We find recent applications of the components applied to the linear momentum, circular equations applied to engineering. Just simply replace the vector or scalar fields to thereby reasoning and use the right button.

Momento_Lineal_y_Circular.mw

(in spanish)

Atte.

L.AraujoC.

Maplesoft will be hosting the 2015 Maple T.A. User Summit this June 15 - 17 in New York City. Don’t miss this opportunity to learn about new trends in online education while networking and socializing with fellow educators and Maple T.A. users in the city that never sleeps!

We are happy to announce that the schedule has been finalized! The event will include keynote presentations, talks and discussions from users and Maplesoft staff, training sessions, a welcome reception and a boat cruise around New York City, 

If you'd like ot sign-up but still haven't - don't hesitate to do so today using the following link: https://webstore.maplesoft.com/taconference/register.aspx .

I hope to see you there!

Jonny
Maplesoft Product Manager, Maple T.A.

Developed and then implemented with open code components. It is very important to note this post is held for students of civil engineering and mechanics. Using advanced mathematical concepts to concepts in engineering.

Metodos_Energeticos_full.mw

(in spanish)

Atte.

L.Araujo.C

This post is related to the this thread

The recursive procedure  PosIntSolve  finds the number of non-negative or positive solutions of any linear Diophantine equation

a1*x1+a2*x2+ ... +aN*xN = n  with positive coefficients a1, a2, ... aN .  

Formal parameters: L is the list of coefficients of the left part, n  is the right part,  s (optional) is nonneg (by default) for nonnegint solutions and  pos  for positive solutions.

The basic ideas:

1) If you make shifts of the all unknowns by the formulas  x1'=x1-1,  x2'=x2-1, ... , xN'=xN-1  then  the number of positive solutions of the first equation equals the number of non-negative solutions of the second equation.

2) The recurrence formula (penultimate line of the procedure) can easily be proved by induction.

The code of the procedure:

restart;

PosIntSolve:=proc(L::list(posint), n::nonnegint, s::symbol:=nonneg)

local N, n0;

option remember;

if s=pos then n0:=n-`+`(op(L)) else n0:=n fi;

N:=nops(L);

if N=1 then if irem(n0,L[1])=0 then return 1 else return 0 fi; fi;

add(PosIntSolve(subsop(1=NULL,L),n0-k*L[1]), k=0..floor(n0/L[1]));

end proc:

Examples of use.

Finding of the all positive solutions of equation 30*a+75*b+110*c+85*d+255*e+160*f+15*g+12*h+120*i=8000:

st:=time():

PosIntSolve([30,75,110,85,255,160,15,12,120], 8000, pos);

time()-st;

                                       13971409380

                                             2.125

To test the procedure, solve (separately for non-negative and positive solutions) the simple equation  2*x1+7*x2+3*x3=2000  in two ways (by the  procedure and brute force method):

ts:=time():

PosIntSolve([2,7,3], 2000);

PosIntSolve([2,7,3], 2000, pos);

time()-ts;

                47905

                47334

                 0.281

ts:=time():

k:=0:

for x from 0 to 2000/2 do

for y from 0 to floor((2000-2*x)/7) do

for z from 0 to floor((2000-2*x-7*y)/3) do

if 2*x+7*y+3*z=2000 then k:=k+1 fi;

od: od: od:

k; 

k:=0:

for x from 1 to 2000/2 do

for y from 1 to floor((2000-2*x)/7) do

for z from 1 to floor((2000-2*x-7*y)/3) do

if 2*x+7*y+3*z=2000 then k:=k+1 fi;

od: od: od:

k;

time()-ts; 

                   47905

                   47334

                   50.063

Another example - the solution of the famous problem: how many ways can be exchanged $ 1 using the coins of smaller denomination.

PosIntSolve([1,5,10,25,50],100);

                        292

 Number-of-solutions.mw

 Edit.  The code has been slightly edited 

Here we have a very brief introduction to the use of embedded components, but effective for the study of the polynomials in operations and some products made with maple 2015 to strengthen and raise the mathematics today.

Operaciones_con_Polinomios.mw

(in spanish)

Atte.

