MaplePrimes Posts

MaplePrimes Posts are for sharing your experiences, techniques and opinions about Maple, MapleSim and related products, as well as general interests in math and computing.

Latest Post
  • Latest Posts Feed
  • Earlier today, we published an update that improves the way MaplePrimes handles tags.

    New features include: 

    • There are now tags for Maple Commands and Maple Packages. These tags are denoted with special icons, and cannot be edited. The hope is that these special tags will be useful to anyone looking for assistance with a particular command or package, and will provide another centralized location to find support. For example, a command tag for the plot command will look as follows:.  A package tag looks like:
    • The tags page has been completely updated to show tag use over time, and also provides information about specific tags. Users with moderator privileges can also edit tags directly from this page.
       
    • Hundreds of inappropriate or 'garbage' tags have been removed.

     

    In addition to the changes to our tagging, we made a few other improvements and updates, including:

    • New academically- and techically-focused social networks have been added to user profiles
    • Updates to the message editor to improve WYSIWYG consistency
    • A variety of smaller fixes and improvements

    I hope you find these improvements valuable, and look forward to your comments and suggestions for future improvements.

     

    I noticed Mapleprime have entries of users who clearly create an account just to put a bad website URL in there and they are just spam.

    Why do not the moderators of Mapleprime purge these out? Mapleprime is full of these spam marketing users.   Here are just few I found in few clicks

    http://www.mapleprimes.com/users/Frenettees8d
    http://www.mapleprimes.com/users/Ingegneriaq7r
    http://www.mapleprimes.com/users/Inabinetaq6s
    http://www.mapleprimes.com/users/Bruggemanse5l
    http://www.mapleprimes.com/users/vito5854
    http://www.mapleprimes.com/users/deblogepa
    http://www.mapleprimes.com/users/organicjunk80

    There are hundereds of these spam URLS in there. They make an account, only to add their infected web site URL there so if someone clicks on it they get virus.

    Moderators of mapleprime should do better job and remove these cleary spam entries from Mapleprime.

    The is and coulditbe commands of Maple are known to be buggy.
    Here are some math inventions done by these commands in Maple 2016.2.

    restart; assume(x::real, y::real);
    is(exp(x+I*y) <> 0);
                                 false
    coulditbe(exp(x+I*y) = 0);
                                  true
    coulditbe(exp(x+I*y) = infinity);
                                  true
    coulditbe((x+I*y)^2 = infinity);
                                  true
    

    It should be noticed that

    is((-infinity)::real);
                                 false

    though

    exp(-infinity+0*I);
                                   0

    The latter means

    limit(exp(x),x=-infinity);
                                       0

    , no more and no less.

    This worksheet is designed to develop engineering exercises with Maple applications. You should know the theory before using these applications. It is designed to solve problems faster. I hope you use something that is fully developed with embedded components.

    In Spanish

    Vector_Force.mw

    Lenin Araujo Castillo

    Ambassador Of Maple

     

     

    I am very pleased to announce a new user community centered around Maplesoft's online testing and assessment and courseware products. The new site is specifically for instructors and administrators currently using Maple T.A. or Möbius. This community of users are a small, specialised group who we want to bring together so they can share ideas and best practices. To find the community, go to either mapletacommunity.com or mobiuscommunity.com.

    "The Maple T.A. Community has grown organically to support new developers as they pool their knowledge and queries. This has resulted in a fluid searchable structure, with answers available for all levels of question - from beginner to pushing the frontiers of what Maple T.A. has been designed to do. Our summer student interns rely on the Community as they become proficient in their question writing skills - and many have become contributors as they realise that they are in a position to teach others. Opening it out more broadly will be great in sharing good practice on a 'need to know now' basis.”

    ----Professor Nicola Wilkin, University of Birmingham

     

    What content is in the community?

    The community has many posts from active Maple T.A. and Möbius users from beginners to advanced users. The site is broken down into categories like 'Best Practices' - longer form posts that cover a broader concept in more detail and 'Quick Code snippets' that are small piece of code that you can drop straight into your question algorithms.

    Much of the content is openly available and can be found by google, however there is additional content that can only be accessed by members of the community, such as the Maple T.A. school material which teaches you how to author content in Maple T.A. and Möbius.

     

    Who runs the community

    The community is jointly run by users based at the University of Birmingham, TU Wien, The University of Turin and TU Delft.

