§2.1 Methods for setting functions. Replacement of replacements. Maple's top mathematical theory Maple operations with 4 vectors
04. 01 The reorganization of the ranks. Team lhsі rhs
* Entering and Manipulating Equations: Thelhs andrhs commands*
It seems that rhubarb, as well as virus, can be given a name. At the offensive command line We will introduce equal value and give it to you eq1 " :
> eq1:=x^3-5*x^2+23=2*x^2+4*x-8;
We can display on the screen the left and right parts of the equation, together with additional commands lhsі rhs :
> lhs(eq1);
> rhs(eq1);
Speeding up teams lhsі rhs in order to bring the level to a standard appearance, in which all members are evil, and the right-hander has lost less than 0:
> eq2:=lhs(eq1)-rhs(eq1)=0;
04. 02 Finding the exact roots. Team solve
* Finding Exact Solutions: Thesolve command*
Let's take a look at rational attitudes first. It appears that there are algorithms for identifying exact roots of rational roots up to the 4th order inclusive. The Maple team solve and these algorithms are laid down.
Speed up as a team solve to find the exact roots of a cubic square 
:
> solve(3*x^3-4*x^2-43*x+84=0,x);
Restore respect: the team is instructed to ensure that any changeable trace of respect is released. I want in our specific vipadku it’s not obov’yazkovo:
> solve(3*x^3-4*x^2-43*x+84=0);
Maple knows all 3 active roots and views of them ( a disorganized look ).
Sometimes it is important to choose a specific root, so that you can then use it in further transformations. For this purpose, immediately assign a name to the result of the search command solve. Namely Yogo X. Todi design X will be similar to the first root in the list (under the name: It's not necessarily a smaller root!), X- Another root, etc. ( The arms are square!):
> X:=solve(x^2-5*x+3=0,x);
However, wonder what will be displayed as a result of running a similar command:
> x=%;
Let’s say it again: practice shows that it is entirely possible to assign a name to jealousy. Traditionally in Maple, names begin with the letter eq :
> eq1:=7*x^3-11*x^2-27*x-9=0;
(Don't confuse the assignment operator) := with a sign of zeal = " !)
Now there is great jealousy for the help of the team solve. Bezlіch roots nadamo іm'ya X :
> X: = solve(eq1, x);
For the sake of clarity, let’s check that there are no third-party roots found. Verification can be made by means of a non-median substitution
> subs(x=X,eq1);
> subs(x=X,eq1);
> subs(x=X,eq1);
Of course, there is often a “precise” decision to add bulkiness, or otherwise. For example, there is a lot of jealousy 
:
> eq1:=x^3-34*x^2+4=0;
> X: = solve(eq1, x);
Now you understand what's going on? For yourself, respect that one is obvious in Maple sign up for help great literature I . It is clear that it is impossible to know the closest meanings of the roots. Feeling like a solution in your hands, you yourself will understand how to make it:
> evalf(X);
In such situations, the best alternative is the command solveє fsolve, the specifics of which will be discussed in the next paragraph
Team solve When exact solutions are found, not only rational considerations are chosen. Below is a series of illustrations. Ale for many types of irrational, demonstrative, logarithmic, trigonometric and generally rational equations, more precisely the solution is to joke carefully. The team calls for help fsolve .
Let's unleash jealousy 
:
> solve(5*exp(x/4)=43,x);
Inode (a in trigonometry - always ) Maple, for getting ready, do not write down all the anonymous roots:
> solve(sin(x)=1/2,x);
There are no hopeless situations! Taking the result as a basis, use your knowledge of trigonometric equations and write down the solution ( yak?).
Right 4.1
Virishity Rivalry 
Find out how many different roots there are in the vine. How can Maple find the obvious roots?
Porada: divide the left part of the row into multipliers
> solve(x^3-11*x^2+7*x+147=0,x);
> factor(x^3-11*x^2+7*x+147);
The root x = 7 is a yard, and the cubic equal has only two different roots. Multiplying the left side is a confirmation of this.
04. 03 The sound of a nearby root. Team fsolve
* Finding Approximate Solutions: The fsolve command*
To quickly untie the rivalry, the Maple team is using vikory fsolve. In times of rational jealousy, fsolve display the entire list of active roots (div. Application 01). For transcendental ranks, this is the command for the minds to deduce only one root(Div. Apply 02 and 03).