L.AraujoC.

This post is related to the question. There were  proposed two ways of finding the volume of the cutted part of a sphere in the form of a wedge.  Here the procedure is presented that shows the rest of the sphere. Parameters procedure: R - radius of the sphere, H1 - the distance the first cutting plane to the plane  xOy,  H2 -  the distance the second cutting plane to the plane  zOy. Necessary conditions:  R>0,  H1>=0,  H2>=0,  H1^2+H2^2<R^2 . For clarity, different surfaces are painted in different colors.

restart;

Pic := proc (R::positive, H1::nonnegative, H2::nonnegative)

local A, B, C, E, F;

if R^2 <= H1^2+H2^2 then error "Should be H1^(2)+H2^(2)<R^(2)" end if;

A := plot3d([R*sin(theta)*cos(phi), R*sin(theta)*sin(phi), R*cos(theta)], phi = arctan(sqrt(-H1^2-H2^2+R^2), H2) .. 2*Pi-arctan(sqrt(-H1^2-H2^2+R^2), H2), theta = 0 .. Pi, color = green);

B := plot3d([R*sin(theta)*cos(phi), R*sin(theta)*sin(phi), R*cos(theta)], phi = -arctan(sqrt(-H1^2-H2^2+R^2), H2) .. arctan(sqrt(-H1^2-H2^2+R^2), H2), theta = 0 .. arccos(sqrt(R^2-H2^2-H2^2*tan(phi)^2)/R), color = green);

C := plot3d([R*sin(theta)*cos(phi), R*sin(theta)*sin(phi), R*cos(theta)], phi = -arctan(sqrt(-H1^2-H2^2+R^2), H2) .. arctan(sqrt(-H1^2-H2^2+R^2), H2), theta = arccos(H1/R) .. Pi, color = green);

E := plot3d([r*cos(phi), r*sin(phi), H1], phi = -arccos(H2/sqrt(R^2-H1^2)) .. arccos(H2/sqrt(R^2-H1^2)), r = H2/cos(phi) .. sqrt(R^2-H1^2), color = blue);

F := plot3d([H2, r*cos(phi), r*sin(phi)], phi = arccos(sqrt(-H1^2-H2^2+R^2)/sqrt(R^2-H2^2)) .. Pi-arccos(sqrt(-H1^2-H2^2+R^2)/sqrt(R^2-H2^2)), r = H1/sin(phi) .. sqrt(R^2-H2^2), color = gold);

plots[display](A, B, C, E, F, axes = none, view = [-1.5 .. 1.5, -1.5 .. 1.5, -1.5 .. 1.5], scaling = constrained, lightmodel = light4, orientation = [60, 80]);

end proc:

Example of use:

Pic(1,  0.5,  0.3);

Here we have an application to understand how algebraic expressions, calculating degrees relative abosulutos polynomial operations and introduction to work.Here we have an application to understand how algebraic expressions, calculating degrees relative abosulutos polynomial operations and introduction to work.

Grados_de_Polinomios.mw

(in spanish)

Atte.

L.AraujoC.

We’re trying out something new with our webinars and are hosting our first ever live streaming webinar. Broadcast in real time, and featuring Jonny Zivku, our Maple T.A. Product Manager, this will be your chance to see the face behind the voice, as well as learn more about how academic institutions around the world are using Maple T.A. We hope you can join us.

Here are the full details:

Transforming Testing and Assessment with Maple T.A.

In this webinar, you will learn how Maplesoft's testing and assessment system, Maple T.A., is being used to improve learning, save money, reduce drop-out rates, and increase student satisfaction at academic institutions around the world.

The following Maple T.A. case studies will be presented:

• The University of Waterloo saved $100,000/year on their grading budget
• At the Amsterdam University of Applied Science, student pass rates went up approximately 20% within one year
• The University of Canterbury continued to offer their full academic program after an earthquake damaged classrooms
• At the University of Guelph, drop-out rates were reduced by more than 10%
• ...And more!

All attendees of this webinar will be sent a complimentary copy of the Maplesoft magazine Transforming Testing and Assessment.