     

    How does this fit into Mapleprimes?

    It began as an offshoot of a private, internal customer forum. As this community grows, the ultimate goal is to eventually roll it into MaplePrimes proper. But this alternative site gave us the quickest way to get up and running. Maple T.A. and Möbius questions and posts are still welcome on MaplePrimes, and will continue to be monitored by Maplesoft.

     

    How do I access the community?

    You can find the community by going to either mapletacommunity.com or mobiuscommunity.com.

     

    Where else can I get support for Maple T.A. and Mobiüs?

    Official support for Maple T.A. and Möbius is provided by the wonderful Customer Success Team at Maplesoft. You can contact them at help@maplesoft.com. For other contact methods see www.maplesoft.com/support/.

     

     

    I am pleased to announce the public release of Möbius, the online courseware environment that focuses on science, technology, engineering, and mathematics education. After months of extensive pilot testing at select leading academic institutions around the world, Möbius is now available to everyone for your online learning needs.

    We are very excited about Möbius. As you can imagine, many of us here at Maplesoft have backgrounds in STEM fields, and we are truly excited to be working on a project that gives students a hands-on approach to learning math-based content.  You can’t learn math (or science, or engineering, or …) just by reading about it or listening to someone talk about it. You have to do it, and that’s what Möbius lets students do, online, with instant feedback.  Not only can students explore concepts interactively, but they can find out immediately what they’ve understood and what they haven’t - not a few hours after the lecture as they are reviewing their notes, not two weeks later when they get their assignments back, but while they are in the middle of learning the lesson.

    During its pilot phase, Möbius was used by multiple institutions around the world for a variety of projects, such as preparing students in advance for their first year math and engineering courses, and for complete online courses.  Over one hundred thousand students have already used Möbius, and the experiences of these students and their instructors has fed back into the development process, resulting in this public release.  You can read about the experiences of the University of Waterloo, the University of Birmingham, and the Perimeter Institute for Theoretical Physics on our web site.

    We are also happy to announce that Maplesoft has partnered with the University of Waterloo, one of the largest institutions in the world for STEM education, to provide institutions and professors with rich online courses and materials that enable students to learn by doing.  These Möbius courses are created by experts at the University of Waterloo for use by their own students and for their outreach programs, and will be made available to other Möbius users.  Course materials range from late high school to the graduate level, with initial offerings available soon and many more to follow.

    Visit the Möbius section of our web site for lots more information, including videos, whitepapers, case studies, and upcoming user summits.

    Let us consider 

    sol := pdsolve({diff(u(x, t), t)-(diff(v(x, t), x))+u(x, t)+v(x, t) = (1+t)*x+(x-1)*t^2, diff(v(x, t), t)-(diff(u(x, t), x))+u(x, t)+v(x, t) = (1+t)*x*t+(2*x-1)*t}, {u(0, t) = 0, u(x, 0) = 0, v(0, t) = 0, v(x, 0) = 0}, time = t, numeric, timestep = 0.1e-1, spacestep = 0.1e-1, range = 0 .. 1); 
    sol:-plot3d(v(x, t), x = 0 .. 1, t = 0 .. 1);

    A nice plot similar to the one produced by Mma (see the  attached pdf file pdesystem.pdf) is expected. 
    The exact solutions u(x,t)=x*t,v(x,t)=x*t^2 are known

    pdetest({u(x, t) = x*t, v(x, t) = x*t^2}, {diff(u(x, t), t)-(diff(v(x, t), x))+u(x, t)+v(x, t) =
    (1+t)*x+(x-1)*t^2, diff(v(x, t), t)-(diff(u(x, t), x))+u(x, t)+v(x, t) = (1+t)*x*t+(2*x-1)*t});
                                  {0}

    But the wrong result

                   module() ... end module         
    Error, (in pdsolve/numeric/plot3d) unable to compute solution for t>HFloat(0.26000000000000006):
    solution becomes undefined, problem may be ill posed or method may be ill suited to solution

    is obtained. Also 

    sol:-plot3d(v(x, t), x = 0 .. 1, t = 0 ..0.1);


     

    The plot 

    sol:-plot3d(v(x, t), x = 0 .. .5, t = 0 .. .1);

    is not better.