For further help fsolve we know the close meanings of all the four active roots of rational justice 
:
> eq:=x^4-x^3-17*x^2-6*x+2=0;
> fsolve(eq, x);
These are the roots of becoming the primary solution to the output rational equation ( I want it close).
Vikorist team fsolve, know I'd like one active root rivnyanya 
:
> eq:=x^3+1-exp(x)=0;
> fsolve(eq, x);
Maple and viviv have only one root. This time Maple did not become a “painting”. How can we now get to grips with something that has no other effective root? The offensive butt provides such a toolkit.
Otrimati all
effective root justice 
and transfer with someone.
Croc first ( Main idea ) : we know the graphical solution of the equation for which we will find the graph of the function that stands on the left side of the equation. The abscise points of the cross-section of this graph from the whole Ox and will be the same roots.
> plot(x^3+1-exp(x),x=-3..5,y=-5..15);
Because We have carefully selected the ranges of changes in the abscist and ordinate points of the graph, then it is easy to see 4 dots cross the line from the whole point Oh. One of them resembles the root found in Appendix 02 ( like yourself?).
Another root is obvious: x = 0. How can we know more accurately?
Croc is different ( More details ) : let's stagnate the team fsolve more "seeing". Maple has added the ability to insert a space where the root is located. Zokrema, the meaning of the negative root of our rіvnyannya, perhaps, is what jokes can be traced to the “region” [-1;-0.2]. About this, it is clear to see the graphic solution.
> fsolve(eq,x=-1..-.2);
The root, which has lost its obvious place in the gaps and. Let's talk about this team fsolve :
> fsolve(eq, x = 1..2);
fsolve(eq,x=4..5);
Well, what will happen if we give Maple an “empty plot”? For example, a glimpse of our rival. There is clearly no graphic design there:
> fsolve(eq,x=2..4);
Maple shows the name of the command, the command itself, the name of the argument and the section. Tobto. nothing new. Saying: “Just joke around, but I don’t know.”
Krok third ( Additional analysis ) : How can we now jump into what we have found? everything is root, and not just the visible galusa of the graphic design? To expand the search interval:
> plot(x^3+1-exp(x),x=-3..50,y=-10..15);
There are no new points on the crossbar. We understand that the exponential addition between the intervals makes a real contribution to the value of the function on the left side of the equation. The significance of the function of this galusa is to be explained until we know the additional roots.
Let's try in other places: right-handed and left-handed in the area of the identified root.
> fsolve(eq,x=5..50);
> fsolve(eq,x=-50..-1);
And here's a great additional root! Having realized that with the influx of the display part, everything has become clear, we are timid about the remaining constructions.
Vicherpne decision vynyannya 
consists of four roots: -.8251554597, 0, 1.545007279, 4.567036837.
Let's stagnate the team fsolve for nearby unleashing of transcendental jealousy 
.
As a first step, let’s find out the beginning of a clearer graphic solution. For what else is it necessary to figure out how to distribute the offending parts of your member. Aside from the graphic possibilities of the Maple table, it is a miracle that in the future you can take all the members of the army from one side.
Let's look at the same thing, equivalent to this: 
. The abscise point of the crossline of the graph of the function, which stands at the left side of the line, from all Ox and will be found to the roots.
> eq:=x^2/20-10*x-15*cos(x+15)=0;
> plot(lhs(eq),x=-10..10);
The graph shows the area where the roots are searched: span. The time of command is coming fsolve :
> fsolve(eq, x = 1..2);
The root has been found. Ale, obviously, is not the only one. Expand the search area and set up the team again fsolve to pick up another root.
Right 4.2
Find out all the action 
, Having started with a graphic solution.
Let's look at the graph of the left side of the equation:
> eq:=x^5-4*x^3+3*x^2+7*x-1=0;
> plot(lhs(eq),x=-5..5,y=-5..5);
The result shows the root level of loyalty to the first closest: -2; -1.5; 0 . We are now stagnating the team fsolve without insertion in the search range ( Maple's feasibility is appreciated):
> fsolve(eq, x);
Because of satisfaction, it means that Maple derives all three roots (It is important to remember that rationalism prevailed.)
