text:
### Help Support The Rocketry Forum:

#### Reed Goodwin

##### Well-Known Member
I've heard of this tool and seen the results that it can give, but I'm having trouble finding it locally. It's a tool that you can chuck into a drill press and then it has an adjustable arm that produces different diameter circles and then cuts them out, allowing for custom centering rings. Where have people been able to find this thing? So far I have looked at a Lowes, Home Depot, and a Northern Tool and came up empty-handed. Any ideas? I've heard Tractor Supply might have them, but the closest one is a solid 30 minutes away.
Thanks,
Reed

#### Brent

##### Well-Known Member
They are called fly cutters. I have not seen them at TSC. Harbor Freight has them but I would recommend a good one from someone like Wood Workers Supply.

#### troj

##### Wielder Of the Skillet Of Harsh Discipline, Potent
Get a good one, and always, Always, ALWAYS securely clamp the piece you are cutting. Never try to hold the piece by hand, or get your hands anywhere near it -- they inflict nasty injuries.

-Kevin

#### Chrisn

##### Well-Known Member
Make sure all the screws are torqued up well. I personally dont like them though, tools breaking on a CNC machine running at very high revs dont scare me as much as standing in front of one of these disk cutters on a drill press.

#### n5wd

##### Well-Known Member
...I'm having trouble finding it locally.
I bought one from these folks (Ebay auction link) for $15 postage paid - arrived in less than a week, and I've definitely been putting it to good use. It's nothing fancy, but seems to work well, and keeps the dimensions set rather well. My guess is that I'll probably buy a couple of additional units later - that way I can keep one or two set to the rings/bulkheads I wind up needing the most. #### rocdoc ##### Well-Known Member I've never used one of those, but I have used both the Jasper 200 and 400 Circle Cutting Jigs (http://www.amazon.com/dp/B00009K77A/?tag=skimlinks_replacement-20). They use a 1/4" bit in a plunge router to cut out holes and disks at 1/16" intervals over a large size range. Nowhere near as many dangerous-looking parts. Never had any difficulty using them and never worried about impaling myself. Last edited by a moderator: #### Reed Goodwin ##### Well-Known Member I've never used one of those, but I have used both the Jasper 200 and 400 Circle Cutting Jigs (http://www.amazon.com/dp/B00009K77A/?tag=skimlinks_replacement-20). They use a 1/4" bit in a plunge router to cut out holes and disks at 1/16" intervals over a large size range. Nowhere near as many dangerous-looking parts. Never had any difficulty using them and never worried about impaling myself. Maybe I'll look into whether I have access to a router. Actually thinking about it, if I have access to a drill press, I'll probably have access to a router. Thanks for the suggestion! Reed Last edited by a moderator: #### Gillard ##### Well-Known Member I bought one from these folks (Ebay auction link) for$15 postage paid - arrived in less than a week, and I've definitely been putting it to good use. It's nothing fancy, but seems to work well, and keeps the dimensions set rather well.

My guess is that I'll probably buy a couple of additional units later - that way I can keep one or two set to the rings/bulkheads I wind up needing the most.
i've recently purchased a hole cutter, like the one in the link, an it worked well, even my students were able to produce some good centering rings with it.

#### Micromeister

##### Micro Craftman/ClusterNut
TRF Supporter
I've found it actually works better of you buy two and sit it up to cut both holes at the same time inner first then the outer.

As others have already posted. SECURELY CLAMP the work, Wear SAFETY Glasses and a full FACE Sheild isn't a bad idea either, Gloves but always KEEP you Hands AWAY for the cutter while the press is turning.

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#### Brent

##### Well-Known Member
That's a great idea. I have 2 fly cutters but never thought about combining them.

#### rocketsmith

##### Well-Known Member
I have used these with varying success. The one thing I have found works well is to "onion skin" the cuts. Leave a thin layer of material at the bottom of the cut and use a hobby knife to remove the pieces and trim the "flashing"

#### jcDerRedMax

##### Member
1st trick with those is to drill 1/2 way from each side. The ridge in the middle makes for a tighter fit to the tube.

2nd trick is to dip the ends of the cross bar in safety orange. When the drill is on, you'll see an orange circle.

#### sodmeister

##### Well-Known Member
I have two similar cutters ,one was a cheap "generic" circle cutter and the other ,while looking very much the same ,is of much better quality.I bought the more expensive one at lee Valley Tools and the old saying"you get what you pay for" is very true.These particular cutters have a counter weight on one end ,and work alright ,but they take a bit of set up.What I now do when making CRs is to cut the outside ring with the circle cutter and use a toothed Forstner bit (also from Lee Valley) to cut the engine tube hole (24 ,29,38mm) ,I find this does a better job for me.

AND yes ,keep your eyes on that flying blade and clamp that work down !!

I like the idea of coloring the bar orange for visibility......much like propellers on aircraft.

Paul

#### troj

##### Wielder Of the Skillet Of Harsh Discipline, Potent
The safety orange on the end is a great idea -- even white would work. Anything that stands out and helps you keep your fingers and clothing clear of that nasty bugger!

Something I've not yet seen mentioned -- cutting speed. These need to be run at the slowest speed your drill press has, and take your time with the cutting.

-Kevin

#### Brent

##### Well-Known Member
Speed also depends on the material you are cutting. With this type of cutter you do need to feed slowly though never force. Another thing to look at is the quality of the drill press you are using and how you clamp your work. I prefer to use a mill with this type of tool but I do not have one at home. Another thing to remember is to always respect tools or machines you are using and use personal protective gear.

#### sodmeister

##### Well-Known Member
The safety orange on the end is a great idea -- even white would work. Anything that stands out and helps you keep your fingers and clothing clear of that nasty bugger!

Something I've not yet seen mentioned -- cutting speed. These need to be run at the slowest speed your drill press has, and take your time with the cutting.

-Kevin
Good point.I run at 500 RPM on my floor model 3/4 horse drill press for this cutter and Forstner bits.With bigger machines ,it`s too easy to muscle your way into the project,instead of letting the tool/cutter/bit do the work.

Just like making love.....nice and easy (unless my football games are on)

P

#### Commonwealth.Net

##### Well-Known Member
Fly Cutter ?
Or call us and let us LASER cut parts for you !

#### Reed Goodwin

##### Well-Known Member
Fly Cutter ?
Or call us and let us LASER cut parts for you !
Another excellent option! Everything is better with lasers! Will keep it in mind.
Reed

#### Solomoriah

##### Well-Known Member
Something I've not yet seen mentioned -- cutting speed. These need to be run at the slowest speed your drill press has, and take your time with the cutting.
I set my drill press on the slowest speed when I got it, and have never since changed it. I just don't see the need for speed here.

I do want a circle cutter, though. I wish I could buy a set of Forstner bits sized to make BT-5 and BT-20 sized holes... that'd be COOL. With both a circle cutter and a set of those, I could make cluster centering rings from birch plywood really easily.

I do know some people with a laser cutter but I haven't asked them about using it yet. I'm sure it'd cost me some...

#### luke strawwalker

##### Well-Known Member
I got one at Harbor Freight last year... works pretty well. Not the highest quality in the world but not the highest price either...

You really want to cut slow with these things and definitely let the tool do the work-- no down pressure to speak of. Cutting from both sides DEFINITELY is recommended.

You don't much see these things in the local hardware/big box stores because most of the stuff they sell is going to end up being used in a cordless drill or VSR hand drill-- and while I HAVE done it that way with a fly cutter, it's DEFINITELY NOT RECOMMENDED and at least a skill level 5 type of operation...

Later and good luck! OL JR

#### ONAWHIM

##### Well-Known Member
Troj mentioned clamping.

When I cut small items on a drill press I will screw the material I am cutting onto something sacrificial underneath. Obviously the screws would be outside of the cutting area.
If you use something appropriately sized you can clamp it down.

Cut through your material and into was is under it.

Wm.

#### slogfilet

##### Well-Known Member
Over the weekend I tried the Dremel circle cutting attachment (ordered it from Amazon last week.)

I was pretty impressed with the results. I made several 54mm bulkhears and some 54-38mm centering rings, and everything came out 100% useable! I was using 1/8" birch ply; I'm going to try it on some 1/4" for a crayon project.

Haven't heard too many folks mention it, but I found it to be a good tool.

Here's a link... \$15 on Amazon:
http://www.amazon.com/Dremel-678-01-Circle-Cutter-Straight/dp/B000HI5WTY/ref=sr_1_1?ie=UTF8&s=hi&qid=1263242639&sr=8-1

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#### n5wd

##### Well-Known Member
Haven't heard too many folks mention it, but I found it to be a good tool.
I've tried it, but either I lack the proper technique or patience to get it right with the Dremel attachment - glad it's working for you!

#### Stymye

##### Well-Known Member
I use a good quality double back tape and stack cut several at one time.
I cut the outer diameter only as "blanks"

when I need a finished ring, I cut the appropiate inner diameter with a hole saw or appropiate size tool using the pilot hole that the flycutter left for centering.
or I use them as is, for bulkheads

usually all thats needed from that point is a little fine tune sanding.

I set up and cut about 80 different blanks in a couple hours.

this batch has lasted me a long time and I can now whip out a finished ring in minutes

#### slogfilet

##### Well-Known Member
I can see how the fly cutter would be much faster for making multiple pieces (especially at the same size.) The Dremel attachment does takes some time to set up for each cut.

But if you lack a drill rpess but have a rotary tool, it's a decent option. I figure whatever method/tool you use, it'll pay for itself in short order!

#### CF-105

##### Well-Known Member
Troj mentioned clamping.

When I cut small items on a drill press I will screw the material I am cutting onto something sacrificial underneath. Obviously the screws would be outside of the cutting area.
If you use something appropriately sized you can clamp it down.

Cut through your material and into was is under it.

Wm.
For cases where there's not enough clearance for clamps, I tack the material down with small finishing nails.

I now have a collection of these things, all set at specific diameters (and labeled). If I need to cut rings or bulkheads of those sizes again, there's no need for "test" cuts.

#### Micromeister

##### Micro Craftman/ClusterNut
TRF Supporter
For cases where there's not enough clearance for clamps, I tack the material down with small finishing nails.

I now have a collection of these things, all set at specific diameters (and labeled). If I need to cut rings or bulkheads of those sizes again, there's no need for "test" cuts.
Not enough room for clamps LOL!!??? Turn the C-Clamp over LOL!!!

#### CF-105

##### Well-Known Member
Being a packrat, I have a hoard of scrap ply. Often I'm cutting from material that's barely big enough to do the job. Clamps aren't an options in those cases.

#### RocketFeller

##### Well-Known Member
I love my adjustable circle cutter, I'll never buy another centering ring!

I picked up my circle-cutter at my neighbor's junk sale, it was second-hand but seemed brand-new and I got it for a buck. I suspect it is a fairly cheap one as it has to be readjusted after every two or three rings cut.