    Hi everybody,

    The Collatz conjecture can be used to give students a taste of a topic in Number Theory.  See the Wikipedia article for a good explaination.

    https://en.wikipedia.org/wiki/Collatz_conjecture

    Also, a conjecture is something that is probrably true.  Enjoy my little Maple procedure.  (in .mw and .pdf forms)

    Collatz_third_time.mw

    Collatz_third_time.pdf

    Comments are appreciated.

    Matt

     

    Here is a problem from SEEMOUS 2017 (South Eastern European Mathematical Olympiad for University Students)
    which Maple can solve (with a little help).

    For k a fixed nonnegative integer, compute:

    Sum( binomial(i,k) * ( exp(1) - Sum(1/j!, j=0..i) ), i=k..infinity );

    (It is the last one, theoretically the most difficult.)

    Application that allows us to measure the reliability of a group of data through a row and columns called cronbach alpha at the same time to measure the correlation of items through the pearson correlation of even and odd items. It can run on maple 18 to maple 2017. This will be useful when we are developing a thesis in the statistical part.

    In Spanish

    StatisticsSocialCronbachPearson.zip

    Lenin Araujo Castillo

    Ambassador of Maple

     

     

    Let us consider the help to RectangleWindow SignalProcessing-RectangleWindow.pdf SignalProcessing-RectangleWindow.mw.
    Let us execute the example, taking N:=4 (in order to display the outputs).

    with(SignalProcessing):
    N := 4;
    a := GenerateUniform(N, -1, 1);
             Matrix(1, 4, [[.396167882718146, -.826878267806025, -0.908376742154361e-2, .324899681378156]])         
    RectangleWindow(a);
             Vector[row](4, [.396167882718146, -.826878267806025, -0.908376742154361e-2, .324899681378156])      
    c := Array(1 .. N, 'datatype' = 'float'[8], 'order' = 'C_order'):
    RectangleWindow(Array(1 .. N, 'fill' = 1, 'datatype' = 'float'[8], 'order' = 'C_order'), 'container' = c);
                  Vector[row](4, [1., 1., 1., 1.])
    u := `~`[log](FFT(c)):
    plots:-display(Array([plots:-listplot(Re(u)), plots:-listplot(Im(u))]));
    



    We see an uncommented code which (intentionally or unintentionally) produces two empty plots.
    The questions arise:

    • What is the aim of the RectangleWindow command which does nothing 
      but the conversion of a Matrix(1,N,...) /Array(1..N,...) to a Vector[row](N,...)? 
    • Could such help be called friendly to Maple users?

    There are many questions to Maplesoft and there are no answers from them: strategic silence.
    RectangleWindow.mw

     

    Here's a little procedure to fish out data from the Simbad database.  Some star names may not work if the page Simbad brings up is not completely filled, but it should work for most queries.


     

    restart; gc()

    Simbad := proc (a::string) local b, c, c1, c2, c3, c4, c5, d1, d2, d3, d4, d5, e1, e2, e3, e4, e5; b := StringTools:-DeleteSpace(StringTools:-Substitute(a, " ", "+")); c := HTTP:-Get(cat("http://simbad.u-strasbg.fr/simbad/sim-id?Ident=", b, "&submit=submit+id")); c1 := StringTools:-Search("Parallaxes", c[2]); c2 := StringTools:-Search("Radial", c[2]); c3 := StringTools:-Search("Spectral type:", c[2]); c4 := StringTools:-Search("Gal", c[2]); c5 := StringTools:-Search("ICRS", c[2]); d1 := c[2][c1+87 .. c1+93]; d2 := c[2][c2+96 .. c2+110]; d3 := c[2][c3+77 .. c3+90]; d4 := c[2][c4+122 .. c4+140]; d5 := c[2][c5+135 .. c5+164]; e1 := d1[() .. StringTools:-Search(" ", d1)]; e2 := d2[() .. StringTools:-SearchAll(" ", d2)[2]]; e3 := d3[() .. StringTools:-Search(" ", d3)]; e4 := convert(evalf(1000/parse(e1)), 'units', 'parsec', 'ly'); e5 := d5[() .. StringTools:-Search("\n", d5)-1]; print(cat(StringTools:-Capitalize(a), "\nDistance", e4, "lightyears", "\nRight Ascension and declination:", e5, "\nGalactic coordinates", d4, "Spectral Type:", e3, "\nRadial velocity:", e2, "\nParallax", e1, "milliarcseconds")) end proc:
     