Right 4.3
Find out all the roots 
. Be quick with graphic solutions. Turn the skin over with a middle substitution.
Let’s bring the equation to the standard (for this section) form:
> eq:=x^2-2-ln(x+5)=0;
Now we will create the graph of the left side of the equation:
> plot(lhs(eq),x=-10..10);
Obviously, there are two roots. One is approximately the same as -2, and the other is similar to 2.
Let's stagnate the team fsolve, limiting the search range:
> x:=fsolve(eq,x=-5..0);
> x:=fsolve(eq,x=1..3);
The root can be verified by a non-median substitution:
> evalf(subs(x=x,eq));
> evalf(subs(x=x,eq));
Restore respect: in both cases there is no true zeal. In terms of settlements, when rounded, reasonable dispersion is entirely permissible.
Check for the presence of another root. Then wrap it up.
Right 4.4
Function graphs 
і 
the two move to the side [-5; 5].
A). Be in the same coordinate system for the graphics of both functions and use the mouse to find the coordinates and points of the crossbar.
b). Add the lines, roots and abscise points to the crossbar of the graphs.
c). Vikorize the team fsolve to unleash this rivalry.
d). Use the results from point c) to estimate the ordinates of the points of the crossbar of the graphs.
e). Have you ever thought that the lines can move at the third point with coordinates (1; 9)? Vikorist fsolveі graphic possibilities Maple will switch to something else.
> y1:=10-x^2;
> y2:=4*sin(2*x)+5;
Now let's create function graphs:
> plot(,x=-5..5);
The closest coordinates of the crossbar point are: (-1.8, 6.6) and (2.75, 2) .
b) Warehouse level:
> eq: = y1 = y2;
c) Team fsolve will help you know the root root:
> x1:=fsolve(y1=y2,x=-4..0);
> x2:=fsolve(y1=y2,x=0..4);
d) Vikorist team subs to determine the specific ordinates of the cross points:
> y:=subs(x=x1,y1);
> y:=subs(x=x2,y1);
The final points of the charts: (-1.800,6.763) and (2.773,2.311).
e) Graphically trace the area around the point x = 1:
> plot(,x=.5..1.5);
Team fsolve How many times can we bring the number of roots near the point x = 1:
> fsolve(y1=y2,x=.5..1.5);
04. 04 Unraveling the ties of the Zagalny Viglyade
* Solving Literal Equations*
In many instances of Maple, there is a decision to respect the zagalny (symbolic) look. We are talking about jealousy (and not the system!), To take revenge on a few changeable ones. The solution is for the one who expresses himself through the other.
Please don’t forget to be jealous 
good change g. Behind the vikorist team solve. And our hopes are true:
> solve(4-v=2*T-k*g,g);
And so the decision can be made in a basic way:
> g=solve(4-v=2*T-k*g,g);
Right 4.4
The emphasis will remain on the other changes: T,kі v.
> T=solve(4-v=2*T-k*g,T);
> k=solve(4-v=2*T-k*g,k);
> v=solve(4-v=2*T-k*g,v);
Right 4.5
Virishity Rivalry 
shodo u. Assign the sequence of the roots to the name S. How are the roots S and S related?
> S:=solve(x^2+y^2=25,y);
The root becomes more familiar.
— a software package that can be used for various purposes. You can think of it as a stuck-in calculator, which can not only calculate arithmetic operations, but also integrate, multiply matrices and graph functions. At the same time, this system includes daily programming, which is procedural (parallel), object-oriented and applied in one bottle. In addition, you can integrate with MatLab, and also allows you to call external program compilation procedures onto Cі Fortran. Zagalom vin allows you to create a powerful program for obvious reasons. This middle ground allows you to create prototypes for various technical and scientific developments by then writing code with other languages.
Such diversity of features of this middle ground can complicate its conversion into a distant victorious process. As a rule, the cob is cultivated using the method of ticking with the vikoristanny of the administrated Help. It’s a pity that I didn’t understand the riddles of my Russian friends. Slide set three settings on English language, how to read it obov'yazkovo:
All three can be found in private access. In this section I will share my knowledge of working in Maple and putting the robot into practice and fine-tuning.