One trick I figured out for cutting rings without clamping/nailing/screwing is to use a great-big pair of channel-lock pliers to hold the rings.

My method:

I cut the outer circle first. I use a sacrificial piece of plywood under the CR stock and set the height of the platform so the cutter will cut a sixteenth or so into the plywood.

If I am cutting out of a big piece I just hold with the left hand and crank with the right. If it is a smaller scrap I clamp it somehow.

After I cut the discs I switch the cutter and cut out the inside cut holding the ring with the Channel-Locks. This works really well on 4" and under rings, for bigger rings the pliers won't work, of course.

#### THier

##### Well-Known Member
I've never used one of those, but I have used both the Jasper 200 and 400 Circle Cutting Jigs (http://www.amazon.com/dp/B00009K77A/?tag=skimlinks_replacement-20). They use a 1/4" bit in a plunge router to cut out holes and disks at 1/16" intervals over a large size range. Nowhere near as many dangerous-looking parts. Never had any difficulty using them and never worried about impaling myself.
Agree 100% with this,, can't go wrong with it and MUCH safer and more precise than a fly cutter.

Tom

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## Strang, William Gilbert

Compute Distance To:
 Author ID: strang.gilbert Published as: Strang, Gilbert; Strang, G.; Strang, W. Gilbert; Strang, W. G. Homepage: http://www-math.mit.edu/~gs/ External Links: MGP · ORCID · Wikidata · ResearchGate · Math-Net.Ru · dblp · GND · IdRef
 Documents Indexed: 191 Publications since 1957, including 26 Books 3 Contributions as Editor Biographic References: 2 Publications Co-Authors: 73 Co-Authors with 90 Joint Publications 3,022 Co-Co-Authors
all top 5

### Co-Authors

 100 single-authored 11 Kohn, Robert Vita 5 Fix, George J. 5 Shen, Jianhong 4 MacNamara, Shev F. 4 Nguyen, Truong Quang 4 Temam, Roger Meyer 4 Zhou, Dingxuan 3 Edelman, Alan Stuart 3 Strela, Vasily 2 Berger, Alan E. 2 Borre, Kai 2 Flaschka, Hermann 2 Gao, Xiqi Q. 2 Gao, Yang 2 Grinfeld, Pavel 2 Heil, Christopher E. 2 Iserles, Arieh 2 Li, Chi-Kwong 2 Liu, Xiangwei 2 Matthies, Hermann Georg 2 Persson, Per-Olof 1 Abdel Naby, Mokhtar A. 1 Albert, Chase 1 Bathe, Klaus-Jürgen 1 Boyd, Geoff 1 Chan, Raymond Hon-Fu 1 Dharmaraja, Sohan 1 Ehrlich, Louis W. 1 Eisenberg, Bennett 1 Engelman, Michael S. 1 Fujita, Hiroshi 1 Gao, Xiqi 1 Gartling, David K. 1 Genton, Marc G. 1 Gorsich, David J. 1 Green, William H. 1 Hager, William W. 1 He, Li 1 Hoffmann, Roald 1 Horn, Berthold Klaus Paul 1 Klarbring, Anders 1 Lax, Peter David 1 Lee, Steven L. 1 Lindner, Marko 1 Lippert, Ross A. 1 Martins, João A. C. 1 Micchelli, Charles A. 1 Miller, John James Henry 1 Moler, Cleve B. 1 Moreau, Jean Jacques 1 Mosco, Umberto 1 Movassagh, Ramis 1 Nickell, Robert E. 1 Olshevsky, Vadim 1 Ott, Susan 1 Panagiotopoulos, Panagiotis D. 1 Parlett, Beresford Neill 1 Riley, James D. 1 Rota, Gian-Carlo 1 Schneider, Hans 1 Scott, Larkin Ridgway 1 Serre, Denis 1 Speth, Raymond L. 1 Stengle, Gilbert 1 Storch, Joel A. 1 Troesch, B. Andreas 1 Tsuji, Yuta 1 Van Dooren, Paul M. 1 Wang, Liang 1 Wang, Yinghui 1 Wathen, Andrew John 1 Yu, Gexin 1 Zhlobich, Pavel
all top 5

### Serials

 9 American Mathematical Monthly 7 SIAM Review 5 International Journal for Numerical Methods in Engineering 5 Linear Algebra and its Applications 4 Archive for Rational Mechanics and Analysis 4 Numerische Mathematik 4 Proceedings of the American Mathematical Society 4 SIAM Journal on Numerical Analysis 4 Studies in Applied Mathematics 4 IEEE Transactions on Signal Processing 3 Computer Methods in Applied Mechanics and Engineering 3 Communications on Pure and Applied Mathematics 3 Journal of Differential Equations 3 Transactions of the American Mathematical Society 3 Bulletin of the American Mathematical Society 2 Journal of Mathematical Analysis and Applications 2 Advances in Mathematics 2 SIAM Journal on Discrete Mathematics 2 Bulletin of the American Mathematical Society. New Series 2 ELA. The Electronic Journal of Linear Algebra 2 Journal of Mathematics and Physics 1 Computers & Mathematics with Applications 1 IMA Journal of Numerical Analysis 1 Journal d’Analyse Mathématique 1 Journal of Applied Mechanics 1 Journal of the Franklin Institute 1 Journal of Mathematical Physics 1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Mathematics of Computation 1 Mathematics Magazine 1 The Mathematical Intelligencer 1 Applied Mathematics and Optimization 1 Canadian Mathematical Bulletin 1 Duke Mathematical Journal 1 Journal of Mathematics of Kyoto University 1 Journal of Multivariate Analysis 1 Mathematical Programming Study 1 Mathematical Programming 1 Mathematica Scandinavica 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Quarterly of Applied Mathematics 1 SIAM Journal on Scientific and Statistical Computing 1 Journal of Xi’an Jiaotong University 1 Acta Applicandae Mathematicae 1 Physica D 1 The Annals of Applied Probability 1 Journal of Global Optimization 1 Proceedings of the National Academy of Sciences of the United States of America 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Notices of the American Mathematical Society 1 Applied and Computational Harmonic Analysis 1 Computational and Applied Mathematics 1 Journal of Convex Analysis 1 Advances in Computational Mathematics 1 Obozrenie Prikladnoĭ i Promyshlennoĭ Matematiki 1 The Journal of Fourier Analysis and Applications 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Foundations of Computational Mathematics 1 HERMIS-$$\mu\pi$$. Hellenic European Research on Mathematics and Informatics Science 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 1 Journal of Mathematics and Mechanics 1 Journal of the Society for Industrial & Applied Mathematics 1 Journal de Mécanique 1 North-Holland Mathematics Studies 1 Inverse Problems and Imaging 1 Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae 1 Journal of the Society for Industrial and Applied Mathematics. Series B, Numerical Analysis 1 Springer-Lehrbuch
all top 5

### Fields

 77 Numerical analysis (65-XX) 46 Linear and multilinear algebra; matrix theory (15-XX) 29 Mechanics of deformable solids (74-XX) 28 Harmonic analysis on Euclidean spaces (42-XX) 23 Partial differential equations (35-XX) 20 Calculus of variations and optimal control; optimization (49-XX) 16 Information and communication theory, circuits (94-XX) 15 Operations research, mathematical programming (90-XX) 12 Approximations and expansions (41-XX) 10 General and overarching topics; collections (00-XX) 7 Systems theory; control (93-XX) 6 Real functions (26-XX) 4 Combinatorics (05-XX) 4 Convex and discrete geometry (52-XX) 4 Fluid mechanics (76-XX) 3 Probability theory and stochastic processes (60-XX) 3 Biology and other natural sciences (92-XX) 2 Ordinary differential equations (34-XX) 2 Functional analysis (46-XX) 2 Computer science (68-XX) 2 Geophysics (86-XX) 2 Mathematics education (97-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Group theory and generalizations (20-XX) 1 Special functions (33-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX)

