens of $Z$ for which you still have infinitely many orbits and a minorising element (still with $n=2$ if you wish).

Edit: The answer to the first question is also YES. If $G$ acts on $X$ then $G \times \mathbb{Z}_2$ acts in a natural way on $Z$ the disjoint union of two Cantor spaces (which is again a Cantor space), so that the $n$ of a minorising subset $\alpha$ of $X$ gets doubled when $\alpha$ is viewed as a subset of one of the copies in $Z$. Unfortunately $G \times \mathbb{Z}_2$ is not simple. Also, I don´t know if one can get $n=3$ (or any odd number).

-
Could you explain a bit more your construction of $\pi$? Why is $\pi^{-1}\alpha$ minorising? –  Jesse Peterson Dec 16 '11 at 23:43
Jesse: You can see a detailed construction in my article "Basic homogeneity in the class of zero-dimensional compact spaces". The construction uses $CH$ because there I wanted to make sure that the group of autohomeomorphisms of $Z$ was generated by G (i.e. any autohomeomorphism of $Z$ is obtained by pasting finitely many elements of G). Since we don't want that here, we can avoid using $CH$. Also, in the construction, sets of the form $\pi^{-1}U$ with $U$ clopen in $X$ form a $\pi$-base for $Z$ and that is why $\pi^{-1}\alpha$ is still minorising. –  Ramiro de la Vega Dec 17 '11 at 13:06
@Ramiro: Perhaps there is some language or notation that I do not understand, but if $\pi: Z \to X$ is not injective then I don't see why sets of the form $\pi^{-1}U$ should separate points in $Z$. –  Jesse Peterson Dec 17 '11 at 22:30
@Jesse: They don't separate points, they just form a $\pi$-base; this just means that any open subset of $Z$ contains a set of the form $\pi^{-1}U$. –  Ramiro de la Vega Dec 18 '11 at 0:52
Ah, that clears things up. Thanks. –  Jesse Peterson Dec 18 '11 at 5:36

I ran across this question after pondering your more recent question here.

Ramiro has already described examples giving a YES answer to your final question, but here is a large and naturally arising class of examples.

Take $G$ to be the full automorphism group $Aut(T)$ of any finite valence tree $T$ on which $Aut(T)$ acts cocompactly, and take $X$ to be the Cantor set of ends of $T$. Or, you can take $G$ to be any cocompact subgroup of $Aut(T)$, such as the free group of finite rank $n \ge 2$ acting on the universal cover of a rose with $n$ petals, or the fundamental group of any finite graph of groups with finite vertex and edge groups, acting on its Bass-Serre tree.

For such actions, every clopen is minorizing and your number $n$ always equals $2$. The proof uses the fact every orbit of the action of $G$ on $X$ is dense, and that the set of source-sink pairs $x \ne y \in X$ is dense in $X \times X$; these are pairs for which there exists $g \in G$ whose action on $X$ has source--sink dynamics with source $x$ and sink $y$. So, if $C,D$ are any proper clopens then choose a source-sink pair $x,y$ with $x \in D$, $y \not\in D$, then choose a translate of $C$ that contains $x$, then choose $n$ so large that $g^n(C)$ contains $D$. Similarly, if $C$ is any proper clopen in $X$, choose a translate $C_1$ that contains $x$, choose another translate $C_2$ that contains $y$, then choose sufficiently large $n$ so that the pair $g^n(C_1),C_2$ covers $X$.

Also for such actions, there are infinitely many $G$-orbits of clopens. To see this, given any clopen $C$, and letting $D=X-C$, the intersection in $T$ of the convex hulls of $C$ and $D$ is a finite subtree of $T$, the number of vertices of this subtree is an invariant of the orbit of $C$, and this number can be as large as you like.