Start naturally with the installation. The system is not cheap, but for information you can find it on various torrents, for example https://rutracker.org/. Yak for Linux, so for Windows.
Having installed, we launch and most importantly the column with Pallettes|Workbook on the right is a window with a large number of icons divided into two parts:
You can now get acquainted with a variety of ready-made applications of various topics in mathematics, programming, and natural sciences - by clicking on the icons on the right side of the window and launching related documents Maple. These documents can be edited and saved. We begin the independent robot by clicking on the right side of the window New Document or else New Worksheet. The difference between these two types is small, as shown in the table. We will continue to vikorist Worksheet. The rows to be added are marked here with a [> . Maple commands are displayed in bold. After the [> icon, you can enter commands that end with either a dotted line or a doubletted one. For example, for an arithmetic operation:
sin(3.)+1;
After the command it is embossed Enter or a bear sign! beast on the menu. Respect the difference between such a team and two similar ones: sin(3)+1;і sin(3)+1: The result will not appear on the screen - because... The command is completed with the sign:.
This sign is used if you do not need the result, and it is too cumbersome. For example, after entering a value: a:=Pi:
We will not require confirmation that a is older than 3.1415…. We can continue to vikorize like this:
b:=2*a;
the result will appear as $b:=2\pi$. Respect that we invite you for help := . The primary sign of zeal of vikoryst is expressed in a slightly different way. Maple knows what Pi means the number $\pi$. To get rid of this numerical value, you need to use vicoristics special function like this:
b:=evalf(2*a);
As a result, we remove the value of the number pi with the accuracy of present moment Vikorist at Maple. And respect here! Maple You can use a variety of significant numbers. For promotional items 10 characters. This number can be easily changed. I write on the document itself like this:
restart: Digits:=16:
Thus, the document will have 16-digit numbers. This quantity can be changed; the maximum value for your OS can be removed using the command
kernelopts(maxdigits);
I have a maximum value of Digits = 38654705646. Please note that I am also a victor on the cob team restart: This command is very simple, since you edit the document within an hour of one session, for which you do not need to restart Maple closing and opening yogo. You just press the button after correcting !!! V top panel Maple and everything will be over-insuranced let's update all the great ones.
10. PROGRAMMING AT THE MIDDLEMAPLE
The Maple mathematical package allows computer scientists to compile computer programs, procedures and libraries. For this purpose, the package needs to have a wide range of commands and a design similar to high-level algorithmic programming language.
10.1. Brain operator
Maple's mental operator begins with a reserved word if And it’s bound to end, in a word fi It has the following structure:
if Umova then viraz 1 else viraz 2 fi ;
This design makes it possible to place, depending on the value of the logical mind, either Viraz 1 (like the mind is true) or Viraz 2 (like the Mind's mind). Both expressions 1 and 2 can follow any sequence of commands from the Maple package. The mental operator can make notes in a short view:
if Umova then viraz 1 fi ;
[> restart;
[> x: = 4;
x:=4
[>if x>4 then print ('x>4'); else x:=x^2;
print(2*x); fi;
32
p align="justify"> To implement flexible minds, it is necessary to develop a new version of the mental operator, which may lead to the structure.
if Umova 1 then viraz 1 elif Umova2 then viraz2... elif Umova n then viraz n else viraz n +1 fi ;
As follows from the structure of this operator, the contribution of minds can be practically unbounded and can be realized through the use of a service word. elif . How you can express it differently is the sequence of Maple commands.
[> restart;
[>x:=8:
[>if x
x:=c
10. 2 . Loop statements
The Maple mathematical package for implementing a cyclic computational process has several types of cycle operators. The core of all loop operators is the sequence of commands placed between service words do і od . The loop operator of the over-reinforced type, which is found in almost all algorithmic languages, has the following structure:
for Change cycle from cob value of the harvest cycle by time period for increasing the value of the change cycle to end value of the change cycle
[>for i from 0 by 4 to 8 do i od;
0
4
8
The operator for a loop like “yet” in Maple looks like this:
while Umova do viraz od ;
Once the body cycle (viraz) ends until the hour when the meaning of the logical mind is truly accepted, as the mind is hypnotic.