    Simbad("epsilon eridani")

    "Epsilon Eridani
Distance" || (10.48936700) || "lightyears" || "
Right Ascension and declination:" || "03 32 55.84496 -09 27 29.7312" || "
Galactic coordinates" || "195.8446 -48.0513
 " || "Spectral Type:" || "K2Vk: " || "
Radial velocity:" || "V(km/s) 16.43 " || "
Parallax" || "310.94 " || "milliarcseconds"

    (1)

    Simbad("alpha centauri")

    "Alpha Centauri
Distance" || (4.395638513) || "lightyears" || "
Right Ascension and declination:" || "14 39 36.204 -60 50 08.23" || "
Galactic coordinates" || "315.7330 -00.6809
 " || "Spectral Type:" || "G2V+K1V " || "
Radial velocity:" || "V(km/s) -22.3 " || "
Parallax" || "742 " || "milliarcseconds"

    (2)

    Simbad("beta hydri")

    "Beta Hydri
Distance" || (24.32731987) || "lightyears" || "
Right Ascension and declination:" || "00 25 45.07036 -77 15 15.2860" || "
Galactic coordinates" || "304.7720 -39.7821
 " || "Spectral Type:" || "G0V " || "
Radial velocity:" || "V(km/s) 23.10 " || "
Parallax" || "134.07 " || "milliarcseconds"

    (3)

    Simbad("HR6998")

    "Hr6998
Distance" || (42.67386858) || "lightyears" || "
Right Ascension and declination:" || "18 38 53.40045 -21 03 06.7368" || "
Galactic coordinates" || "012.7251 -06.7965
 " || "Spectral Type:" || "G6V " || "
Radial velocity:" || "V(km/s) 36.175 " || "
Parallax" || "76.43 " || "milliarcseconds"

    (4)

    ``


     

    Download star_database_-_simbad.mw

    I found this http://www.atlasoftheuniverse.com/50lys.html and wondered how to do it in Maple. With a bit of data file editing I came up with this.  All stars within 50 light years that are visible to the naked eye.


     

    restart; gc()

    with(plots):

    with(plottools):

    a := readdata("c:/stars3.txt", [string, float, float, float]):

    b := map(proc (a) options operator, arrow; [a[4], a[2], a[3]] end proc, a):

    g := :-changecoords([x, y, z], [x, y, z], spherical, [r, theta, (1/2)*Pi-phi])

    [r*sin((1/2)*Pi-phi)*cos(theta), r*sin((1/2)*Pi-phi)*sin(theta), r*cos((1/2)*Pi-phi)]

    (1)

    tt := [seq(evalf(subs({phi = convert(b[i][3]*degrees, radians), r = b[i][1], theta = convert(b[i][2]*degrees, radians)}, g)), i = 1 .. nops(b))]:

    stars := pointplot3d(tt, color = red, symbol = solidcircle, symbolsize = 5)

