Method of undetermined coefficients
Let us find the expansion into simple fractions for .
The general form of the decomposition in this case
.
Bringing to a common denominator and discarding it, we have
x 2 -1=A(x 2 +1) 2 +(Bx+C)x+(Dx+E)(x 2 +1)x
Equate the coefficients at the same powers of x:
so the desired expansion has the form:
.
Let the denominator Q(x) of a proper rational fraction have a real number and a root of multiplicity a. Then among the simplest fractions, the sum of which decomposes a fraction, there is a fraction. Coefficient , Where .
Rule: to calculate the coefficient A with the simplest fraction corresponding to the real root a of the polynomial Q (x) of multiplicity a, you should delete the bracket in the denominator of the fraction and in the remaining expression put x=a. Note that this technique is applicable only to calculating the coefficients of the highest powers of the simplest fractions corresponding to the real roots of Q(x).
The elimination method is especially effective when the denominator Q(x) has only single real roots, i.e. When
Q(x)=(x-a 1)(x-a 2)×... ×(x-a n). Then the representation
,
all coefficients of which can be calculated by the elimination method. To calculate the coefficient A k, you should cross out the bracket (x-a k) in the denominator of the fraction and put x = a k in the remaining expression.
Find the expansion of a fraction
Task number 4. Increase in the number of transactions:
What calls to action can be? Example: “Call now”, “Find out more on our website”, “Find out more by calling…”.
P.S. If you just read this article and have not implemented any of the indicated methods of increase in your enterprise, then you have wasted your time.
If you are going to implement in your organization 2-3 ways you like to increase sales, then you are in for good results.
If you decide to use each of the methods described here, then the problem of inventory will cease to exist for you. And you will forget that once this question was so relevant for you.
P.P.S. What is a profitable plant? This is an enterprise that is aware of what place its products occupy in the market and sells them competently! Sales work is the same lead generation. Sales funnel analysis, online marketing. All the same!
Graphic method
Graphical methods for determining the most effective project are the least accurate, but the most visual, and therefore they are usually used in various kinds of presentations. The essence of the graphical technique is that no rating is determined for each calculated and analyzed indicator, but the values of the indicators are plotted on the graphical axes. To build symbolic efficiency, as many equidistant axes are plotted on the coordinate plane, according to which indicators it is extremely important to draw a conclusion, and these indicators should not be less than three, but optimally there should be as many as possible.
The points of deposition of indicators on the planes for direct indicators are built from 0, and for inverse ones - from the maximum possible value. The maximum values for inverse indicators are determined based on the average values for projects of different directions. It is important to note that for the creation of industrial enterprises, the maximum payback period is 10 years, for residential construction - 6 years, for the creation of enterprises involved in heavy metallurgy - 12 years.
According to such an indicator as the break-even point, 2 aspects should be taken into account:
1. It is not the break-even volume of production in units of production that is graphically reflected, but the indicator of the profitability threshold, which is such revenue that will fully pay off fixed and variable costs and lead the enterprise to the absence of both profit and loss.
2. At the 0 point, an amount equal to a quarter of investment costs is set aside and advancement along the axis is carried out with a scale of 1=100t.r.
The tax burden indicator is built from one and a half standards determined by the federal tax service (normal values of the tax burden are established for all possible branches of activity).
For those industries where the normal tax burden is up to 20%: 1 division step is 1%, and for those industries where more than 20% - 2%.
For direct monetary indicators, the division step is 1/10 of the investment costs in the project. For direct percentage indicators, the division step is 0.1% (except for GNI, where the division step is 5%).
Having set aside all points for all projects on the coordinate axes, each project is closed by a line separately. And the project with the greatest distance of points from the center is recognized as the most profitable (if there are several such projects, then the one closest to the circular value).
It is based on the principle that if it is impossible to select the best project according to all the available criteria, then it is extremely important to exclude the criteria from the calculation.