-
Indeed, I was having similar thoughts just a few days ago. There are also plenty of simple groups that are of this kind, e.g. they appear in a paper of Burger and Mozes (don't have the reference to hand at the moment). Getting n>2 for a simple group seems harder, though. –  Colin Reid May 21 '12 at 12:54


text:
Mathlish - J.S. Milne, Top
Much of mathematics is written in a peculiar pidgin. If you wish to write in standard English, here are a few things to avoid.

## Don't use "so that" when you mean "such that"

Here are the definitions.

#### so that

1. In order that, as in I stopped so that you could catch up.
2. With the result or consequence that, as in Mail the package now so that it will arrive on time.
3. so ... that. In such a way or to such an extent that, as in The line was so long that I could scarcely find the end of it.
From dictionary.com

#### such that

1. adj : of a degree or quality specified (by the "that" clause); their anxiety was such that they could not sleep. (dictionary.com)
2. A condition used in the definition of a mathematical object. For example, the rationals can be defined as the set of all m/n such that n is nonzero and m and n are integers . (mathworld.wolfram.com)

#### Examples

1. We require x to be a rational number so that mx is an integer for some m. [Correct]
2. We require x to be a rational number so that 3x is an integer. [Incorrect; should be such that 3x is an integer.]
3. Let H be a discrete subgroup of the Lie group G so that G/H is compact. [Incorrect --- not all discrete subgroups of Lie groups have compact quotient; this is from the Annals of Math., 107, p313.]
4. Let N and N' be submodules of a module M such that N contains N', so that N/N' is a submodule of M/N'. [Correct! From Steps in Commutative Algebra.]

Briefly, if omitting the "that" from "so that" renders the sentence nonsense, then it was already nonsense, and you should have used "such that". You won't find "so that" among lists of commonly misused expressions because only mathematicians commonly misuse it. Probably the error arose from the influence of German on American (mathematical) English, since the two are not distinguished in German.
[From Matthias Künzer: They are distinguished:
Sei x in Q, so daß es ein m in Z\{0} mit xm in Z gibt.
Sei y in Q so, daß 3y in Z liegt.
Not very many German writers care. "After all, it's just a comma."]

## Write "Gowers's Weblog", not "Gowers' Weblog" or "Gower's Weblog" (Gowers)

[Incidentally, The Princeton Companion to Mathematics is written in unusually good English.]

See:

Use an apostrophe plus -s to show the possessive form of a singular noun, even if that singular noun already ends in -s. (grammar.about.com)
Form the possessive singular of nouns by adding 's. (Strunk and White, The Elements of Style, Elementary Rules of Usage, Rule 1.)
The possessive of most singular nouns is formed by adding an apostrophe and an s. (The Chicago Manual of Style, 7.17)
If you write "Gowers' Weblog", not only will you commit a solecism, but you will mislead a literate reader into thinking that you are referring to the weblog of two or more persons called Gower.

For a truly gruesome error, see BAMS 46.4 (2009), p601, line 8, where one finds: "the Langland's program". (Should be "the Langlands program" or "Langlands's program".)

In brief: the rule is add 's (not ') to singular nouns, except that some authorities allow a few exceptions. In my reading I virtually always see 's used except in mathematics.

## Don't write "verify" when you mean "satisfy"

"Verify" is often misused by mathematicians for "satisfy", especially by those whose native language is French. For example, Roos (2006) writes: "The reason for this is that AB4* is rarely verified for them." He means satisfied. It is possible for a condition to be always satisfied but rarely verified (for example, the commutativity of a certain class of diagrams).
verify means to prove the truth of; satisfy means to fulfill the requirements of. For example, I believe the function satisfies the Leibniz condition, but I haven't verified [i.e., checked] this.

