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Model of economics - Vіtlіnsky V.V.

2.1.2. Features, the principle of mathematical modeling

Model є by the process of incitement, vivchennya that zososuvannya models. Wonderfully with such categories, as an abstraction, analogy, hypothesis is skinny. The process of modeling obov'yazkovo including the construction of science hypotheses.

The main thing is to model the pole in that he has the method of interposed recognition for the auxiliary object-deputy-deputy. The model of the post is its own instrument of knowledge, which is the first analyst (system analyst) to put between themselves and that’s behind the help of another kind of vivcha object, which is a yogi. Itself is a special model for identifying a specific form of abstract abstraction, analogy, hypothesis, basic categories and methodology.

The need for a vikoristannany model is to be seen as timothy, but a lot of things (chi aspects, so that you can have it), it’s impossible to get up to date without delay, you have to get it right now.

Nekhai є chi need to open the unclear object A. We construct є (materially ’in reality), but we know in real life the most important object B - the model of object A. Can viokremiti such as chotiri main etapi encourage models.

First etap transmission є є яв н де де про про про про про про про про про про про про про про про про про про про про про про про про про про про про про про про про яв яв яв яв яв явн є яв перед яв перед яв яв яв перед The knowledgeable models are able to zoom in, the model of the image, from the perspective of the system analytics, the sutty picture of the original. Nutrition about the need and adequacy of the source and model and the need for analysis. Obviously, the doctor’s touch model is identical to the one with the original (to be sure that it’s not the same as the original), so it’s at the same time as the world’s simplest way. Vivchennya some of the authorities of the modeled object v_dbuvatsya for rahunok vidmovi vid vidobrazheniya іnshikh side. Through the be-yak model, the source is original with strictly separated sense. From the first time, for one thing we can be inspired by the decree of “specialized” models, so as to concentrate respect on the singing sides of the preceding object, to characterize the object from the last detail.

On the other hand is a model of posting as a self-sustaining object. One of the forms of such an accomplishment is the implementation of “model” experiments, in order to understand how to model and systematize data about the “behavior”. The residual result of the whole є stage is the number of knowledge about model B.

On the third stage , transfer knowledge from the model to the original - form the number of knowledge S about the project. The process of transferring knowledge is carried out for singing rules. The knowledge about the model may be butorized with the brains of the quiet authorities of the region, which didn’t know the image of the bullets deformed for an hour, encourage the model. We can transfer the result of the model to the original with a reasonable price, which is the result of the obyazkovo behavior with the signs of the original model. As a result, the singing result of the model achievement is due to the fact that the model is original, the transfer is illegal.

Quarterly etap - a practical breakdown of knowledge gained for the support of knowledge models and victories in order to encourage the ousting theory of management and administration.

For the sake of the daily model, it’s important to have a mother of respect, but the model isn’t just one dzherelo to remove new knowledge about the subject. The process of modeling the "zaurneniy" in the most ignorant process of recognition. To be on the safe side, do not lose yourself on this model, but go on to the final stage, if you need to learn more about the results of the previous year, and also have to learn about the latest ones.

The model is a cyclical process : after the first cycle we can get another one, the third one is skinny. Under tsoyu, knowledge about the progress of the project is being broadened and refined, and the model is being stepped up to speed. Shortcomings, such as appearing in the first cycle of modeling, which are enlarged, for example, inadequate part of the subject by changes in the current model, can be corrected in the upcoming cycles. The methodology model, such a rank, is embedded in self-propulsion.

Of course, three basic ideas go into the genesis of mathematical models. Methodically, you need to turn on and off for changing from simple to folding.

Pershiy is a simplification of a real situation. Suttva it is forgiven to reach it, so long as there are no authorities on the part of the earliest stage of the recognition of the fact that it is not so much to fly. Otzhe, it’s practical for its nature that it’s practical to say goodbye to an idealized analogue, like a mathematical description.

Another is the imposition of simple models on the back of singing, most characteristic features of a real situation, with the up-to-date accelerated updates of such a model, which is a bit of a shame to save the last officials right up to the rejection of the “accepted” version of the model.

The third - the introduction of significant number of officials in the case of interchange and recognition of the model with the requirements of the model. In the skin vipadka, the model “develop” is specified in the world by the availability of the most accurate systematic analytics of daily tasks and the object of delivery.

Systemic analysis of goiters and cherubs also follows the principles of the concept of a “mathematical model” of an object.

Principle 1. The model – object pair is dialectical, be polar, the two poles are “model” and “object”.

Principle 2 Of the two vzakomopov'yazanih poles in a dialectical bet, the model is one object first, the last one is the last one.

Principle 3. The applicability of the pole “obkt” is not enough for the impossibility of the pole “model”, the manifestity of the pole “model” zooms in on the need for the manifestity of the pole “obkt”.

Principle 4. As a “model” for a given “object”, so «“ object ”for a given“ model ”is semantically that interpretation is more meaningful:“ model ”doesn’t mean one’s power, but a bag of words“ about ”,“ about ” 'єkt ”is described not only, but rather by“ models ”.

Principle 5. The “Model” is guilty of an adequate “objec tive” imaging due to the singing accuracy of the main picture and power, and it’s irrelevant to the visual information, an explicit information system, an accepted hypothesis system.

Varto means, basically, the three basic steps of formalizing (formulating a mathematical model) are implemented: practice description; formalized scheme; mathematical model.