### Citations contained in zbMATH Open

157 Publications have been cited 5,822 times in 5,266 Documents Cited by Year
On the construction and comparison of difference schemes. Zbl 0184.38503
Strang, Gilbert
1968
A Fourier analysis of the finite element variational method. Zbl 0278.65116
Strang, G.; Fix, G.
1973
An analysis of the finite element method. Zbl 0356.65096
Strang, Gilbert; Fix, George J.
1973
A simple mesh generator in MATLAB. Zbl 1061.65134
2004
Wavelets and filter banks. Zbl 1254.94002
Strang, Gilbert; Nguyen, Truong
1996
A note on the joint spectral radius. Zbl 0095.09701
Rota, Gian-Carlo; Strang, W. Gilbert
1960
Linear algebra and its applications. Zbl 0338.15001
Strang, Gilbert
1976
Introduction to applied mathematics. Zbl 0618.00015
Strang, Gilbert
1986
A proposal for Toeplitz matrix calculations. Zbl 0621.65025
Strang, Gilbert
1986
Optimal design and relaxation of variational problems. I. Zbl 0609.49008
Kohn, Robert V.; Strang, Gilbert
1986
Wavelets and dilation equations: A brief introduction. Zbl 0683.42030
Strang, Gilbert
1989
Linear algebra and its applications. 2nd ed. Zbl 0463.15001
Strang, Gilbert
1980
Functions of bounded deformation. Zbl 0472.73031
Temam, Roger; Strang, Gilbert
1980
Accurate partial difference methods. II: Non-linear problems. Zbl 0143.38204
Strang, G.
1964
Toeplitz equations by conjugate gradients with circulant preconditioner. Zbl 0666.65030
Chan, Raymond H.; Strang, Gilbert
1989
The discrete cosine transform. Zbl 0939.42021
Strang, Gilbert
1999
The solution of nonlinear finite element equations. Zbl 0419.65070
Matthies, Hermann; Strang, Gilbert
1979
Approximation in the finite element method. Zbl 0221.65174
Strang, Gilbert
1972
Fourier analysis of the finite element method in Ritz-Galerkin theory. Zbl 0179.22501
Fix, G.; Strang, G.
1969
Optimal design and relaxation of variational problems. III. Zbl 0694.49004
Kohn, Robert V.; Strang, Gilbert
1986
An analysis of the finite element methods. 2nd ed. Zbl 1171.65081
Strang, Gilbert; Fix, George J.
2008
Geometric nonlinearity: Potential energy, complementary energy, and the gap function. Zbl 0691.73012
Gao, Yang; Strang, Gilbert
1989
Approximation by translates of refinable functions. Zbl 0857.65015
Heil, Christopher; Strang, Gilbert; Strela, Vasily
1996
Duality and relaxation in the variational problems of plasticity. Zbl 0465.73033
Temam, Roger; Strang, Gilbert
1980
Optimal design and relaxation of variational problems. II. Zbl 0621.49008
Kohn, Robert V.; Strang, Gilbert
1986
Trigonometric polynomials and difference methods of maximum accuracy. Zbl 0111.31601
Strang, G.
1962
Accurate partial difference methods. I: Linear Cauchy problems. Zbl 0113.32303
Strang, G.
1963
Topics in nonsmooth mechanics. Zbl 0646.00014
1988
Computational science and engineering. Zbl 1194.65001
Strang, Gilbert
2007
The correctness of the Cauchy problem. Zbl 0213.37304
Flaschka, H.; Strang, G.
1971
Maximal flow through a domain. Zbl 0513.90026
Strang, Gilbert
1983
A Fourier analysis of the finite element variational method. Zbl 0272.65099
Strang, Gilbert; Fix, George
1971
Piecewise polynomials and the finite element method. Zbl 0285.41009
Strang, Gilbert
1974
One-sided approximation and variational inequalities. Zbl 0278.35026
Mosco, Umberto; Strang, Gilbert
1974
Pascal matrices. Zbl 1089.15025
Edelman, Alan; Strang, Gilbert
2004
The asymptotic probability of a tie for first place. Zbl 0787.60029
Eisenberg, Bennett; Stengle, Gilbert; Strang, Gilbert
1993
Introduction to linear algebra. 3rd ed. Zbl 1046.15001
Strang, Gilbert
2003
Linear algebra and its applications. 4th edition. Zbl 1329.15004
Strang, Gilbert
2007
Variational crimes in the finite element method. Zbl 0264.65068
Strang, Gilbert
1972
Introduction to linear algebra. 2nd ed. Zbl 1067.15500
Strang, Gilbert
1998
The fundamental theorem of linear algebra. Zbl 0802.15002
Strang, Gilbert
1993
The optimal accuracy of difference schemes. Zbl 0573.65071
Iserles, Arieh; Strang, Gilbert
1983
Approximate boundary conditions in the finite element method. Zbl 0266.73050
Berger, Alan; Scott, Ridgway; Strang, Gilbert
1972
Inhomogeneous refinement equations. Zbl 0932.42026
Strang, Gilbert; Zhou, Ding-Xuan
1998
A framework for equilibrium equations. Zbl 0900.49028
Strang, Gilbert
1988
Operator splitting. Zbl 1372.65236
MacNamara, Shev; Strang, Gilbert
2016
Introduction to linear algebra. Zbl 1067.15501
Strang, Gilbert
1993
Introduction to linear algebra. 5th edition. Zbl 1351.15002
Strang, Gilbert
2016
Explicit relaxation of a variational problem in optimal design. Zbl 0527.49002
Kohn, Robert V.; Strang, Gilbert
1983
Wavelet transforms versus Fourier transforms. Zbl 0771.42021
Strang, Gilbert
1993
Continuity of the joint spectral radius: Application to wavelets. Zbl 0823.15009
Heil, Christopher; Strang, Gilbert
1995
Necessary and insufficient conditions for well-posed Cauchy problems. Zbl 0131.09102
Strang, G.
1966
On strong hyperbolicity. Zbl 0174.15103
Strang, G.
1967
The interplay of ranks of submatrices. Zbl 1063.15002
Strang, Gilbert; Nguyen, Tri
2004
Eigenvalues of Jordan products. Zbl 0101.25401
Strang, W. Gilbert
1962
Functions of difference matrices are Toeplitz plus Hankel. Zbl 1304.65195
Strang, Gilbert; MacNamara, Shev
2014
Comparison theorems for supremum norms. Zbl 0103.33103
Schneider, Hans; Strang, W. Gilbert
1962
Dual extremum principles in finite deformation elastoplastic analysis. Zbl 0732.73026
Gao, Yang; Strang, Gilbert
1989
Finite element multiwavelets. Zbl 0857.65118
Strela, V.; Strang, G.
1995
Linear algebra, geodesy, and GPS. Zbl 1007.86001
Strang, Gilbert; Borre, Kai
1997
Strang, Gilbert; Kohn, Robert V.
1986
On the Kantorovich inequality. Zbl 0095.09601
Strang, W. G.
1960
Wiener-Hopf difference equations. Zbl 0197.07104
Strang, G.
1964
The application of quasi-Newton methods in fluid mechanics. Zbl 0461.76020
Engelman, M. S.; Strang, G.; Bathe, K.-J.
1981
Green’s matrices. Zbl 1195.15012
Olshevsky, V.; Strang, G.; Zhlobich, P.
2010
The Laplacian eigenvalues of a polygon. Zbl 1069.65121
Grinfeld, P.; Strang, G.
2004
Hencky-Prandtl nets and constrained Michell trusses. Zbl 0487.73111
Strang, Gilbert; Kohn, Robert V.
1983
Matrix theorems for partial differential and difference equations. Zbl 0144.13404
Miller, John; Strang, G.
1966
Eigenstructures of spatial design matrices. Zbl 1003.62084
Gorsich, David J.; Genton, Marc G.; Strang, Gilbert
2002
Hyperbolic initial-boundary value problems in two unknowns. Zbl 0179.14604
Strang, G.
1969
Toeplitz operators in a quarter-plane. Zbl 0203.13701
Strang, G.
1970
Linear algebra and its applications. (Linejnaya algebra i ee primeneniya). Transl. from the English by Yu. A. Kuznetsov and D. M. Fage. Zbl 0548.15004
Strang, Gilbert
1980
Implicite difference methods for initial-boundary value problems. Zbl 0147.13802
Strang, G.
1966
On factorization of $$M$$-channel paraunitary filterbanks. Zbl 1369.94153
Gao, Xiqi; Nguyen, Truong Q.; Strang, Gilbert
2001
Fast transforms: banded matrices with banded inverses. Zbl 1205.65348
Strang, Gilbert
2010
Existence de solutions relaxees pour les équations de la plasticite: Étude d’un espace fonctionnel. Zbl 0404.73026
Temam, Roger; Strang, Gilbert
1978
The change in solution due to change in domain. Zbl 0259.35020
Strang, Gilbert; Berger, Alan E.
1973
Matrices with prescribed Ritz values. Zbl 1141.15010
Parlett, Beresford; Strang, Gilbert
2008
Asymptotic analysis of Daubechies polynomials. Zbl 0876.42024
Shen, Jianhong; Strang, Gilbert
1996
Introduction to linear algebra. (Lineare Algebra. Übersetzt aus dem Englischen von der djs$$^2$$ GmbH, unter Mitarbeit von Michael Dellnitz.) Zbl 1042.15001
Strang, Gilbert
2003
Calculus. Zbl 1213.26003
Strang, Gilbert
1991
Linear algebra and learning from data. Zbl 1422.15001
Strang, Gilbert
2019
Balanced splitting and rebalanced splitting. Zbl 1284.65121
Speth, Raymond L.; Green, William H.; Macnamara, Shev; Strang, Gilbert
2013
Trees with Cantor eigenvalue distribution. Zbl 1141.05325
He, Li; Liu, Xiangwei; Strang, Gilbert
2003
Barriers to stability. Zbl 0529.65058
Strang, Gilbert; Iserles, Arieh
1983
On multiple characteristics and the Levi-Lax conditions for hyperbolicity. Zbl 0176.08901
Strang, G.
1969
Approximating semigroups and the consistency of difference schemes. Zbl 0177.16903
Strang, G.
1969
Localized eigenvectors from widely spaced matrix modifications. Zbl 1037.15009
Liu, Xiangwei; Strang, Gilbert; Ott, Susan
2003
Laplace eigenvalues on regular polygons: a series in $$1/N$$. Zbl 1227.65108
Grinfeld, Pavel; Strang, Gilbert
2012
Maximum area with Minkowski measures of perimeter. Zbl 1135.53003
Strang, Gilbert
2008
The Jordan forms of $$AB$$ and $$BA$$. Zbl 1190.15014
Lippert, Ross A.; Strang, Gilbert
2009
Permutations as product of parallel transpositions. Zbl 1237.05002
Albert, Chase; Li, Chi-Kwong; Strang, Gilbert; Yu, Gexin
2011
Difference methods for mixed boundary-value problems. Zbl 0091.26904
Strang, Gilbert
1960
Polynomial approximation of Bernstein type. Zbl 0119.28703
Strang, G.
1962
The potential theory of several intervals and its applications. Zbl 0983.41006
Shen, J.; Strang, G.; Wathen, A. J.
2001
Maximum flows and minimum cuts in the plane. Zbl 1192.49050
Strang, Gilbert
2009
Maximum flows and minimum cuts in the plane. Zbl 1207.49042
Strang, Gilbert
2010
Optimal stability for trapezoidal-backward difference split-steps. Zbl 1185.65137
Dharmaraja, Sohan; Wang, Yinghui; Strang, Gilbert
2010
Groups of banded matrices with banded inverses. Zbl 1241.15011
Strang, Gilbert
2011
Compactly supported refinable functions with infinite masks. Zbl 0946.42022
Strang, Gilbert; Strela, Vasily; Zhou, Ding-Xuan
1999
Linear algebra for everyone. Zbl 1455.15001
Strang, Gilbert
2020
Linear algebra and learning from data. Zbl 1422.15001
Strang, Gilbert
2019
Multiplying and factoring matrices. Zbl 1393.15017
Strang, Gilbert
2018
The Green’s function for the Hückel (tight binding) model. Zbl 1362.82048
Movassagh, Ramis; Strang, Gilbert; Tsuji, Yuta; Hoffmann, Roald
2017
Operator splitting. Zbl 1372.65236
MacNamara, Shev; Strang, Gilbert
2016
Introduction to linear algebra. 5th edition. Zbl 1351.15002
Strang, Gilbert
2016
The algebra of elimination. Zbl 1325.15011
Strang, Gilbert
2015
Random triangle theory with geometry and applications. Zbl 1321.51016
Edelman, Alan; Strang, Gilbert
2015
Functions of difference matrices are Toeplitz plus Hankel. Zbl 1304.65195
Strang, Gilbert; MacNamara, Shev
2014
Differential equations and linear algebra. Zbl 1339.34001
Strang, Gilbert
2014
The core ideas in our teaching. Zbl 1338.97028
Strang, Gilbert
2014
Symmetric elimination without pivoting. Zbl 1291.65088
Van Dooren, Paul; Strang, Gilbert
2014
Balanced splitting and rebalanced splitting. Zbl 1284.65121
Speth, Raymond L.; Green, William H.; Macnamara, Shev; Strang, Gilbert
2013
The main diagonal of a permutation matrix. Zbl 1283.15092
Lindner, Marko; Strang, Gilbert
2013
Laplace eigenvalues on regular polygons: a series in $$1/N$$. Zbl 1227.65108
Grinfeld, Pavel; Strang, Gilbert
2012
Banded matrices with banded inverses and $$A=LPU$$. Zbl 1247.15012
Strang, Gilbert
2012
Essays in linear algebra. Zbl 1244.15001
Strang, Gilbert
2012
Permutations as product of parallel transpositions. Zbl 1237.05002
Albert, Chase; Li, Chi-Kwong; Strang, Gilbert; Yu, Gexin
2011
Groups of banded matrices with banded inverses. Zbl 1241.15011
Strang, Gilbert
2011
Green’s matrices. Zbl 1195.15012
Olshevsky, V.; Strang, G.; Zhlobich, P.
2010
Fast transforms: banded matrices with banded inverses. Zbl 1205.65348
Strang, Gilbert
2010
Maximum flows and minimum cuts in the plane. Zbl 1207.49042
Strang, Gilbert
2010
Optimal stability for trapezoidal-backward difference split-steps. Zbl 1185.65137
Dharmaraja, Sohan; Wang, Yinghui; Strang, Gilbert
2010
Scientific computing. Translation from the 2007 English ed. (Wissenschaftliches Rechnen.) Zbl 1213.65006
Strang, Gilbert
2010
Calculus. 2nd ed. Zbl 1210.26003
Strang, Gilbert
2010
The Jordan forms of $$AB$$ and $$BA$$. Zbl 1190.15014
Lippert, Ross A.; Strang, Gilbert
2009
Maximum flows and minimum cuts in the plane. Zbl 1192.49050
Strang, Gilbert
2009
An analysis of the finite element methods. 2nd ed. Zbl 1171.65081
Strang, Gilbert; Fix, George J.
2008
Matrices with prescribed Ritz values. Zbl 1141.15010
Parlett, Beresford; Strang, Gilbert
2008
Maximum area with Minkowski measures of perimeter. Zbl 1135.53003
Strang, Gilbert
2008
Computational science and engineering. Zbl 1194.65001
Strang, Gilbert
2007
Linear algebra and its applications. 4th edition. Zbl 1329.15004
Strang, Gilbert
2007
A simple mesh generator in MATLAB. Zbl 1061.65134
2004
Pascal matrices. Zbl 1089.15025
Edelman, Alan; Strang, Gilbert
2004
The interplay of ranks of submatrices. Zbl 1063.15002
Strang, Gilbert; Nguyen, Tri
2004
The Laplacian eigenvalues of a polygon. Zbl 1069.65121
Grinfeld, P.; Strang, G.
2004
Introduction to linear algebra. 3rd ed. Zbl 1046.15001
Strang, Gilbert
2003
Introduction to linear algebra. (Lineare Algebra. Übersetzt aus dem Englischen von der djs$$^2$$ GmbH, unter Mitarbeit von Michael Dellnitz.) Zbl 1042.15001
Strang, Gilbert
2003
Trees with Cantor eigenvalue distribution. Zbl 1141.05325
He, Li; Liu, Xiangwei; Strang, Gilbert
2003
Localized eigenvectors from widely spaced matrix modifications. Zbl 1037.15009
Liu, Xiangwei; Strang, Gilbert; Ott, Susan
2003
Smoothing by Savitzky-Golay and Legendre filters. Zbl 1049.93083
2003
Eigenstructures of spatial design matrices. Zbl 1003.62084
Gorsich, David J.; Genton, Marc G.; Strang, Gilbert
2002
A study of two-channel complex-valued filterbanks and wavelets with orthogonality and symmetry properties. Zbl 1369.94152
Gao, Xiqi Q.; Nguyen, Truong Q.; Strang, Gilbert
2002
On factorization of $$M$$-channel paraunitary filterbanks. Zbl 1369.94153
Gao, Xiqi; Nguyen, Truong Q.; Strang, Gilbert
2001
The potential theory of several intervals and its applications. Zbl 0983.41006
Shen, J.; Strang, G.; Wathen, A. J.
2001
Theory and lattice structure of complex paraunitary filterbanks with filters of (Hermitian-)symmetry/antisymmetry properties. Zbl 1369.94151
Gao, Xiqi Q.; Nguyen, Truong Q.; Strang, Gilbert
2001
The limits of refinable functions. Zbl 0963.42019
Strang, Gilbert; Zhou, Ding-Xuan
2001
Binomial matrices. Zbl 0996.15005
Boyd, Geoff; Micchelli, Charles A.; Strang, Gilbert; Zhou, Ding-Xuan
2001
On wavelet fundamental solutions to the heat equation – heatlets. Zbl 0953.35051
Shen, Jianhong; Strang, Gilbert
2000
Row reduction of a matrix and $$A=CaB$$. Zbl 0983.15010
Lee, Steven L.; Strang, Gilbert
2000
Special issue for R. Temam’s 60th birthday. Zbl 0945.00029
2000
The discrete cosine transform. Zbl 0939.42021
Strang, Gilbert
1999
Compactly supported refinable functions with infinite masks. Zbl 0946.42022
Strang, Gilbert; Strela, Vasily; Zhou, Ding-Xuan
1999
The asymptotics of optimal (equiripple) filters. Zbl 0978.94026
Shen, Jianhong; Strang, Gilbert
1999
Introduction to linear algebra. 2nd ed. Zbl 1067.15500
Strang, Gilbert
1998
Inhomogeneous refinement equations. Zbl 0932.42026
Strang, Gilbert; Zhou, Ding-Xuan
1998
Asymptotics of Daubechies filters, scaling functions, and wavelets. Zbl 0929.42022
Shen, Jianhong; Strang, Gilbert
1998
The discrete cosine transform, block Toeplitz matrices, and wavelets. Zbl 0931.65145
Strang, Gilbert
1998
Linear algebra, geodesy, and GPS. Zbl 1007.86001
Strang, Gilbert; Borre, Kai
1997
Every unit matrix is a LULU. Zbl 0918.15004
Strang, Gilbert
1997
Wavelets from filter banks. Zbl 0888.65140
Strang, Gilbert
1997
Wavelets and filter banks. Zbl 1254.94002
Strang, Gilbert; Nguyen, Truong
1996
Approximation by translates of refinable functions. Zbl 0857.65015
Heil, Christopher; Strang, Gilbert; Strela, Vasily
1996
Asymptotic analysis of Daubechies polynomials. Zbl 0876.42024
Shen, Jianhong; Strang, Gilbert
1996
Eigenvalues of Toeplitz matrices with $$1\times 2$$ blocks. Zbl 0894.93017
Strang, Gilbert
1996
Condition numbers for wavelets and filter banks. Zbl 0862.42025
Strang, Gilbert
1996
Creating and comparing wavelets. Zbl 0852.94007
Strang, Gilbert
1996
Wavelets from filter banks. Zbl 0898.42009
Strang, Gilbert
1996
Continuity of the joint spectral radius: Application to wavelets. Zbl 0823.15009
Heil, Christopher; Strang, Gilbert
1995
Finite element multiwavelets. Zbl 0857.65118
Strela, V.; Strang, G.
1995
The asymptotic probability of a tie for first place. Zbl 0787.60029
Eisenberg, Bennett; Stengle, Gilbert; Strang, Gilbert
1993
The fundamental theorem of linear algebra. Zbl 0802.15002
Strang, Gilbert
1993
Introduction to linear algebra. Zbl 1067.15501
Strang, Gilbert
1993
Wavelet transforms versus Fourier transforms. Zbl 0771.42021
Strang, Gilbert
1993
The optimal coefficients in Daubechies wavelets. Zbl 0780.42021
Strang, Gilbert
1992
Calculus. Zbl 1213.26003
Strang, Gilbert
1991
Inverse problems and derivatives of determinants. Zbl 0723.94010
Strang, Gilbert
1991
Wavelets and dilation equations: A brief introduction. Zbl 0683.42030
Strang, Gilbert
1989
Toeplitz equations by conjugate gradients with circulant preconditioner. Zbl 0666.65030
Chan, Raymond H.; Strang, Gilbert
1989
Geometric nonlinearity: Potential energy, complementary energy, and the gap function. Zbl 0691.73012
Gao, Yang; Strang, Gilbert
1989
Dual extremum principles in finite deformation elastoplastic analysis. Zbl 0732.73026
Gao, Yang; Strang, Gilbert
1989
Patterns in linear algebra. Zbl 0685.15006
Strang, Gilbert
1989
Topics in nonsmooth mechanics. Zbl 0646.00014
1988
A framework for equilibrium equations. Zbl 0900.49028
Strang, Gilbert
1988
Paradox lost: Natural boundary conditions in the Ritz-Galerkin method. Zbl 0661.73060
Storch, Joel; Strang, Gilbert
1988
Optimal design of a two-way conductor. Zbl 0656.73047
Strang, Gilbert; Kohn, Robert V.
1988
The Toeplitz-circulant eigenvalue problem $$Ax=\lambda Cx$$. Zbl 0635.65030
Strang, G.; Edelman, A.
1987
The constrained least gradient problem. Zbl 0668.73060
Kohn, Robert V.; Strang, Gilbert
1987
Introduction to applied mathematics. Zbl 0618.00015
Strang, Gilbert
1986
A proposal for Toeplitz matrix calculations. Zbl 0621.65025
Strang, Gilbert
1986
Optimal design and relaxation of variational problems. I. Zbl 0609.49008
Kohn, Robert V.; Strang, Gilbert
1986
Optimal design and relaxation of variational problems. III. Zbl 0694.49004
Kohn, Robert V.; Strang, Gilbert
1986
Optimal design and relaxation of variational problems. II. Zbl 0621.49008
Kohn, Robert V.; Strang, Gilbert
1986
Strang, Gilbert; Kohn, Robert V.
1986
Duality in the classroom. Zbl 0543.15003
Strang, Gilbert
1984
Maximal flow through a domain. Zbl 0513.90026
Strang, Gilbert
1983
The optimal accuracy of difference schemes. Zbl 0573.65071
Iserles, Arieh; Strang, Gilbert
1983
Explicit relaxation of a variational problem in optimal design. Zbl 0527.49002
Kohn, Robert V.; Strang, Gilbert
1983
Hencky-Prandtl nets and constrained Michell trusses. Zbl 0487.73111
Strang, Gilbert; Kohn, Robert V.
1983
Barriers to stability. Zbl 0529.65058
Strang, Gilbert; Iserles, Arieh
1983
...and 57 more Documents
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### Cited by 7,535 Authors