To join us for the live streaming webinar, please click here to register.

With this application we can meet safety characteristics of a relationship and simple or compound functions. Made with maple 2015.

Relaciones_y_Funciones.mw

(in spanish)

L.AraujoC.

PLATFORM_2.mw

Two platforms (tripod) and abstract mechanism.

https://vk.com/doc242471809_379935473
https://vk.com/doc242471809_380837279
https://vk.com/doc242471809_378352452
https://vk.com/doc242471809_380217387

And six degrees of freedom of a rigid body



https://vk.com/doc242471809_383336706

Maplesoft regularly hosts live webinars on a variety of topics. Below you will find details on upcoming webinars we think may be of interest to the MaplePrimes community.  For the complete list of upcoming webinars, visit our website.

Case Study: Transforming a University's Placement Testing Process

This webinar will feature the story of how the University of the Virgin Islands moved their placing testing process from paper and pen to using the Mathematical Association of America’s (MAA) placement tests offered through the Maple T.A. testing environment. Instructors at the university now handpick questions to create their own placement tests that best fit the course they are teaching. From there, they are able to analyze the data and craft lessons based on student performance. The end result is that students are more satisfied with the education they are receiving and instructors have made enormous gains with regards to efficiency and flexibility.

To join us for the live presentation with Dr. Celil Ekici from the University of the Virgin Islands, please click here to register.

Getting Started with Maple

This webinar is designed for the user who comes to Maple for the first time. It will demonstrate “how to get started” by clarifying the user interface and the ways math can be entered into Maple, and then “processed.” Coverage includes

• Entering mathematical expressions and interacting with them in a syntax-free way.
• The difference between input in mathematical notation and “linear” or text form.
• The role of the Context Sensitive Menu system for interacting with mathematical objects.
• Graphing and interacting with various types of graphs, including animations, surfaces, and implicit plots.
• Use of built-in tools such as Assistants, Tutors, and Task Templates.
• The Maple help system and the Maple Portal.
• Introduction to differential equations and matrix manipulations.

To join us for the live presentation, please click here to register.

Another application for the study of rational numbers in operations, generating fraction, etc.

Numeros_Racionales.mw

(in spanish)

Atte.

L.AraujoC.

The work contains two procedures called  SetPartition  and  NumbPart .

The first procedure  SetPartition  generates all the partitions of a set  S  into disjoint subsets of specific sizes defined by a list  Q. The third optional parameter is the symbol  `ordered`  or  `nonordered`  (by default) . It determines whether the order of subsets in a partition is significant.

The second procedure  NumbPart  returns the number of all partitions of the sizes indicated by  Q .

Codes of these procedures:

SetPartition:=proc(S::set, Q::list(posint), K::symbol:=nonordered)  # Procedure finds all partitions of the set  S  into subsets of the specific size given Q.

local L, P, T, S1, S2, n, i, j, m, k, M;

uses ListTools,combinat;

if `+`(op(Q))<>nops(S) then error "Should be `+`(op(Q))=nops(S)" fi;

L:=convert(Q,set);

T:=[seq([L[i],Occurrences(L[i],Q)], i=1..nops(L))];

P:=`if`(K=ordered,convert(T,list),convert(T,set));

S1:=S;  S2:={`if`(K=ordered,[],{})}; n:=nops(P);

for i to n do

m:=P[i,1]; k:=P[i,2];

for j to k do

S2:={seq(seq(`if`(K=ordered,[op(s),t],{op(s),t}), t=choose(S1 minus `union`(op(s)),m)), s=S2)};

od; od;

if K=ordered then {map(op@permute,S2)[]} else S2 fi;

end proc:

NumbPart:=proc(Q::list(posint), K::symbol:=nonordered)  # Procedure finds the number of all partitions of a set into subsets of the specific size given  Q

local L, T, P, n, S, N;

uses ListTools;

L:=convert(Q,set);

T:=[seq([L[i],Occurrences(L[i],Q)], i=1..nops(L))];

P:=`if`(K=ordered,convert(T,list),convert(T,set));

n:=nops(P);  N:=add(P[i,2], i=1..n);

