The qualitative analysis of mathematical models of processes and devices of the crude hydrocarbons preprocessing on the basis of the models general concept
Theorems of existence and uniqueness of the decision of system of the equations in the private derivatives, representing the generalized mathematical model of processes and devices of preprocessing of crude hydrocarbons are formulated and proved. Generalization gives the chance to apply the principl...
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| Опубліковано в: : | Математичне та комп'ютерне моделювання. Серія: Технічні науки |
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| Дата: | 2013 |
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| Мова: | Англійська |
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Інститут кібернетики ім. В.М. Глушкова НАН України
2013
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| Цитувати: | The qualitative analysis of mathematical models of processes and devices of the crude hydrocarbons preprocessing on the basis of the models general concept / S.A. Polozhaenko // Математичне та комп'ютерне моделювання. Серія: Технічні науки: зб. наук. пр. — Кам’янець-Подільський: Кам'янець-Подільськ. нац. ун-т, 2013. — Вип. 9. — С. 99-107. — Бібліогр.: 11 назв. — англ. |
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| author | Polozhaenko, S.A. |
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| citation_txt | The qualitative analysis of mathematical models of processes and devices of the crude hydrocarbons preprocessing on the basis of the models general concept / S.A. Polozhaenko // Математичне та комп'ютерне моделювання. Серія: Технічні науки: зб. наук. пр. — Кам’янець-Подільський: Кам'янець-Подільськ. нац. ун-т, 2013. — Вип. 9. — С. 99-107. — Бібліогр.: 11 назв. — англ. |
| collection | DSpace DC |
| container_title | Математичне та комп'ютерне моделювання. Серія: Технічні науки |
| description | Theorems of existence and uniqueness of the decision of system of the equations in the private derivatives, representing the generalized mathematical model of processes and devices of preprocessing of crude hydrocarbons are formulated and proved. Generalization gives the chance to apply the principle of unification and typification when developing a method of numerical realization of mathematical models of a class of processes (devices) of preprocessing of crude hydrocarbons, and the proof of the corresponding theorems (an essence ― the qualitative analysis) provides a correctness of application of the generalized model in applied problems of mathematical modelling of studied processes (devices). Proofs of the formulated theorems are strict, logically true and are consistently executed within terms of the functional analysis. Practical applicability of theorems of existence and uniqueness of the decision as component of the qualitative analysis, is defined by possibility of research on their basis of adequacy of algorithmic means of mathematical modelling of a studied class of processes (devices).
Сформульовано і доведено теореми існування та єдиності розв’язків систем рівнянь з частинними похідними, які становлять собою узагальнену математичну модель процесів і апаратів первинної переробки сирих вуглеводнів. Узагальнення дає змогу застосувати принцип уніфікації та типізації щодо розробки методу чисельної реалізації математичних моделей класу процесів (апаратів) первинної переробки сирих вуглеводнів, а доведення відповідних теорем (суть ― якісний аналіз) забезпечує коректність застосування узагальненої моделі в прикладних задачах математичного моделювання досліджуваних процесів (апаратів).
|
| first_indexed | 2025-12-07T16:12:56Z |
| format | Article |
| fulltext |
Серія: Технічні науки. Випуск 9
99
UDC 004.942
S. A. Polozhaenko, Dr. of Tech. Sciences, Professor
Odessa National Polytechnic University, Odessa
THE QUALITATIVE ANALYSIS OF MATHEMATICAL
MODELS OF PROCESSES AND DEVICES OF THE CRUDE
HYDROCARBONS PREPROCESSING ON THE BASIS
OF THE MODELS GENERAL CONCEPT
Theorems of existence and uniqueness of the decision of sys-
tem of the equations in the private derivatives, representing the
generalized mathematical model of processes and devices of pre-
processing of crude hydrocarbons are formulated and proved. Gen-
eralization gives the chance to apply the principle of unification
and typification when developing a method of numerical realiza-
tion of mathematical models of a class of processes (devices) of
preprocessing of crude hydrocarbons, and the proof of the corre-
sponding theorems (an essence ― the qualitative analysis) pro-
vides a correctness of application of the generalized model in ap-
plied problems of mathematical modelling of studied processes
(devices). Proofs of the formulated theorems are strict, logically
true and are consistently executed within terms of the functional
analysis. Practical applicability of theorems of existence and
uniqueness of the decision as component of the qualitative analy-
sis, is defined by possibility of research on their basis of adequacy
of algorithmic means of mathematical modelling of a studied class
of processes (devices).
Key words: mathematical model, synthesis of the mathemati-
cal description, system of the equations in private derivatives,
theorems of existence and uniqueness of the decision.
1. Introduction.
Solving the mathematical modelling problems are primarily and largely
determined by the selected mathematical model (MM ) of the object (or proc-
ess). Adequately chosen MM provides the reliability of mathematical model-
ling. In addition, the results of mathematical modelling (in particular, its accu-
racy) is affected by numerical methods that implement the selected MM object
(process). Therefore, the development of MM that meets the criteria, will im-
prove the effectiveness of the workflow.
2. The research purpose and problem formulation.
The purpose of this paper is carring out a qualitative analysis (state-
ment and proof of existence and uniqueness theorems) of generalized MM
processes and apparatuses of primary processing of raw hydrocarbons pre-
sented in the form of a system of partial differential equations (PDEs).
© S. A. Polozhaenko, 2013
Математичне та комп’ютерне моделювання
100
To achieve this goal in this paper the problem of determining the
conditions and scope of constraint region (CR) of PDE is solved with ap-
propriate initial (IC) and the boundary conditions (BC), that is summarized
formalizes the dynamics of a class of processes and machines of primary
processing of crude hydrocarbons.