 43 Strang, William Gilbert 34 Gao, David Yang 28 Hughes, Thomas J. R. 24 Li, Zi-Cai 19 Geiser, Jürgen 19 Serra-Capizzano, Stefano 18 Jin, Xiaoqing 18 Ng, Michael Kwok-Po 17 Bao, Weizhu 17 Chan, Raymond Hon-Fu 17 Panagiotopoulos, Panagiotis D. 16 Faragó, István 16 Glowinski, Roland 16 Huang, Ting-Zhu 15 Kohn, Robert Vita 14 Guglielmi, Nicola 14 Patera, Anthony T. 14 Protasov, Vladimir Yu. 13 Conti, Sergio 13 Ortiz, Michael 13 Simo, Juan Carlos 12 Babuška, Ivo 12 Calo, Victor Manuel 12 Carstensen, Carsten 12 Wang, Hong 11 Arcangeli, Remi 11 Belytschko, Ted Bohdan 11 Charina, Maria 11 Hlaváček, Ivan 11 Huang, Hung-Tsai 11 Paulino, Glaucio H. 11 Ruas, Vitoriano 11 Tyrtyshnikov, Evgeniĭ Evgen’evich 11 Zhou, Dingxuan 10 Carey, Graham Francis 10 Haslinger, Jaroslav 10 Jiang, Qingtang 10 Li, Song 10 Schillinger, Dominik 9 Feistauer, Miloslav 9 Fix, George J. 9 Grabovsky, Yury 9 Havasi, Ágnes 9 Kozyakin, Viktor Sergeevich 9 Křížek, Michal 9 Kurganov, Alexander 9 Shen, Jianhong 9 Wathen, Andrew John 8 Basaran, Osman A. 8 Csomós, Petra 8 Dai, Xiongping 8 Dal Maso, Gianni 8 Deng, Quanling 8 Ghosh, Somnath 8 Kilic, Emrah 8 Morris, Ian D. 8 Nochetto, Ricardo Horacio 8 Nordström, Jan 8 Sun, Haiwei 8 Taylor, Robert Leroy 8 Thomée, Vidar 8 Weng, Zhifeng 8 Yang, Yidu 8 Yee, Helen C. 8 Zhai, Shuying 7 Abrashkevich, A. G. 7 Atzberger, Paul J. 7 Brezzi, Franco 7 Cai, Tony Tony 7 Chan, Tony Fan-Cheong 7 Conti, Costanza 7 Cui, Lihong 7 Gmeineder, Franz 7 Gunzburger, Max D. 7 Hager, William W. 7 Harari, Isaac 7 Hu, Hsin-Yun 7 Huang, Yunqing 7 Ishihara, Kazuo 7 Jia, Rong-Qing 7 Korotov, Sergey 7 Krysl, Petr 7 Liang, Dong 7 Lin, Fu-Rong 7 Lin, Qun 7 Liu, Gui-Rong 7 Liu, Wing Kam 7 Maday, Yvon 7 Massot, Marc 7 Matthies, Hermann Georg 7 Neittaanmäki, Pekka J. 7 Nicaise, Serge 7 Pedregal, Pablo 7 Persson, Per-Olof 7 Sandu, Adrian 7 Saurel, Richard 7 Scott, Larkin Ridgway 7 Shankar, Varun 7 Svärd, Magnus 7 Talischi, Cameron ...and 7,435 more Authors
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### Cited in 618 Serials