    PLOT3D(POINTS([3.141656625, -3.065814279, -0.5363263369e-1], [-5.772842366, -6.234102660, -1.330509322], [-6.747305264, -1.909294949, -7.815271235], [-9.249301903, -6.168517561, 2.566691531], [1.523622092, 11.26895208, -1.155073477], [7.242651534, -3.194389926, -8.791403287], [-3.375068769, .4084281956, -11.40403864], [-12.10139419, -4.596888455, -10.15024015], [14.09808071, 8.106755961, 3.279135277], [11.15052984, 12.25427229, -2.594493178], [-3.419769677, 17.11427532, 7.015900193], [15.04843187, -6.018943313, 10.40502857], [-10.42150660, 16.29565570, -1.726327245], [19.37009401, -.5748909284, 2.345071093], [16.86849035, 1.535152882, -10.13730432], [-3.624453569, -10.40801291, -16.40104276], [14.53624850, -8.460298659, -10.67366976], [-7.231982853, 19.97813208, -1.187881627], [9.620796689, 4.103617543, 19.18392802], [-15.19214319, 4.528974584, -17.36108506], [23.35174623, -3.365038049, .5765994043], [-6.811639233, 11.11558498, -20.54249842], [-13.85405602, 12.08566336, -15.98159795], [10.68989447, -15.38074244, -15.60587447], [-14.13228719, 19.88605992, -3.385259168], [10.27598870, 2.927192384, -22.50208215], [9.961208544, 3.724343264, -22.70260980], [9.143348930, 22.07399698, 8.320326164], [-23.59749508, -4.800964644, -10.27138571], [-5.411799069, 22.54176541, 12.37819224], [4.496828592, -12.62856178, -22.94041979], [-9.282551806, -2.504624702, 25.44407764], [-4.991684031, 4.803604874, 26.40640965], [15.07681588, 19.57764444, 11.83914952], [13.33734565, -14.86471460, 19.35333487], [10.71939792, -13.57311193, -22.05778867], [-27.91856076, -4.172456862, -1.331228297], [27.18654831, -8.676334271, -2.647341036], [-23.15604687, -10.84708496, -13.14156540], [24.14988887, 6.742770129, -14.12821003], [-18.24903039, -19.43324358, -12.03679499], [-19.47836941, -6.366512513, -21.22052411], [1.737082939, 1.648430159, 29.76381731], [-8.166167580, 1.661425568, 28.68397239], [-21.79918531, .6850669983, -20.40938762], [19.48447839, -12.08088844, -19.44250077], [9.550472834, -26.52745875, 10.65373179], [7.061767869, -26.72771859, 14.26858765], [-8.925013073, -.5615142310, 29.80743604], [27.25388910, 6.643782013, 15.16765603], [-20.51315816, 25.24143542, .9653395827], [-6.514439942, 18.29467278, 26.63134657], [7.897693130, -27.90985562, -15.94604661], [-30.24778274, -6.539802137, 13.39182687], [-17.39717901, -3.729632012, -28.80846417], [-27.77451873, 19.73832304, -4.425416699], [-16.72100652, 29.91871832, 7.975859507], [16.27294095, 21.36128840, 22.77346814], [-25.44324866, 19.59393922, -15.24864399], [.1513479143, -17.34275050, 31.03237984], [1.717990984, -16.62465483, -31.43293430], [-3.952184454, -11.22283603, 34.16753707], [13.79744768, 29.99780276, 14.83921382], [-13.23790880, 23.68644879, -24.00672435], [22.42836846, 11.77515669, 25.95817545], [-24.22192093, -3.619990337, 27.00973559], [-28.14737644, 22.63107168, -6.108739192], [12.64368664, 3.411528480, 34.29464625], [10.76859270, .9989721406, 35.37371292], [16.76571480, 7.324760688, 32.87131102], [-2.125303532, -30.39325725, -22.70975559], [26.50575552, 7.450431864, 26.68129662], [4.681906269, 34.62812576, -15.77746051], [21.22229159, 16.34336469, -27.73774271], [8.642995477, -16.39289961, 33.84907047], [4.194125964, -26.48066899, -28.95298045], [29.05143012, -24.81226531, -9.951698266], [-12.02418205, -37.67674179, 3.460082988], [-36.31468346, 14.37800028, 8.301913818], [31.32513775, -24.56204547, -5.240626617], [-11.18258143, 31.40433711, -22.91113229], [-30.95713334, -9.346509576, 24.99311013], [-23.18290754, -32.62151994, 9.092350346], [-26.39556889, 28.60460399, -13.63041355], [-40.27955197, 8.782362586, 1.079537348], [-11.43139039, -7.856576969, -38.95407568], [3.769221962, 22.28497845, 34.93658256], [-4.619258428, 34.61973164, 22.85528894], [-23.40542087, 11.26426836, 32.88997769], [39.51971345, -13.14645885, 5.261489147], [6.069471167, -26.08199826, 32.48539497], [-40.13923071, 12.57887241, 3.384394608], [41.02326573, 9.244992210, -5.014408062], [-29.06950326, -20.65862072, -24.78609025], [-27.49729080, 30.53883527, -15.52814989], [-29.74467917, 7.692497076, 31.48332336], [25.85459060, -9.924647480, -34.69169378], [-13.64550398, 34.99890783, -24.20893992], [30.42203099, 31.61316765, -8.607657127], [-33.27978250, -2.970141446, -29.76905838], [-1.180761099, 27.04387545, -35.92262524], [-21.03852595, 37.95450550, 11.87164852], [-19.67481024, -7.473759355, -40.42995379], [39.79319523, 3.271596183, 22.31470081], [-20.50141444, 1.505529746, 41.05062102], [-.6748395635, 38.66153119, 24.82404273], [-16.85106712, -16.67552070, -39.45541086], [40.49802876, 12.53623404, -18.78641538], [-32.93404980, 18.55738333, 27.16384339], [34.92406817, 25.28080920, 17.94659157], [-6.296985384, 45.37992800, 9.404414370], [22.24424377, 32.85461078, 25.08249928], [39.53312079, -25.57512282, 6.115214927], [-1.588926894, 23.92244252, 41.02855658], [-35.74198886, 5.341675996, 31.19429964], [36.98453431, 14.41966737, -26.57424156], [-46.68814535, -5.898084394, -8.552109953], [35.05110270, 5.991394707, 32.01789951], [36.60612781, 13.32354091, -27.78663643], [13.51762166, -35.96304965, 29.05652877], [-10.38961406, -43.95116043, 17.78996954], [-28.30533977, -7.584392920, 38.74662727], [9.914015961, -13.79681314, -45.68312418], [-9.191698604, 47.28718983, 7.802201960], [21.29072957, 42.51660453, 11.24023016], [-35.75149122, -29.78701952, -15.57013949], [5.493536467, -15.01179385, -46.42496206], [-3.928870403, 39.36220535, 29.27122934], [33.42605444, 36.35056112, -1.638197365], [-17.62503890, -46.15541461, -4.148747474], [44.66028688, -18.77345598, 11.18456642], [45.91393827, -16.62061368, -9.934504171]), SYMBOL(_SOLIDCIRCLE, 5), COLOUR(RGB, 1.00000000, 0., 0.))