[> restart;
[>n:=0:
[>while n
1
2
9
The preceding operator of the cycle is a symbiosis of the two preceding ones and has the following structure:
for Change cycle from cob value of the harvest cycle by value of increased amount while Umova do virazi od ;
For this operator, the calculation cycle is completed until the hour when the logical expression is true, and the change in the cycle changes to the cob value from the specified time.
[> restart;
[> for y from 0 by 2 while y
0
2
4
6
The fourth statement in the assignment cycle for working with analytical viruses and the attack structure:
for Change cycle in viraz 1 do viraz 2 od ;
Here the body of the cycle of expression 2 is condensed, since the symbolic change given to its names sequentially takes on the values of the skin operands of algebra 1. It is significant that the work of this construction lies in the internal supply in Iraza 1. So if you have 1 sum, then im' During the alternating cycle, the daily value of the skin supplement is taken, as is the solid content of the skin substance.
[> restart;
[> a:=5*x^2+x+6/x;
[> b:=simplify(%);
[> for m in a do m; od;
[> for m in b do m; od;
10.3. Function procedures
Maple function procedures can be specified in two ways. To create procedure-functions, the first method is to use the vikory symbol ( ) and is determined by the offensive structure:
Function names: = (list of formal parameters) viraz;
The name of the function is indicated by a set of characters in the Latin alphabet, the list of formal parameters is entered through whom. Viraz is a Maple command that implements the body of a function procedure.
[> f1:=(x1,x2)->simplify(x1^2+x2^2);
[> f 1 (cos(x), sin(x));
1
Another way to define procedure-functions is the vikory command unapply It has the following structure:
These are the functions:= unapply (Viraz or operation, list of changes);
This method of assigning procedure-functions to a new function is via an input or if the virus passes the vikory function as a function.
butt .
[> f3:=unapply(diff(z(r)^2,r)-2,z);
[ > f3(sin);
[ > combine(%);
10.4. Procedures
Any procedure in Maple begins with a title, which is the name of the procedure, followed by an assignment sign and a service word proc , further in round temples through whom formal parameters are specified. The procedure will inevitably end with a service word end . All definitions and commands linked between service words proc і end add up the body of the procedure.
Name of procedure: = proc (List of formal parameters); command (or virazi); end ;
If the procedure is important, this click will affect them. The value that is rotated is the value of the remaining specified operator (command) from the body of the procedure, in which the type of result of the procedure is the same as the type of value that is rotated.
[> f:=proc(x,y);x^2+y^2;simplify(%);end:
[ > f(sin(x),cos(x));
1
When writing procedures in Maple, you can use low commands and service words, in addition to a designated minimum set of obligations that allow you to describe changes, determine the exit from the procedure, and notify about errors.
When describing the formal parameters of a procedure, you can specify their type using a double checkbox. With such a description, Maple automatically checks the type of the actual parameter and provides notifications about changes in different areas with the type of the formal parameter.
After the title of the procedure, a part of the procedure can be described, which is supported by a new gap. When describing local changes that are used in the middle of this procedure, you can use the description, which is specified by the service word local , after which it is necessary to indicate the names of local changes through the pass. The selection of global variables for a procedure can be specified using a service word global , which may be located in the description part of the procedure.
To exit the procedure in any place of the body and the result of the work from the required command, you can use the command RETURN ( val ), de val - meaning, what to turn around, as you can mother different type when leaving different places of the procedure.
For an emergency exit from the procedure, you can use the command ERROR (‘ string ’) , here string – a notification that is displayed on the monitor screen in an emergency situation. Thus, the basic structure of the procedure can be represented as follows:
Name of procedure: = proc (List of procedure parameters) local list of local changes, induced through coma; global overflow global changes, induced through coma; RETURN ( val ); ERROR (‘ error in body of procedure ’);… end ;
[>
[ > examp(-1);
[> examp(0);
[ >examp(2);
11. METHODS OF ENTERING AND RECORDING INFORMATION
AT SREDOVYSHCHIMAPLE
To save names (identifiers) and their values in external memory as a file with them name . txt you need to enter the command:
save list of names of changed ones, recovered through coma, “file names with extensions” txt ”;
What is the extension of the indicated symbol? m , The file will be recorded in the internal Maple format, with all other extensions in text format. To display the information saved in the file on the screen, use the command
read “ File name ”;
[> restart;
[> examp:=proc(x) local y,w; Global z; if x
[ > examp(-1);
[> examp(0);
Error, (in examp) Variablex = 0
[ >examp(2);
[ > read "nnn.txt";
To record an entire file instead of the screen, you can use the following two commands.