S:=add(P[i,1]*P[i,2],i=1..n)!/mul(P[i,1]!^P[i,2],i=1..n)/mul(P[i,2]!,i=1..n);

if K=nonordered then return S else  S*N! fi;

end proc:

Examples of use:

SetPartition({a,b,c,d,e}, [1,1,3]);  nops(%);  # Nonordered partitions and their number

SetPartition({a,b,c,d,e}, [1,1,3], ordered);  nops(%);  # Ordered partitions and their number

Here's a more interesting example. 5 fruits  {apple, pear, orange, mango, peach}  must be put on three plates so that  on each of two plates there are 2  fruits, and there is one fruit  on one plate. Two variants to solve: 1) plates are indistinguishable and 2) different plates. In how many ways can this be done?

SetPartition({apple,pear,orange,mango,peach}, [1,2,2]);  nops(%);  # plates are indistinguishable

NumbPart([1,2,2], ordered);  # Number of ways for  different plates

                                                              90

Another example - how many ways can be divided  100 objects into 10 equal parts?

NumbPart([10$10]);

    64954656894649578274066349293466217242333450230560675312538868633528911487364888307200

 SetPartition.mws

Application of the properties of real numbers such as divisible factors, quantity and sum of prime divisors, DCM and MCM among others. All the technology embedded components of Maple.

Propiedad_de_los_Numeros.mw

Atte.

L.AraujoC.

I would like to pay attention to an article by David Austin "The Stable Marriage Problem and School Choice"

Here is its inroduction:

" Every year, 75,000 New York City eighth graders apply for admission to one of the city's 426 public high schools. Until recently, this process asked students to list five schools in order of preference. These lists were sent to the schools, who decided which applicants to accept, wait-list, or reject. The students were then notified of their status and allowed to accept only one offer and one position on a waiting list. After the students had responded to any offers received, schools with unfilled positions made a second round of offers, and this process continued through a concluding third round.

This process had several serious problems. At the end of the third round of offers, nearly half of the students, usually lower-performing students from poor families, had not been accepted into a school. Many of these students waited through the summer only to learn they had been matched with a school that was not on their list of five schools.

This process also encouraged students and their parents to think strategically about the list of schools they submitted. Students that were rejected by the school at the top of their list might find that their second-choice school had no vacancies in the second round of offers. This made it risky for many students to faithfully state their true preferences, a view encouraged by the Education Department's advice that students "determine what your competition is" before creating their lists of preferred schools.

Lastly, schools would often underrepresent their capacity hoping to save positions for students who were unhappy with their initial offerings.

In the end, the process couldn't place many students while it encouraged all parties, both students and schools, to strategically misrepresent themselves in an effort to obtain more desirable outcomes not possible otherwise. Widespread mistrust in the placement process was a natural consequence.

Using ideas described in this column, economists Atila Abdulkadiroglu, Parag Pathak, and Alvin Roth designed a clearinghouse for matching students with high schools, which was first implemented in 2004. This new computerized algorithm places all but about 3000 students each year and results in more students receiving offers from their first-choice schools. As a result, students now submit lists that reflect their true preferences, which provides school officials with public input into the determination of which schools to close or reform. For their part, schools have found that there is no longer an advantage to underrepresenting their capacity.

The key to this new algorithm is the notion of stability, first introduced in a 1962 paper by Gale and Shapley. We say that a matching of students to schools is stable if there is not a student and a school who would prefer to be matched with each other more than their current matches. Gale and Shapley introduced an algorithm, sometimes called deferred acceptance, which is guaranteed to produced a stable matching. Later, Roth showed that when the deferred acceptance algorithm is applied, a student can not gain admittance into a more preferred school by strategically misrepresenting his or her preferences.

This column will present the game-theoretic results contained in the original Gale-Shapley paper along with Roth's subsequent analysis. Pathak calls the deferred acceptance algorithm "one of the great ideas in economics," and Roth and Shapley were awarded the 2012 Nobel Prize in economics for this work"

It would be nice to realize that in Maple.