 450 Journal of Computational Physics 407 Computer Methods in Applied Mechanics and Engineering 199 Linear Algebra and its Applications 186 Journal of Computational and Applied Mathematics 182 Numerische Mathematik 138 Computers & Mathematics with Applications 117 Mathematics of Computation 114 Applied Mathematics and Computation 106 Applied Numerical Mathematics 90 Journal of Scientific Computing 64 Computers and Fluids 61 International Journal for Numerical Methods in Engineering 56 Applied and Computational Harmonic Analysis 54 SIAM Journal on Scientific Computing 51 Journal of Mathematical Analysis and Applications 50 Archive for Rational Mechanics and Analysis 43 International Journal of Computer Mathematics 40 Numerical Algorithms 38 Computational Mechanics 36 Computer Physics Communications 36 Calcolo 34 Applied Mathematical Modelling 33 Journal of Fluid Mechanics 33 Journal of Approximation Theory 33 Journal of Optimization Theory and Applications 33 Advances in Computational Mathematics 32 Numerical Functional Analysis and Optimization 30 Mathematical and Computer Modelling 29 BIT 29 Mathematics and Computers in Simulation 29 RAIRO. Modélisation Mathématique et Analyse Numérique 28 Proceedings of the American Mathematical Society 27 Applied Mathematics Letters 26 Computing 25 SIAM Journal on Numerical Analysis 25 Engineering Analysis with Boundary Elements 24 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 23 Numerical Methods for Partial Differential Equations 23 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 21 International Journal for Numerical Methods in Fluids 21 Communications in Computational Physics 19 Journal of the Mechanics and Physics of Solids 19 Automatica 19 The Journal of Fourier Analysis and Applications 18 Aplikace Matematiky 18 Transactions of the American Mathematical Society 18 Physica D 18 Numerical Linear Algebra with Applications 18 Archives of Computational Methods in Engineering 18 International Journal of Wavelets, Multiresolution and Information Processing 17 Journal of the Franklin Institute 17 Journal of Differential Equations 17 Computer Aided Geometric Design 17 Calculus of Variations and Partial Differential Equations 17 Communications in Numerical Methods in Engineering 17 Structural and Multidisciplinary Optimization 16 Applicable Analysis 16 Applied Mathematics and Optimization 16 Circuits, Systems, and Signal Processing 16 Signal Processing 16 Physics of Fluids 16 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 15 Journal of Mathematical Physics 15 Journal of Functional Analysis 15 RAIRO. Analyse Numérique 15 Statistics & Probability Letters 15 Constructive Approximation 15 Communications in Nonlinear Science and Numerical Simulation 15 Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Série Rouge 14 International Journal of Control 14 Publications of the Research Institute for Mathematical Sciences, Kyoto University 13 Acta Mechanica 13 Applications of Mathematics 13 Journal of Global Optimization 13 Computational Mathematics and Mathematical Physics 13 Nonlinear Dynamics 13 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 13 Computational Geosciences 12 Journal of Mathematical Biology 12 Advances in Applied Mathematics 12 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 12 International Journal of Computational Methods 12 Science China. Mathematics 12 Nonlinear Analysis. Theory, Methods & Applications 11 International Journal of Systems Science 11 Mathematical Methods in the Applied Sciences 11 Applied Mathematics and Mechanics. (English Edition) 11 SIAM Journal on Matrix Analysis and Applications 11 Multidimensional Systems and Signal Processing 11 Journal of Mathematical Imaging and Vision 11 Journal of Mathematical Sciences (New York) 10 International Journal of Engineering Science 10 Mathematical Notes 10 Wave Motion 10 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Computational and Applied Mathematics 10 Mathematical Problems in Engineering 10 Foundations of Computational Mathematics 9 ZAMP. Zeitschrift für angewandte Mathematik und Physik 9 The Annals of Statistics ...and 518 more Serials
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### Cited in 63 Fields

 2,822 Numerical analysis (65-XX) 1,351 Partial differential equations (35-XX) 874 Mechanics of deformable solids (74-XX) 852 Fluid mechanics (76-XX) 350 Linear and multilinear algebra; matrix theory (15-XX) 342 Calculus of variations and optimal control; optimization (49-XX) 293 Harmonic analysis on Euclidean spaces (42-XX) 252 Approximations and expansions (41-XX) 205 Information and communication theory, circuits (94-XX) 185 Computer science (68-XX) 185 Operations research, mathematical programming (90-XX) 181 Biology and other natural sciences (92-XX) 171 Systems theory; control (93-XX) 168 Ordinary differential equations (34-XX) 152 Probability theory and stochastic processes (60-XX) 145 Operator theory (47-XX) 143 Statistics (62-XX) 132 Statistical mechanics, structure of matter (82-XX) 101 Optics, electromagnetic theory (78-XX) 101 Classical thermodynamics, heat transfer (80-XX) 91 Dynamical systems and ergodic theory (37-XX) 90 Quantum theory (81-XX) 85 Functional analysis (46-XX) 80 Geophysics (86-XX) 72 Combinatorics (05-XX) 70 Integral equations (45-XX) 62 Mechanics of particles and systems (70-XX) 62 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 51 Number theory (11-XX) 48 Real functions (26-XX) 37 Difference and functional equations (39-XX) 28 Special functions (33-XX) 21 Group theory and generalizations (20-XX) 21 Measure and integration (28-XX) 21 Functions of a complex variable (30-XX) 21 Potential theory (31-XX) 21 Convex and discrete geometry (52-XX) 21 Differential geometry (53-XX) 20 Global analysis, analysis on manifolds (58-XX) 18 Astronomy and astrophysics (85-XX) 14 Commutative algebra (13-XX) 13 Algebraic geometry (14-XX) 12 History and biography (01-XX) 11 General and overarching topics; collections (00-XX) 11 Topological groups, Lie groups (22-XX) 11 Abstract harmonic analysis (43-XX) 10 Several complex variables and analytic spaces (32-XX) 9 Relativity and gravitational theory (83-XX) 8 Sequences, series, summability (40-XX) 7 Integral transforms, operational calculus (44-XX) 7 Mathematics education (97-XX) 6 Mathematical logic and foundations (03-XX) 5 Geometry (51-XX) 5 General topology (54-XX) 5 Manifolds and cell complexes (57-XX) 4 Field theory and polynomials (12-XX) 4 Associative rings and algebras (16-XX) 4 Algebraic topology (55-XX) 3 Nonassociative rings and algebras (17-XX) 2 Category theory; homological algebra (18-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 $$K$$-theory (19-XX)

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# NEAR INFRARED SPECTRUM OF HYDROGEN $SELENIDE^{*}$

Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/8224

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1963-E-08.jpg 89.19Kb JPEG image

 Title: NEAR INFRARED SPECTRUM OF HYDROGEN $SELENIDE^{*}$ Creators: Hill, R. A.; Edwards, T. H. Issue Date: 1963 Publisher: Ohio State University Abstract: “Ground state combination differences in four band’s, $2\nu_{1}$ and $\nu_{1} + \nu_{3}$ near $4600\;cm^{-1}$, and $2\nu_{1} + \nu_{2}$ and $\nu_{1} + \nu_{2} + \nu_{3}$ near $5600\;cm^{-1}$ have been analyzed simultaneously to obtain ground state constants for the two isotopic species $H_{2}{^{80}} Se^{1}$ and $H_{2}{^{78}}$Se, using an energy expression in which the centrifugal distortion energy is written in terms of the four distortion constants $\tau_{aaaa}, \tau_{bbbb_{1}}, \tau_{aabb}$ and $\tau_{abab}{^{2}}$.$^{2}$ Due to a Coriolis interaction between the bands $2\nu_{1}$ and $\nu_{1} + \nu_{3}$ (and also between the bands $2\nu_{1} + \nu_{2}$ and $\nu_{1} + \nu_{2} + \nu_{3})$ the first order energy expression is not able to fit either set of upper state rotational energy levels. However, buy coupling the sum rules for the interacting submatrices, $E^{+}$ with $E^{-}$ and $O^{+}$ with $O^{-}$, of the two vibrational states, we have obtained values for certain upper state constants.” Description: $^{*}$Supported by the National Science Foundation. $^{1}$R.A. Hill and T.H. Edwards, J. Opt. Soc. Am. 53, 516, Abstract TB16. $^{2}$ R.A. Hill and T.H. Edwards, J. Mol. Spectroscopy 9, 494 (1962). Author Institution: Department of Physics and Astronomy, Michigan State University URI: http://hdl.handle.net/1811/8224 Other Identifiers: 1963-E-8


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•   Wikis

# Physics in the Classical Limit: Wikis

Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles.