Initially, criteria such as the payback period of the project, IDI, IRR and TSP are used in the cross-out method. In order to cross out any indicator, it is extremely important to evaluate the rating of this criterion. Prior to the start of deletion, all criteria are equivalent, that is, each criterion is initially assigned, then each criterion is initially assigned 25 rating points.
Calculations begin with the TSP, determining on the basis of which the investor has set the maximum allowable payback period for himself.
If the optimal value of the payback period is determined from the extreme importance of financing another project, then the significance of the payback period increases by 3 points. And in this regard, the significance of the 3 remaining indicators is extremely important to reduce by 3 points, that is, a reduction of 1 point for each indicator. If a five-year payback period is set on the basis of average payback period values for the industry, then the payback period rating increases by 1.5 points, while the rating of other indicators decreases by 0.5 points for each.
If the payback period is set on a different basis, then the rating of the payback period and other indicators does not change.
If the GNI indicator is within the sum of the inflation rate and the refinancing rate, then the GNI rating is increased by 6 points. At the same time, the ratings of other indicators are reduced by 2 points each.
If GNI is set higher than the sum of the refinancing rate and inflation, then for every 0.5% excess, the GNI rating is additionally increased by 0.3 points.
Next, the investor determines how critical it is to adjust the rating of the merchant. If the minimum allowable TPP indicator is determined on the basis of the critical importance of repayment of borrowed funds, then the TPP rating is increased by 6 points, while the ratings of other indicators are reduced by 2 points.
If the TPP is established by the investor on the basis of an investment agreement, that is, it is associated with the extreme importance of investing the funds received in another investment project, then the rating value of the TPP increases by 4.5 points. With a simultaneous reduction in the ratings of other indicators by 1.5 points.
If the minimum TPP score is set on a different basis, then the rating of the TPP is reduced by 1.5 points, while others are increased by 0.5 points.
If the IDI indicator is set (if the projects have the same implementation period) in the amount of the inflation rate, increased taking into account the number of years of project implementation, then the IDI rating is increased by 3 points. If the IDI is set below this value, then the rating is increased by 4.5 points.
After all recalculations, the investor determines the final number of rating points after making all changes.
1. The investor crosses out from the list of criteria that are significant for him the one that scored the least number of points.
3. If it is impossible to select the most significant criterion, then an additional criterion is introduced into the calculation in the form of the Fisher point. The quantitative indicator of this criterion is not set, it is taken into account only for equivalence and the method of deletion is again applied, but only for three criteria.
If, based on the results of new calculations, it is impossible to choose the criterion that is paramount, then the investor can include other projects in the calculation, or can use the search for the optimal or ideal solution.
Hello Srgy!
Psht et chttl Vshy rssylk, ktryu n nhdt all plzny ... D w prktk-t nt. I n smm for wn zntrsvn vmzhnstyu svt skrchtn. N for me, this pchm-t vsgd kzl mchty. I was not at this tm rzgvry with brtm. n skzl sldsch: sl chtt chn is fast,t n spvsh the whole nfrmtsyu plntsn brbtt. Skrst read prktchsk straight prprtsnln skrst thinking. vlcht skrst thought - skrst read tzh vlchtsya. Tue brtn, to szhlnyu, n distvt. Spsby sskstng vyshn skrst reading - at fktsya.
And here is the original
Hello Sergey!
This is written by a reader of your mailing list, which he finds very useful ... But there is no practice. I've actually been interested in learning how to speed read for a long time. But for some reason it always seemed like a dream to me. I had conversations with my brother on this subject. He said the following: if you read very quickly, you do not have time to fully process all the information. The speed of reading is almost directly proportional to the speed of thinking. Increase the speed of thinking - and the speed of reading will also increase. But the opposite, unfortunately, does not work. Ways to artificially increase reading speed are fiction.
Even after the text has been shortened by 50% by eliminating some of the letters, it can still be read.