Persha team
writeto ("file name")
As a result of this command, all information that fits on the screen will be saved in a file with designated names. Moreover, since the instructions file is from external memory The information being saved will be replaced with a new one.
Another team
appendto ("file name")
Allows you to add information that is displayed on the screen after this command to the end of the file.
[ > f:=12;
[> f1:=factor (y^2-3*y); save f,f1, "n1.txt";
[> appendto("n1.txt");
[> solve(x^2-3*x+2=0,x);
As a result of the victory of the team save f , f 1, " n 1. txt "; a text file will be created n 1. txt , We respect this information:
f:= 12;
f1:= y*(y-3);
and as a result, the victory of the team appendto (" n 1. txt "); Instead of the file I will look:
f:= 12;
f1:= y*(y-3);
[ > solve ( x ^2-3* x +2=0, x );
2, 1
The Maple package has a few commands for displaying information on the screen. The simplest of them are commands
print (perelik Maple
lprint (perelik Maple -Virazhen, what to play it safe through a coma);
Moreover, since nothing is assigned to the change, then their names are displayed, otherwise their values are displayed.
[> x:=y^2: print (x, "primer 1", y, factor(x-5*y));
[> x:=y^2: lprint (x, "primer 2", y, factor(x-5*y));
y^2, primer 2, y, y*(y-5)
At the pointing of the butts, the command screams print display expressions through coma in natural mathematical form, and the command lprint display information in the style of a series of displays and are reinforced with one type of space.
The Maple package can be used to analyze and graphically interpret numerical information contained in a text file extracted from either the package or other software add-ons. As a rule, in a text file, numbers are written in rows. To read numeric information from a text file, you can use the following command:
readdata (“file name”, change type( integer / float - The remaining type is installed for the purpose), number healer);
Before using this command, you must activate the additional commands:
readlib(readdata):
[> restart;
[> readlib(readdata):
[> ff:=readdata("aa.txt",integer,8);
[ > x:=ff;
[ > y:=x;
[ > y1:=ff;
[ > f:=readline("aa.txt");
Changed indexation ff is connected with the fact that the numbers are given at a glance two-world massif, in which the number of rows in the array corresponds to the number of rows, and the number of columns is determined by the remaining command parameter readdata . How the command screams from the pointed butt readline display numerical data in variable form string .
12. VIKORISTANNA MATHEMATICAL PACKAGEMAPLEFOR SCIENTIFIC DOSLIDZHEN
This section will look at how Maple solves applied engineering tasks. We aim to show the capabilities of the Maple package for advanced engineering tasks related to advanced research modes of robot ownership, including design and technological parameters, complexes and illustrate the capabilities of software and command modes of robots koristuvacha in the middle of Maple. Below are fragments of the investigation, which are accompanied by short explanations.
12.1. The investigation is in progress changing parameters flat grinding chamber with flow-through effect on energy efficiency
12 .1.1. Statement of the problem
The jet streams contain a variety of impact components and are composed of a split-type apparatus (one or several units), in which the gas-energy stream imparts fluidity to the particles of the material that are formed, and the chambers, as There is an interaction between the material flows among themselves and/or with special liquids surfaces. As energy carriers in stream valleys, wind is most often stagnated, and sometimes inert gas, water vapor, and combustion products.
The strumenevy broom allows the broom to be combined with mixing, drying and other technological processes. And the robot in a closed cycle will ensure minimal sawing of the saw in the middle.
Any jet device includes a projector, which is a chamber in which the energy of two flows (main and projected) is mixed and exchanged, and a grinding chamber in which the mixed flows interact . With the acceleration of energy transfer at the ejector discharge tubes, the particles are transported to the grinding chamber, and then to the jet zone (Fig. 12.1).