# Encyclopedia

(Redirected to Classical physics article)

 Classical physics ${ \partial^2 u \over \partial t^2 } = c(u)^2 \nabla^2 u$ Wave equation History of physics This box: view • talk • edit

What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics. When discussing general relativity, it refers to the result of modifying Newtonian physics to incorporate special relativity. When discussing quantum mechanics, it refers to non-quantum physics, often including even general relativity. In other words, it is the physics preceding the physics of interest in one's discussion.

## Overview

### Scope

Among the branches of theory included in classical physics are:

### Differences

In contrast to classical physics, modern physics is a slightly looser term which may refer to just quantum physics or to 20th and 21st century physics in general and so always includes quantum theory and may include relativity.

A physical system on the classical level is a physical system in which the laws of classical physics are valid. There are no restrictions on the application of classical principles, but, practically, the scale of classical physics is the level of isolated atoms and molecules on upwards, including the macroscopic and astronomical realm. Inside the atom and among atoms in a molecule, the laws of classical physics break down and generally do not provide a correct description.

Moreover, the classical theory of electromagnetic radiation is somewhat limited in its ability to provide correct descriptions, since quantum effects are observable in more everyday circumstances than quantum effects of matter. Unlike quantum physics, classical physics is generally characterized by the principle of complete determinism (although the Many-worlds interpretation of quantum mechanics is in a sense deterministic).

Mathematically, classical physics equations are ones in which Planck's constant does not appear. According to the correspondence principle and Ehrenfest's theorem as a system becomes larger or more massive (action >> Planck's constant) the classical dynamics tends to emerge, with some exceptions, such as superfluidity. This is why we can usually ignore quantum mechanics when dealing with everyday objects; instead the classical description will suffice. However, one of the most vigorous on-going fields of research in physics is classical-quantum correspondence. This field of research is concerned with the discovery of how the laws of quantum physics give rise to classical physics in the limit of the large scales of the classical level.

However, when pursuing ideas of modern physics, it is often useful to look at it's classical physics analogue. The most famous example of this is the spin property in quantum mechanics, which seems in many ways to behave much like angular momentum does classically.

Classical Physics
$\left\{ \partial^2 u \over \partial t^2 \right\} = c\left(u\right)^2 \nabla^2 u$
Wave equation
History of physics

What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics. When discussing general relativity, it refers to the result of modifying Newtonian physics to incorporate special relativity. When discussing quantum mechanics, it refers to non-quantum physics, including special relativity, and general relativity. In other words, it is the physics preceding the physics of interest in one's discussion.

## Overview

### Scope

Among the branches of theory included in classical physics are:

### Differences

In contrast to classical physics, modern physics is a slightly looser term which may refer to just quantum physics or to 20th and 21st century physics in general and so always includes quantum theory and may include relativity.

A physical system on the classical level is a physical system in which the laws of classical physics are valid. There are no restrictions on the application of classical principles, but, practically, the scale of classical physics is the level of isolated atoms and molecules on upwards, including the macroscopic and astronomical realm. Inside the atom and among atoms in a molecule, the laws of classical physics break down and generally do not provide a correct description.

Moreover, the classical theory of electromagnetic radiation is somewhat limited in its ability to provide correct descriptions, since quantum effects are observable in more everyday circumstances than quantum effects of matter. Unlike quantum physics, classical physics is generally characterized by the principle of complete determinism (although the Many-worlds interpretation of quantum mechanics is in a sense deterministic).

Mathematically, classical physics equations are ones in which Planck's constant does not appear. According to the correspondence principle and Ehrenfest's theorem as a system becomes larger or more massive (action >> Planck's constant) the classical dynamics tends to emerge, with some exceptions, such as superfluidity. This is why we can usually ignore quantum mechanics when dealing with everyday objects; instead the classical description will suffice. However, one of the most vigorous on-going fields of research in physics is classical-quantum correspondence. This field of research is concerned with the discovery of how the laws of quantum physics give rise to classical physics in the limit of the large scales of the classical level.


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# Powerplants, Primary Energy, and Electricity!

Power Plants! Primary Energy vs. Electricity!

Energy and electricity are the backbone of our civilization and economy, right?  (Hint: the answer is yes) How do we get all this electricity we got kickin’ around? That’s a pretty complicated topic. This is gonna take a few posts, but we’ll get there. Today is energy and electricity, and how they relate. Later will be a more detailed look at some power plants. I don't think most people will want to skip the math section this time, as it is both interesting and kind of fun.

# First, The Math!

The great bulk of our electricity generation amounts to complicated ways to boil water. Even nuclear plants generate electricity by harvesting the heat of a nuclear reaction to boil water. In all these power plants, application of heat turns that water into steam. That water to steam thing expands the water a whole lot and creates positive pressure (and thus wind) to drive a turbine. Driving a turbine spins a coil of metal in a magnet, converting mechanical energy into electric energy.

Picture!

Block diagram of a coal / thermal / steam / fossil fuel power plant. Source is TVA website (government authority that built powerplants in a huge chunk of the south)

Nuclear plants, coal plants, and natural gas plants all produce electricity via boiling water. For this reason, these powerplants are called thermal plants. Thermal --as in heat. Right? Cool.

Hokay, so how efficient are these thermal plants? The maximum efficiency of a heat engine (which a thermal plant is) is $1 - \frac{cold temp}{hot temp}$ (temperature in Kelvin!). Kelvin is the celcius scale, but is always positive. Absolute zero is 0 kelvin. 273.15°K is 0°C. Using Kelvin makes it way easier to do science.

The hot temperature is the temperature of our steam that drives the turbine. The cold temperature comes from whatever cold water they have handy. Often it is seawater, a lake, or a river. The cold water will probably be around 20C, or 293K. The hot temperature is the temperature of the steam in the thermal plant. Lets say that is 650K (roughly 377 celcius, quite a bit above the boiling temperature of water at 100C! This is very hot steam!)

$1-\frac{293^\circ}{ 650^\circ} = .55$ or 55% efficient.

This is the maximum theoretical efficiency of a thermal power plant. It is how much heat can be converted to electricity. So say that our gallon of gasoline with 33kwh of power was burnt in a perfectly efficient power plant with 650°K steam. We would only obtain 33*.55 or roughly 18kwh of our 33kwh. The other 15kwh will just become waste heat. This maximum efficiency is never attained. There are always extra heat losses and efficiency losses throughout the power plant. Many coal-fired power plants only achieve 35% efficiency. The same gallon of gas would actually only be able to produce closer to 12kwh of electricity from our 33kwh of energy in the gallon of gasoline.

More math! (only slightly related, cause I want to do more math). Calculating how much heat is produced from stopping a bicycle is a fun way to get an idea of how heat and motion relate. For the setup, assume that I weigh 90kg and am bicycling at 10 meters per second.

The amount of kinetic energy (the energy just from moving) that I have is .5*mass*velocity2

$.5 \cdot 90kg \cdot (10 \frac{m}{s})^2=450 J$ . This is all of .125 watt hours. Not much at all. All of this kinetic energy is converted to heat energy in the brakes. Compare this to the energy from the first post about heating up a cup of tea, which took 31kj, or nearly 100 times as much. How bout a car? It travels at about 30m/s on the highway (about 70mph). It weighs 1000kg.

$.5 \cdot 1000kg \cdot (30 \frac{m}{s})^2=450kJ$ , or 125 watt hours. Stopping this car requires dissipation of a lot of heat at the brakes! That’s like 15 cups of tea worth of heat. Another way to look at this is that stopping this car would provide only enough energy to power a 100 watt lightbulb for an hour and 15 minutes. So that is how much energy the car has in its motion. It takes a lot more energy to get the car going that fast, though. Why? Cause the engine in our car is also a heat engine. It’s not very efficient at converting energy. A car is about 25% efficient. The other 75% is all converted to waste heat. The energy it takes to accelerate your car to 70mph could power a 100 watt incandescent lightbulb for 5 hours.

Okay! Back to the big picture!

Electricity Generation and Primary Energy

What is primary energy? Let’s step back and figure out all the way we use power plants and fossil fuels to make our lives easier. The first one is obvious: electricity. It powers our houses, lights, electronics, etc., and sometimes even is used for heating our houses. And it is definitely used to cool our houses with an air conditioner. The next obvious one is your car, which doesn’t run on electricity. We pour gasoline in, and then the engine converts the gasoline to kinetic energy and the car moves. After electricity production and transportation, what we have left is heating for home and industrial purposes. This can be done with coal (many poorer countries use low-quality coal to cook with), wood, natural gas, or any other combustible. As discussed above, electricity is produced by burning fossil fuels to produce heat. Electricity is a byproduct of primary energy.

So that is what primary energy is. All that stuff added together. When most people think “Energy” they equate it with electricity. Now you know differently! A great example of this error was the reporting on the Fukushima nuclear meltdown in Japan. During the reporting, news organizations would regularly say that 20% of energy supplied in the US is from nuclear power. This, however, is wrong! Only about 10% of energy supplied in the US is nuclear. The 20% number is how much of our electricity comes from nuclear. First, what causes these two numbers to be different? And second, why do we even care?

That difference in between resource inputs and electricity output is part of the difference between primary energy and electricity. If we live in a tiny country that uses only one power plant to provide all of its electricity needs, and it uses only electricity for everything. It burns 100 gallons of gasoline an hour (this would never be a power plant input, but let’s keep it simple with numbers we know). It would burn 3340kwh of energy in that hour, and produce 1200kwh of electricity in that hour. Since this is our only energy use in the entire country, the former is primary energy use (3340kwh), and the latter is electricity use (1200kwh)!

This pretty picture from the DOE pretty much explains it all. And now you can explain it to others!

Primary Power is all the things that produce energy, whether it is burning coal in a power plant or gasoline in your car. These are our sources of energy, and where they end up.

What about power plants that don’t use fossil fuels, like hydroelectricity? Easy! A 10MW hydro plant run for an hour registers as 10MWh both primary energy use and electricity use. An important takeaway here: if we lived in a 100% renewable and 100% efficient economy, primary energy use could nearly equal electricity use.

So this is one reason we care about the difference between primary energy use and electricity use. It is a measure of how efficiently we are using our resources, and how much we are getting for all that CO2 we are shoving into the air when we make electricity.

Let’s go back to everything that is primary energy. We have the inputs of heating, cars, and electricity production. Cars and heat are entirely primary energy use. We don’t really use electricity in many places to run either. So now we have everything we need to know to analyze primary energy vs. electricity, efficiencies of power plants, and energy efficiencies of whole economies! Pretty sweet, eh?

Okay, we are pretty much done here. I want to mention one last thing. That small powerplant we had, the one that burned 100 gallons of oil in an hour to produce 1200kwh? A real powerplant in the US produces in megawatts. Like 600 to 1000 MW. 600 times the size of our small powerplant. Even a small 600MW powerplant one would require 60,000 gallons of oil per hour. This is the scale we are talking when we have power plants.