Not every word (each letter) carries an information load. Some words can be taken as hieroglyphs.
To increase your reading speed enough, start reading through the word. You might object that in school you were taught to read carefully and carefully in every word. Maybe this reading rule is still relevant and has not outlived its usefulness as the recommendations that when reading it is necessary to run your finger along the lines or read the text aloud (from reading textbooks of the last century).
There are developments on the software implementation of the method. If anyone is interested in creating an Expert Advisor, write.I give a description of the method.
Money management is based on the Martingale modification - Labouchere,
also known as the "deletion method". This method is not as extreme as the regular martingale.
What is the principle of transaction management?At the dawn of the casino, to play on an equal footing (for example, red - black), a method was invented to double the bet when losing. I will not go into the description in detail, but this method, despite the fact that mathematically, of course, allows you to win, has negative features. The stakes grow exponentially and sooner or later, you will either win, or you will face the lack of the necessary amount in your pocket for the next doubling of the bet, or with a limit on the maximum bet on the gaming table.
Let me remind you that the mathematical probability of winning when playing classic roulette is 49%. 1% - ZERO, this is the advantage of the casino.
The elimination method is as follows. We divide our deposit into 100 parts.
1% of the deposit is one contract.We start the game with 1 contract. We take paper and a pen, write down the rates in a column one under the other.
-1
We add 1 more contract to the lost one. The next bet is 2 contracts. For example, we won. Write in a column
-1
+2
In total, we won 1 contract. We cross out everything, we start anew. The next bet is 1 contract.Consider a more interesting series.
For example, we lost the first bet. We write down on paper
-1
We add 1 more contract to the lost one. The next bet is 2 contracts. For example, we lost. Write in a column
-1
-2
Now to the first bet in the column (-1), add the last bet (-2). Total 3 contracts. Let's say we lost. We write in a column.
-1
-2
-3
Now, to the first bet in the column (-1), we add the last bet (-3). Total 4 contracts. Let's say we lose again. Write in a column
-1
-2
-3
-4
Now, to the first bet in the column (-1), we add the last bet (-4). Total 5 contracts. Let's say we lose again. Write in a column
-1
-2
-3
-4
-5
Five losses in a row. It happens… The next bet is 6 Contracts.
For example, we won. We write in a column.
-1
-2
-3
-4
-5
+6
6 contracts that we won made up for the loss of -1 and - 5 contracts! Now, cross out -1, -5 and +6.
Left:
-2
-3
-4
Now to the first bet in the column (-2), add the last bet (-4). Total 6 contracts. The next bet is 6 Contracts. Let's say we win again. Write in a column
-2
-3
-4
+6
6 contracts that we won made up for the loss of -2 and - 4 contracts! Now, cross out -2, -4 and +6.
There are -3 contracts left. Since there is nothing else in the column, we add 1.
The next bet is 4 contracts. If we win, then we cross out everything, remain in the black in 1 contract and start the streak again.We had such a series
-1
-2
-3
-4
-5
+6
+6
+4Three profitable trades compensated for 5 losing trades.
I advise you to practice on paper, several times, until the principle reaches automatism.So pay attention! In order for the system to function and win, it is necessary to have the number of profitable transactions above 33% -40% percent!!!
If anyone is in doubt, write your own long series. You can practice at any online casino that has a test game for virtual money. Divide your deposit into 100 parts. Bet only on red or only on black. Keep in mind that such a method of playing can be considered by the casino as dishonest, and the casino computer, after some time, will begin to suit you with series of the opposite color 10-20-30 in a row, of course, there will be no talk of any 33-40 percentage ratio and you will lose.But the principle remains the same, 33% of wins compensate for 66% of losses.
Thus, applying such money management in practical Forex trading, we need a trading system that has a 50% probability of winning, and the ratio of possible profit to possible loss is greater than or equal to 1,
those. Profit factor >=1.