The string that comes out of the heating tube does not immediately fill the entire cross-section of the marked chamber; the string at the entrance to it breaks through the walls and then collapses, looking like a strong string, To resolve the middle part of the surface section. The surface of the section is unstable, vortices arise on it, as a result of which the liquid mixes with the excess medium.
When the jet from the flame tube is completed, the fluid flow in its outlet section 1-1 at all points the intersection is equal to each other. By stretching the cob, the axial fluidity is constant according to the magnitude and the previous fluidity in the section of the heating tube V 0 . In the area of the tricutaneous ABC (Fig. 12.1.) at all points of the fluid flow stream the energy flow is equal to each other and also equal V 0 - This area creates the so-called core of the jet. Further, the axial liquidity changes step by step and continues at the main level l basic axial fluidity V OS V 0 .
Rice. 12.1. Diagram of the jet at the grinding chamber
It is clear that the fluidity of energy supply from the section of the heating tube to the surface of the jets changes according to the law
,
(12.1)
de V z – fluidity of energy supply with a grinding chamber on the riser z view through the discharge tube, m/s;
V 0 - Energy density at the cut of the heating tube, m/s;
z 0 - Stand in front of the outlet tube to the plane of the nostrils, m.
When there is a significant change in the kinetic energy of the end circuit of the biological medium, it is necessary to know the work of the forces of intercomponent interaction of particles of the material and energy. This robot lies in the force vector of the dynamic influx of energy onto the particle, which is calculated as such
,
(12.2)
de R - Vector of the force of the dynamic inflow onto the particle, N;
F m - Area of cutting of a particle, m2;
,
(12,3)
Significantly
,
(12.8)
de m - Mass of a piece of trimmed material, kg.
,
(12.9)
de 
- Hardness of particles of trimmed material, kg/m.
Viraz (12.7) I can see
.
(12.10)
The grinding can be removed in order to change the fluidity of the particles added to the material in the grinding chamber in the section between the pipes distributing to the area of mutual interaction of the jet streams.
A system of differential equations that describes the process of changing the fluidity of particles and energy transfer in the grinding chamber through the fermentation tube until the constriction flows are closed
.
(12.11)
Vidstan l Store – between the cut of the heating tube and the middle surface of the grinding chamber is chosen wisely
,
(12.12)
de d tr = 18 diameter of the heating tube, mm.
U Maple There are many ways to present the function.
Method 1. Assignment of functions to additional operator ( := ): I guess it’s called for, for example:
> f:=sin(x)+cos(x);
How to specify the specific value of the change X, then you will see the value of the function f for whom X. For example, if you continue to live the front butt and calculate the values f when , record the following:
> x:=Pi/4;
After the demise of these teams X may given value.
To avoid specifying a specific value at all, it is better to use the substitution command subs((x1=a1, x2=a2,…, ),f), de in curly temples make excuses xi and their new meanings ai(i=1,2,…), which trace should be substituted for the function f . For example:
> f:=x*exp(-t);
> subs((x=2,t=1),f);
All calculations in Maple behind the minds they vibrate symbolically, so that the result is misplaced by clearly irrational constants, such as these. To find the closest values to the numbers with the floating coma, follow the command evalf(expr,t), de expr- Viraz, t- Accuracy, expressed in numbers after the coma. For example, by stretching the front butt, the numerical value of the function is brought closer:
> evalf(%);
Here is the Wikorista symbol ( % ) to call out the front command.
Method 2. Significant functions behind an additional functional operator, which is assigned to a set of variables (x1, x2, ...) one or a few virasivs (f1, f2, ...). For example, the assigned function of two substitutions for an additional function operator looks like this:
> f:=(x,y)->sin(x+y);
Reversing this function is done in the most mathematically analogous way, if instead of the arguments of the function, the specific values of the variables are assigned to the handles. By pulling the front butt the function values are calculated:
Method 3. For additional commands unapply (expr, x1, x2, ...), de expr- Viraz, x1, x2, ...- A set of changes, such as those that are stored, can be converted into expr y functional operator. For example:
> f:=unapply(x^2+y^2,x,y);
U Mapleє possibility of assigning non-elementary functions of the form
call for help
> piecewise(cond_1, f1, cond_2, f2, …).
For example, function
register in this way.