-Jason Munster


text:
# Math Help - Find X

1. ## Find X

upd: here's a pic...

ΔABC is isosceles.
Find X WITHOUT using trig or algebra, by constructing segments || to those given and such and deriving angles from there, knowing that vertically opposite angles are congruent, etc...

I already solved this prolbem using sine and cosine laws, but that was not acceptable ... Spend days on this one, even tried solving backwards having X be known (from solving it the other way), but still nothing...

i don't want the solution, but if you could just point me in the right direction, get me started, i'd appreciate it!

2. Originally Posted by Solarmew
upd: here's a pic...

ΔABC is isosceles.
Find X WITHOUT using trig or algebra, by constructing segments || to those given and such and deriving angles from there, knowing that vertically opposite angles are congruent, etc...

I already solved this prolbem using sine and cosine laws, but that was not acceptable ... Spend days on this one, even tried solving backwards having X be known (from solving it the other way), but still nothing...

i don't want the solution, but if you could just point me in the right direction, get me started, i'd appreciate it!
You should be able to figure it out if you realise that the sum of the angles in a triangle is $180^\circ$ and a straight line makes $180^\circ$.

To get you started, since $\triangle ABC$ is isosceles, then $\angle ABC$ and $\angle ACB$ are equal.

3. haha, i know that ... it's just that i already scribbled up ten pages drawing parallel lines here and there and yet i can't seem to find any angles that are helpful...
at this point my papers look like a tokyo subway map... only much much more confusing X.X

kinda like this only a lot more lines and numbers...

here's the proof i came up with... seems legit to me >.> ... i'll use "=~" as "similar to" and "/_" as "angle" for this occasion X.X ...

if:

ΔABC =~ ΔCFG =~ΔAEH
then
/_BGD = /_DBE = /_DEO = 30°

5. any comments? does that look right? or at least as a starting point?

6. Originally Posted by Solarmew
here's the proof i came up with... seems legit to me >.> ... i'll use "=~" as "similar to" and "/_" as "angle" for this occasion X.X ...

if:

ΔABC =~ ΔCFG =~ΔAEH
then
/_BGD = /_DBE = /_DEO = 30°
That is an ingenious construction, and it has the big advantage of giving the correct answer (which I can only get by using trigonometry).

But I don't see how the construction works. Starting from ABC, you construct two similar triangles, a small one AEH and a large one FGC. It's clear how to get the first of these, you just choose H on the line AC so that AH = AE. But how do you construct the large triangle? It looks as though you construct FG to be the line through B parallel to AE. Then F is the point where this line meets AC (extended), and presumably G is chosen so that FG = FC. But then how do you know that D, E and G are collinear? And why is the angle BDG equal to 30º? Either I'm misunderstanding something, or more explanation is needed!

7. yeah it definitely looks pretty bare ... i didn't think this was going to be it, i was just hooping someone who's done this before could tell me if im on the right track so that i dun waste my time trying to make smth work that's just not ment to X.X ...
i guess i'll try anyways... see if i can throw some more angles in there, maybe it'll magically make more sense XD

as far as D, E and G be colinnear...
instead of drawing a bigger similar triangle outside of ABC and a smaller one inside, we could also draw two smaller similar triangles, one inside ABC and the second inside the first one following the same procedure, this way we would be sure that all the lines are straight as we wouldn't have to extent any, but instead use the ones already given...
so technically its the same thing


text:
# Mathematics behind rotating triangles

I created a Trefoil knot from a list of points. Could someone explain the mathematics behind the amount of scaling between the different triangles. Thank you.
Here is the project: Snap! Build Your Own Blocks

Well, let's see... Start by imagining that the angle at the bottom right is 90° instead of 60°. And suppose the length of the base of the outer triangle is 10. Then we have the following computation of lengths of bottom-ish sides:

triangle #     bottom endpoint    top endpoint    length
0              [0, 0]             [10, 0]         10
1              [1, 0]             [10, 1]         √82
2              [2, 0]             [10, 2]         √68
...
n              [n, 0]             [10, n]         √[(10-n)²+n²]

This is a quadratic function, not a linear one, so the change from one triangle to the next isn't constant. If you want to compare areas rather than side lengths, to a first approximation just don't take the square roots. (The area of the outer isosceles right triangle is half the square value; the area of the actual outer equilateral triangle is umm something with √3? times the square value. That's just a constant factor difference for all the triangles, I think.)

Does that help? I'm too lazy to work out the details today.

Thank you, I don't understand were this is taking me. I have added the script so far and some scribblings (first iteration) to explain my thinking. Somewhere this goes wrong.

Your diagram looks fine to me; I was just trying to avoid the trig. But there's a subtlety that your diagram doesn't capture, namely, all the smaller triangles are relative to the original base, not recursively drawn relative to the next-bigger one. I think that that's not reflected in your code, although what I'd really like is for you to add a third triangle to your diagram.

I also think you could avoid some of the computation by taking more advantage of turtle graphics. But my script ended up longer than yours:

Thank you for your time and insight..it is beautiful. The only restraint...the script, not really draws the triangles in one take. It's in some sense similar to the first project were I started this post with my question. The Trefoil project from a list of points that draws the triangles from reference points in a list. Snap! Build Your Own Blocks
But again thank you...still wondering about how you came to the quadratic function.

You did too! In your diagram there's a √(base²+height²). I tried to simplify the math by making an isosceles right triangle instead of an equilateral one. But of course that just complicates the code. ("Of course" because the three legs of the smaller triangles aren't a REPEAT 3.)

That's right...perhaps I wasn't clear enough, I was referring to my initial question and project.
Thanks anyway...trying to make the REPEAT of 3 ⃤


text:
# On the $H$-triangle of generalised nonnesting partitions

Abstract : With a crystallographic root system $\Phi$ , there are associated two Catalan objects, the set of nonnesting partitions $NN(\Phi)$, and the cluster complex $\Delta (\Phi)$. These possess a number of enumerative coincidences, many of which are captured in a surprising identity, first conjectured by Chapoton. We prove this conjecture, and indicate its generalisation for the Fuß-Catalan objects $NN^{(k)}(\Phi)$ and $\Delta^{(k)}(\Phi)$, conjectured by Armstrong.
Keywords :
Document type :
Conference papers
Domain :

Cited literature [12 references]

https://hal.inria.fr/hal-01207593
Contributor : Coordination Episciences Iam <>
Submitted on : Thursday, October 1, 2015 - 9:28:59 AM
Last modification on : Saturday, April 11, 2020 - 6:38:03 PM
Long-term archiving on: : Saturday, January 2, 2016 - 10:43:36 AM

### File

dmAT0108.pdf
Publisher files allowed on an open archive

### Identifiers

• HAL Id : hal-01207593, version 1

### Citation

Marko Thiel. On the $H$-triangle of generalised nonnesting partitions. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.83-90. ⟨hal-01207593⟩

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text:
# Particles, help controlling direction

This topic is 2585 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Hello,

I am trying to modify this Digiben sample in order to get the effect of particles that generate from a spot (impact point) and float upwards kind of like the sparks of a fire. The sample has the particles rotating in a circle... I have tried removing the cosine/sine functions and replace them with a normal glTranslate with increasing Y value but I just can't get any real results... could anyone please point out roughly where I should add/modify the translation in this code to obtain that result?

 void ParticleMgr::init(){ tex.Load("part.bmp"); GLfloat angle = 0; // A particle's angle GLfloat speed = 0; // A particle's speed // Create all the particles for(int i = 0; i < P_MAX; i++) { speed = float(rand()%50 + 450); // Make a random speed // Init the particle with a random speed InitParticle(particle,speed,angle); angle += 360 / (float)P_MAX; // Increment the angle so when all the particles are // initialized they will be equally positioned in a // circular fashion } }

 void ParticleMgr::InitParticle(PARTICLE &particle, GLfloat sss, GLfloat aaa) { particle.speed = sss; // Set the particle's speed particle.angle = aaa; // Set the particle's current angle of rotation // Randomly set the particles color particle.red = rand()%255; particle.green = rand()%255; particle.blue = rand()%255; }

 void ParticleMgr::DrawParticle(const PARTICLE &particle) { tex.Use(); // Calculate the current x any y positions of the particle based on the particle's // current angle -- This will make the particles move in a "circular pattern" GLfloat xPos = sinf(particle.angle); GLfloat yPos = cosf(particle.angle); // Translate to the x and y position and the #defined PDEPTH (particle depth) glTranslatef(xPos,yPos,PDEPTH); // Draw the first quad glBegin(GL_QUADS); glTexCoord2f(0,0); glVertex3f(-5, 5, 0); glTexCoord2f(1,0); glVertex3f(5, 5, 0); glTexCoord2f(1,1); glVertex3f(5, -5, 0); glTexCoord2f(0,1); glVertex3f(-5, -5, 0); glEnd(); // Done drawing quad // Draw the SECOND part of our particle tex.Use(); glRotatef(particle.angle,0,0,1); // Rotate around the z-axis (depth axis) //glTranslatef(0, particle.angle, 0); // Draw the second quad glBegin(GL_QUADS); glTexCoord2f(0,0); glVertex3f(-4, 4, 0); glTexCoord2f(1,0); glVertex3f(4, 4, 0); glTexCoord2f(1,1); glVertex3f(4, -4, 0); glTexCoord2f(0,1); glVertex3f(-4, -4, 0); glEnd(); // Done drawing quad // Translate back to where we began glTranslatef(-xPos,-yPos,-PDEPTH); }

 void ParticleMgr::run(){ for(int i = 0; i < P_MAX; i++) { DrawParticle(particle); // Increment the particle's angle particle.angle += ANGLE_INC; } }

For now I am adding a glPushMatrix(), glTranslate(x, y, z) in the run() function above, right before the loop, with x,y,z as the position of the enemy for placing them on top of the enemy....is that the best place for that?

Thanks for any input!