I’ll look at the complete report, call me the model of the first situation, where I can formulate the “task” (the report), redefine the first analysis, the clear point for the description (description). On the verbal level (with modern incidents), there is evidence of the nature (sutility) of the environment, the characteristics of the manifestations (processes), the nature of the relationship between the warehouse items, and the large amount of the goods are important. On a regular basis I will describe the formalization to reduce the number of suttvies (keys) of officials, characterize the object (by using the current model), its structure, power, and frequency. The skinner of the virachnical officials is guilty of buty of descriptions on the yakisnom and kilkisnom ravines (the interval of the most important is the scale of the vimyryuvannya is thin). I will describe in the form of a sertificate a better terminology, a text, a number of numeric values ​​with a final comment.

At the same time, with the following list (more often), a diagram can be formed, such as the graphic symbols, graphs, graphs, the image table, and the relative permissions to pay (so that we can provide ob'kta doslіdzhennya. Laws and laws can be described by descriptive viras, name them as mathematical symbols, and ideology are mathematical symbols (operators).

Farther than repetition of the graduate description of that formalized scheme into a single group of mathematical symbols and a complete relationship, an encouraging mathematical model will end. The laws and laws of “materializing” through the rules of formal logic and logical logic of forms, irregularities, differences of mathematical symbols, and accuracy of the rules of communication and interpretation of laws. Such a model is a mathematical model of the preobject and analogue counterparts.

Is it possible to form the image of a mathematical model. To find out how to distinguish between the chotyrma to find by your larger groups - invariant, algorithm, analitichny, circuit.

The invariant form - the image of a mathematical model is harmless to the methods; for some reason, the task of modeling is posed.

Butt of the invariant form:

de a , b , c - vіdomі characteristics of the object; f ( Z , p ) - function function; y ( Z , p ) - nevidoma funktsiya.

Algorithmic form - the image of a mathematical model in a forensic view of the last, the desired view, so that when the tasks are set, the model must go all the way to the result.

Butt algorithm:

  • The significance of the characteristics of the object a , b , c .
  • Calculate d :

  • Maybe d ? 0, then the result is calculated ( x , y ):


The analytical form is the image of the mathematical model of the formulas and the formulas that are more mathematical, because of the kind of fun in the task of modeling, the results are visualized through the data.

Butt of the analytical form:

de a , b are the characteristics of the object, x is the mean, y is the result.

The schematic form is an image of a mathematical model of a forensic table of tributes, diagrams, diagrams, graphs, graphs.

Scheme form butt:

Here F 1, F 2 - transfer function functions.

Vikoristannya analogs in pobudov_ models . Analogs in the incentive models are respected in the majestic number of cases: because for good reason you need to have a model of the right object, because if it’s impossible to directly express the fundamental laws, we must be aware of it. scho admit mathematical formalization. One іz plіdnih pіdhodіv to this genus ob'єktіv Je vikoristannya analogіv s already vivchenimi yavischami.

Hello, what’s the biggest share of the radioactive fallout and the dynamic population, the view, the winter population of our planet? However, on a simple basis, such an analogy is overlooked, but one of the simplest models of populations is the model of Malthus. The Maltus model has a simpler statement: the size of the population in an hour t is proportional to the number of N ( t ) multiplied by the algebraic sum of the number of people that mortality .

The result is maєmo rivnyannya


a yaku is similar to a radioactive active decay and want to know a <b (aka i postіnі). It is not marvelous, however, for the introduction of the Vikings, the same signs were seen. Integrated Rivne (2.1) yes:

de N (0) = N ( t = t 0) - cob number.

If a = b, then the number will be lost permanently, since the value N ( t ) = N (0) is equally important for the first time. Rivnage between people and death is unclear, so as to keep the ruin of rvnost a small, a = b should be reduced by the hour until all the most important functions are N ( t ) vid vnivnazhnogo value N ( t ). For think a <b, the population is reduced straight down to zero, if t ® ?, and for a> b grow for the singing exponential law to inconsistency, t ® ?. Remaining the rest of the servant, I served for the battle to defeat Malthus most of the Maybuty, which was bound up with the overpopulated lands, with usable squeaks. Yak to the given application, so in the lower vipadkіv it is possible to enter into a number of obvious marriages, but the model is encouraged. Sounds well, even the more folding process of the change in the population size, which is why the people themselves had to lie before, cannot be described as simple laws. Navigate to the ideal forum for the use of biologic populations, the model of not realizing the real world is replicated, although I want to use shared resources, which are necessary for the third party. Zroblena’s respect already didn’t apply the role of analogy in the conjunction of mathematical models after the folding collisions.

At the same time, we can see the analogy of one’s rule behind one of the most powerful models of power - the most universal, the more common, the principle of different nature. So, an appropriation (hypothesis) of the type “identity size proportionality value of the self-value (the number of functional functions) is widespread in the economy.

Ієrarhіchny pіdkhіd to form models . Moreover, if you do not need to understand the problems of buoy with manual and good luck to get mathematical models, you should find simple objects in full in good condition, with urahuvannyam usuth suttvih officials. That’s natural to us є pidkhid, which realizes the principle of в simple from simple to foldable ’, since the up-and-coming croc to work hard to finish a detailed vivchenna isn’t even a folding model. Otzhe, wineryє lanyuzhok (ієrarhіya) has a lot of more detailed models, leather with some uzagalnuyu anterior, including a yak of a frequent vipadok.

Substantially, a practical model bank and a good adaptation model for practical models.