    (2)

    lines := seq(`if`(tt[i][3] > 0, line(tt[i], [tt[i][1], tt[i][2], 0], color = blue), line(tt[i], [tt[i][1], tt[i][2], 0], color = blue, linestyle = dot)), i = 1 .. nops(b)):

    c1 := circle([0, 0], 10, color = blue):

    c2 := circle([0, 0], 20, color = blue):

    c3 := circle([0, 0], 30, color = blue):

    c4 := circle([0, 0], 40, color = blue):

    c5 := circle([0, 0], 50, color = blue):

    l1 := line([-50*cos((1/4)*Pi), -50*sin((1/4)*Pi)], [50*cos((1/4)*Pi), 50*sin((1/4)*Pi)], color = blue):

    l2 := line([-50*cos(2*Pi*(1/4)), -50*sin(2*Pi*(1/4))], [50*cos(2*((1/4)*Pi)), 50*sin(2*((1/4)*Pi))], color = blue):

    l3 := line([-50*cos(3*((1/4)*Pi)), -50*sin(3*((1/4)*Pi))], [50*cos(3*((1/4)*Pi)), 50*sin(3*((1/4)*Pi))], color = blue):

    l4 := line([-50*cos(4*((1/4)*Pi)), -50*sin(4*((1/4)*Pi))], [50*cos(4*((1/4)*Pi)), 50*sin(4*((1/4)*Pi))], color = blue):

    t1 := textplot([55, 0, "0"], color = blue):NULL

    t2 := textplot([55*cos((1/2)*Pi), 55*sin((1/2)*Pi), "90"], color = blue):

    t4 := textplot([55*cos(3*Pi*(1/2)), 55*sin(3*Pi*(1/2)), "270"], color = blue):

    t3 := textplot([55*cos(Pi), 55*sin(Pi), "180"], color = blue):

    a1 := arrow([60, 0], [80, 0], 1.5, 4, .4, color = blue):

    a2 := textplot([95, 5, "Galactic Center"]):

    d := display(c1, c2, c3, c4, c5, l1, l2, l3, l4, t1, t2, t3, t4, a1, a2, axes = none, scaling = constrained):

    to3d := transform(proc (x, y) options operator, arrow; [x, y, 0] end proc):

    display(to3d(d), stars, lines, orientation = [-46, 75])

     

    ``

    ``

    NULL

    NULL

    The modified data file and the maple worksheet below

    stars3.txt

    Download Stars50LY.mw

     

    I have proposed a SE site for maple.

    This will help to put maple on SE.

    Please follow this site.

    http://area51.stackexchange.com/proposals/107315/maple

     Update

    We have moved to the next phase Commitment. Come and join us.

    1 2 3 4 5 6 7 Last Page 2 of 250