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Hello,

I am trying to modify this Digiben sample in order to get the effect of particles that generate from a spot (impact point) and float upwards kind of like the sparks of a fire. The sample has the particles rotating in a circle... I have tried removing the cosine/sine functions and replace them with a normal glTranslate with increasing Y value but I just can't get any real results... could anyone please point out roughly where I should add/modify the translation in this code to obtain that result?

 void ParticleMgr::init(){ tex.Load("part.bmp"); GLfloat angle = 0; // A particle's angle GLfloat speed = 0; // A particle's speed // Create all the particles for(int i = 0; i < P_MAX; i++) { speed = float(rand()%50 + 450); // Make a random speed // Init the particle with a random speed InitParticle(particle,speed,angle); angle += 360 / (float)P_MAX; // Increment the angle so when all the particles are // initialized they will be equally positioned in a // circular fashion } }

 void ParticleMgr::InitParticle(PARTICLE &particle, GLfloat sss, GLfloat aaa) { particle.speed = sss; // Set the particle's speed particle.angle = aaa; // Set the particle's current angle of rotation // Randomly set the particles color particle.red = rand()%255; particle.green = rand()%255; particle.blue = rand()%255; }

 void ParticleMgr::DrawParticle(const PARTICLE &particle) { tex.Use(); // Calculate the current x any y positions of the particle based on the particle's // current angle -- This will make the particles move in a "circular pattern" GLfloat xPos = sinf(particle.angle); GLfloat yPos = cosf(particle.angle); // Translate to the x and y position and the #defined PDEPTH (particle depth) glTranslatef(xPos,yPos,PDEPTH); // Draw the first quad glBegin(GL_QUADS); glTexCoord2f(0,0); glVertex3f(-5, 5, 0); glTexCoord2f(1,0); glVertex3f(5, 5, 0); glTexCoord2f(1,1); glVertex3f(5, -5, 0); glTexCoord2f(0,1); glVertex3f(-5, -5, 0); glEnd(); // Done drawing quad // Draw the SECOND part of our particle tex.Use(); glRotatef(particle.angle,0,0,1); // Rotate around the z-axis (depth axis) //glTranslatef(0, particle.angle, 0); // Draw the second quad glBegin(GL_QUADS); glTexCoord2f(0,0); glVertex3f(-4, 4, 0); glTexCoord2f(1,0); glVertex3f(4, 4, 0); glTexCoord2f(1,1); glVertex3f(4, -4, 0); glTexCoord2f(0,1); glVertex3f(-4, -4, 0); glEnd(); // Done drawing quad // Translate back to where we began glTranslatef(-xPos,-yPos,-PDEPTH); }

 void ParticleMgr::run(){ for(int i = 0; i < P_MAX; i++) { DrawParticle(particle); // Increment the particle's angle particle.angle += ANGLE_INC; } }

For now I am adding a glPushMatrix(), glTranslate(x, y, z) in the run() function above, right before the loop, with x,y,z as the position of the enemy for placing them on top of the enemy....is that the best place for that?

Thanks for any input!

You need to push and pop the matrix for each of the particles otherwise glTranslate/glRotate/glScale will concatenate the current transformation with whatever transformation was already there.

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To do particle opperations you can use shaders. Try this

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# Prove that limsup of a sum of iid random variables(with 0 expectation) is infinity

Let $Y_1, Y_2, Y_3,\ldots,Y_n,\ldots$ be iid and bounded random variables with $E[Y_1]=0$. Define $X_n = Y_1+Y_2+ \cdots + Y_n$.

If $\Pr(Y_1 \neq 0) \gt 0$, then $\limsup X_n = \infty$ with probability $1$.

The conclusion seems intuitive, but how would I approach it rigorously?

• Hint: If you assume $\limsup X_n$ is a finite number ... can you show this leads to a contradiction? – WetlabStudent May 18 '15 at 18:48

Suppose that $\limsup X_n = b$ for some $b \in \mathbb{R}$. We know that $|Y_i| \leq c$ for some $c \in \mathbb{R}^{+}$. So $X_n \leq nc$. Now for some large $N$, $n \geq N$ means that $X_n \leq b$. But we can choose a large enough $n$ (say $m$) such that $b < X_m \leq mc$.


text:
## Renormalization of the ETAS branching model of triggered seismicity from total to observable seismicity

Alexander I. Saichev, & Didier Sornette

Submitted 2005, SCEC Contribution #928

Several recent works point out that the crowd of small unobservable earthquakes (with magnitudes below the detection threshold $) may play a significant and perhaps dominant role in triggering future seismicity. Using the ETAS branching model of triggered seismicity, we apply the formalism of generating probability functions to investigate how the statistical properties of observable earthquakes differ from the statistics of all events. The ETAS (epidemic-type aftershock sequence) model assumes that each earthquake can trigger other earthquakes (aftershocks''). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. The triggering efficiency of earthquakes is assumed to vanish below a lower magnitude limit$, in order to ensure the convergence of the theory and may reflect the physics of state-and-velocity frictional rupture. We show that, to a good approximation, the ETAS model is renormalized onto itself under what amounts to a decimation procedure \to m_d$, with just a renormalization of the branching ratio from$ to an effective value (m_d)\$. Our present analysis thus confirms, for the full statistical properties, the results obtained previously by one of us and Werner, based solely on the average seismic rates (the first-order moment of the statistics). However, our analysis also demonstrates that this renormalization is not exact, as there are small corrections which can be systematically calculated, in terms of additional contributions that can be mapped onto a different branching model (a new relevant direction in the language of the renormalization group).

Citation
Saichev, A. I., & Sornette, D. (2005). Renormalization of the ETAS branching model of triggered seismicity from total to observable seismicity. Physical Review E, (submitted).


text:
# Simple Line Formation

I'm working on the first formation for my game's troops. These should simply stand on land, facing the same direction.

To achieve this, I tried to create offsets towards a pivot-unit, that is approximately the unit in the center of the formation. The units are (temporary) elements of a squad list withing the Squad class. I divide the List by 2 and get the closest integer, that should be the pivot point of the formation. Now I generate offsets for all units on the left side (Unit 1 to pivot-1) and right (pivot+1 to last unit) based on the distance/gaps.

This is the code for the line formation. Sadly, the units are only forming a very stange line with no visually detectable system:

int count = (int)(squadMembers.Count / 2);
center = pivot.transform.position;
switch (type) {
case FormationType.Line:
int space = 5;
for (int i = 0; i < squadMembers.Count; i++) {
int dist = 0;
if (i > count) {
dist = (count + 1) * space;
center.x -= dist;
}
if (i < count) {
dist = (count - 1) * space;
center.x += dist;
}
tmp.StartMove(center);
}
break;
}

It also appears that this only works along the x axis, any idea how i can realize this with the walking/facing direction ov the pivot?

Is there any (obvious) error? How can I improve this script?

PS: Any idea, how I can transform this into a double line (2 Lines behind with half spacing)

• I think some images would help clarify this question. Image of what you have and an image of what you want.
– House
Mar 1 '17 at 23:52
• @Byte56 Added the current image, I think it's not hard do visualize a straight line in this case, is it? Mar 2 '17 at 6:05

Well I hope I understood your question correctly: you want your squad members at the same distance from one to another, facing the same direction and forming a line.

First I'd tackle the direction issue. Let's say there is a point in world called destination they are aiming to. You may want to create a Vector3 describing the difference between destination and the position of the first member. This will give you the orientation to be aligned to. Once you got that you just have to normalize this vector and multiply it by the distance you want between squad members. This will give you an offset to apply from a member to another. So... adding this offset to the first member position will give you the second member position... and so on.

Once the alignement is not a problem anymore, making your unit members look in the same direction (means, looking at destination point), you can simply use LookAt method on their Transform.

Something like this (edited to use the pivot):

public class Aligned : MonoBehaviour
{
[SerializeField]
private List<Transform> units;
[SerializeField]
private GameObject destination;
[SerializeField]
private float distance = 5;

private void Start()
{
// Find the ID of the pivot
// ie: unit at the center of the line / list
int pivot_id = units.Count / 2;
Transform pivot = units[pivot_id];
// Make the pivot look at the destination and save the rotation
pivot.LookAt(destination.transform);
Quaternion look_rot = pivot.rotation;

// Create the offset between units
Vector3 offset = pivot.position - destination.transform.position;
offset = offset.normalized * distance;
for (int i = 0; i < units.Count; ++i)
{
// Apply position offset
units[i].position = pivot.position + offset * (i - pivot_id);
// Make the unit look at the destination point
units[i].rotation = look_rot;
}
}
}

• Thanks for the reply; this is relatively close to my first attempt, when the lines was ordered from left to right, but in this cas I'm struggeling with the correct offset if I want to form the line based on a unit in the middle Mar 2 '17 at 10:04
• Edit: They,re also standing nearly always infront of the pivot unit, instead next to it. Mar 2 '17 at 10:25
• The offset would be the exact same based on the unit in the middle. Just use position - offset*unit_count/2.0f on the first unit only and it'll do the trick. Mar 2 '17 at 12:41
• Edit: I'm not sure to understand what the pivot unit is for you :S Mar 2 '17 at 12:41
• Jup, did changed that already, was on the train while writing this^^ Pivot unit is the unit in the centre everything is relative to within the formation. Mar 2 '17 at 12:59


text:
# Conditional probability of sum of $n$ Poisson variables given sum of subset of $n$ variables $P(X_1+X_2+...+X_n=z|X_1+X_3=y)$

I have $$n$$ Poisson random variables $$X_i$$ each sampled from an independent Poisson distribution parametrized by $$\lambda_i$$. I want to compute $$P(X_1+X_2+...+X_n=z|X_1+X_3=y)$$. The distribution of the unconditional sum would be a Poisson, but I am not sure how to condition it.

• It is equivalent to computing $P(X+Y=z|Y=y)$ when $Y$ is Poisson with parameter $2\lambda_n$ and $X$ is Poisson with parameter $(n-2)\lambda_n$ Jul 22 at 17:40
• I don't think so cause if the sum and one of the variables are known, the answer is easy to calculate and deterministic. If there were two free variables like $P(X+Y+Z=a|Y=y)$, then it would be similar to this llc.stat.purdue.edu/2014/41600/notes/prob1805.pdf, and the answer would be $\frac{e^{-\lambda}\lambda^{a-y}}{(a-y)!}$. However, when I have more free variables, the summations get complicated, and I am unsure about how to reduce them to a similar Poisson variable. Jul 22 at 19:00
• One proof of the statement by @Xi'an begins by observing that $Y=X_1+X_3$ and $X=X_2+X_4+\cdots+X_n$ have Poisson distributions with parameters $\lambda_1+\lambda_3$ and $\lambda_2+\lambda_4+\cdots+\lambda_n,$ respectively, and are independent. You can go further and rewrite the question as asking for $\Pr(X=z-y\mid Y=y),$ which permits you to write the answer immediately.
– whuber
Jul 22 at 19:44

The sum of independent Poisson random variables is a Poisson random variable as shown here. So for $$Z = X+Y$$ where all are Poisson r.v., $$P(Z=z)=\frac{\exp^{-\lambda}\lambda^z}{z!}$$. Here, $$\lambda=\lambda_x+\lambda_y$$. If $$P(Z)$$ was conditioned with $$X$$, $$P(Z|X)$$ the solution would be deterministic as the sum of two variables is known and one of the variables is known. As per @whuber and @Xi'an suggested, $$P(X_1+X_2+X_3+X_4+...+X_n=z|X_1+X_3=y)=P(X_2+X_4+X_5...+X_n=z-y)$$.
• That's right: but take some care to specify that when $z\lt y,$ the chance is zero!


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# Greek Capital Letter Epsilon

Ε
Symbol Format Data
Ε Code Point
U+0395
TeX
\Epsilon
SVG

## Usage

The capital Greek letter (capital epsilon) is visually very similar to the upper-case Latin letter E. For that reason, refer to the usage of Capital E for how the symbol appears in math.

## Related

The Greek letter ε (epsilon).