## Don't use "associate to"

Instead use "associate with" or "attach to", whichever is more appropriate. In English, you may associate with gangsters, or attach yourself to the Crips, but you may not associate to either: "associate to" is not English (native French and Italian speakers please take note). Alas,this particular illiteracy has become almost standard in scientific journals -- where once we had two expressions "attach to" and "associate with" with distinct uses, we now have only one "associate to = attach-to-associate-with". [Even Google Translate gets this right: it translates "associé à" correctly as "associated with".]
Normally pure mathematicians are relatively respectful of grammar, but many of them have adopted the habit of using the dreadful phrase "associated to" when they seem to feel that "associated with" has not a sufficiently specific flavour. I am at a loss to understand why they do not use the perfectly grammatical "assigned to" instead. (Penrose, The Road to Reality, p.354.)

## The verbs "permit", "allow", "reduce" normally require objects

For example, the following are incorrect:
The preceding result permits (or allows) to assume that x is positive. [Should be: permits (or allows) us to assume.]
By taking a shortcut, we reduce to 10 miles. [Should be: By taking a shortcut, we reduce the distance to 10 miles.]
We use the local theory to construct the formal group associated to the Neron-model, which then allows to simplify the global steps (Faltings 2008, p93). [Should be: ... formal group attached to... allows us...]

## Let now us praise famous men.

Only mathematicians write "Let now" --- real people write "Now let" or "Let us now".

## Be careful with your use of "any"

The word "any" can mean "one, some, every, all" (see any dictionary). Sometimes it is clear from the context which of these you mean, but usually it is better to choose a more precise word. Compare (in increasing order of ambiguity):
If it is true for one element, then it is true for all.
If it is true for any element, then it is true for all.
If it is true for one element, then it is true for any.
If it is true for any element, then it is true for any.
The next sentence, from an actual article, is truly ambiguous:
... he introduced the "associate form" of a cycle, apparently the first treatment valid in any characteristic.
Because of its ambiguity, Halmos decreed that "any" should never be used in mathematical writing.

## Be careful with quantifiers and negatives

The following statements are equivalent:
1. a(n) \neq 0 for all n.
2. a(n) is not equal to zero for all n.
3. a(n) is not zero for all n.
4. There exists an n for which a(n) is not zero.
So don't use the first to mean "no a(n) is zero"; instead write "no a(n) is zero" (or at least put a comma before the "for all").

## Write sentences that can be parsed by a nonexpert

Serre gives the example of an article that announces its main result in the form:
formula A = formula B = formula C
(no words). Only someone very expert in the field will recognize that the main result is "formula A = formula B" --- the second equality is only an aside.

## Don't write "issue" or "challenge" when you mean "problem"

The first is an illiterate euphemism invented by software companies to avoid admitting that their stuff doesn't actually work. The second is feel-good English best left to the New Age crowd.

## Don't write "address" when you mean "solve", "examine", "study", or ...

Instead, write "solve", "examine", "study", or whatever it is you actually mean. For example, don't write "the conjecture is successfully addressed"; write "the conjecture is proved" (if that is what you mean).

The last two are part of a plague that is spreading into mathematics. Soon people will be writing "Matiyasevich addressed Hilbert's tenth issue", which should mean that Matiyasevich spoke to Hilbert's tenth child...

## Be wary of using :=

Personally, I consider the use of "A := B" for "B is defined to be A" or "B equals A by definition" to be ugly programming jargon (especially ugly if the symbols aren't vertically centred--use the package mathtools to fix this), but if you do choose to use it, use it only when the colon genuinely adds something. Note that "We define A:=B" is shorthand for "We define A is defined to be B".
choose to use it, use it only when the colon genuinely adds something. Note that "We define A:=B" is shorthand for "We define A is defined to be B".


text:
# 1 2 dia 4200 psi tank container discharge hose

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text:
# Recent questions and answers in Three Dimensional Geometry

### Find the vector equation of the line which is parallel to the vector $3\hat i+2\hat j+6\hat k$ and which passes through the point $(1,-2,3).$

To see more, click for all the questions in this category.


text:
# Suppose a jar contains 13 red marbles and

Kimberlee Ann 2022-07-23

Suppose a jar contains 13 red marbles and 31 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. Round your answer to 4 decimal places.

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