3. Main part.
In modern industrial technologies during the initial processing of
crude hydrocarbons (oil in particular) are applied processes such as desali-
nation, dehydration and primary topping, with the first two processes are
implemented under the scheme Built-in (thermal) desalting and dehydra-
tion [1]. By going on physico-chemical phenomena of technological de-
vices that provide these processes can be categorized as follows:
surface heat exchange machines in which heat exchange is performed
at an interface specific reagents (phases). To this class of devices in-
clude, among others: recycling heat exchangers, heat exchangers of
kerosene fraction, heat exchangers of diesel fraction, heat exchangers
of weighted diesel fraction;
volumetric heat exchange machines, in which heat exchange is per-
formed within the total volume of the reactants involved. This class in-
cludes such devices: termodegidratory, electric dehydrators and mixers
dispersed heat exchange machines, in which heat exchange is carried
out on several individual surfaces. To this class of devices include, for
example: column prior topping kerosene fraction, a column of the die-
sel fraction.
For each of the above classes of processes (devices) of primary proc-
essing of crude hydrocarbons (PPCH) MM developed in the form of a
parabolic or hyperbolic PDE with the appropriate initial and boundary
conditions [2; 3]. Analyzing MM considered an PPCH of devices has been
identified the possibility of a generalized mathematical description that, in
the future, involves unifying and typing approaches to computational and
numerical implementation.
In this case, the generalized MM processes (machines) PPCH was
formulated in the following way:
ftzrA
t
tzr
,,
,,
, (1)
kMRzr , ; ktt ,0 ; dtzr ,, ,
zrzrtzr
t
,,,,, 00
, (2)
0,,
tzr , (3)
Серія: Технічні науки. Випуск 9
101
where tzr ,, ― unknown function, for which the vector space coordi-
nates zrg , is defined on the open space with the boundary ,
which belongs to the space kMR . For fixed 0kt shall consider the dy-
namics of the system (1)–(3) in a time interval kt,0 , which is a cylinder
height ktQ ,0 with the limit kt,0 . The operator A ― is
hyperbolic (or parabolic-hyperbolic). If the statement A contains a para-
bolic component, we assume that the operator A can be unsymmetrical
and time-invariant second order operator. The function f is the external
excitation of the system.
As noted earlier, the study of technological devices PPCH processes
are characterized by a complex mathematical formulation. Therefore, un-
der these conditions, it is necessary to investigate the resulting generalized
MM class of considered devices regarding to the inaccuracies of the meth-
odological and computational nature. This kind of impropriety may arise
in connection with a certain level of formalization, both on stage produc-
tions, as well as numerical solutions of the problem 4]. Considering the
above, we carry out a qualitative analysis of the generalized MM processes
(units) PPCH, the purpose of which is to investigate the existence and
uniqueness of solutions of dynamical equations of the form (1) with initial
and boundary conditions of the form (2), (3).
As noted above, the objectives of the study of technological devices
MSRP processes are characterized by a complex mathematical formula-
tion. Therefore, under these conditions, the resulting generalized MM class
of devices considered is necessary to investigate regarding the inaccura-
cies of the methodological and computational nature. This kind of impro-
priety may arise in connection with a certain level of formalization, both
on the stage of setting as well as the numerical solution of the problem [4].
Considering the above, we carry out a qualitative analysis of the general-
ized MM processes (units) MSRP, the purpose of which is to investigate
the existence and uniqueness of solutions in dynamical equations of the
form (1) with initial and boundary conditions of the form (2), (3).
In [5–7], we have investigated the existence, uniqueness and control
systems similar to (1)–(3). However, these studies were performed without
constraints on the phase coordinates and control variables, that is inherent
in the physical processes that occur in devices MSRP [8]. In this regard,
we formulate and prove the following theorem.
Theorem 1. For the system (1)–(3) are given functions 0 , d and
f , where:
Математичне та комп’ютерне моделювання
102
QLf 2 , (4)
0,1
00 pLH p , (5)
QLd
2 . (6)
Then there is a function tg , , which satisfies the following
conditions:
p
k LHtL 1
0;,0 , (7)
p
k LHtL
t
1
0;,0 , (8)
gg 00, , (9)
dtg , . (10)
In proving the theorem 1, we use the following sequence:
Construct an «approximate» solutions;
For the «approximate» solutions define a priori estimates;
Go to the limit, based on the compactness property (this is necessary
for the transition to the limit in nonlinear terms).
Proving of theorem 1.
1. Construction of the «approximate» solutions. To construct the
«approximate» solutions use Faedo-Galerkin method [7; 8]. Consider a
sequence m ...,,, 21 , which has the following properties:
0,,1
0 piLH p
i ,
where m ...,,, 21 ― linearly independent m .
It is obvious that the linear combination 0, ii ― are compact
[9] in pLH 1
0 . We look for «approximate» solutions tmm ,
...,2,1m in the form of
i
m
i
im tqt
1
,
where the functions tqi are selected so as to satisfy the relation
mjtfta
t
td
jjmj
m
1,,,, , (11)
where
pLHjmjm tAta
1
0
,, .
The system (11) of non-linear ordinary differential equations is sup-
plemented by initial and boundary conditions
Серія: Технічні науки. Випуск 9
103
mm 00 ;
mLH p
i
m
i
imm
,в 1
00
1
0 . (12)
2. Finding a priori estimates. To do this, multiply each equation (11),
which corresponds to an index j , on tqi and sum by j . Then we get
ttfttat
dt
td
mmmm
m
,,, ,
i.e.
ttfttat
dt
d
mmmm ,,
2
1 2
. (13)
We set: vvav , (that is the norm in 1
0H is equivalent to the
norm 1H
v ). According to (13) we write
dtttfttt
kt
mmmmm
0
222
,22 . (14)
From (12) it follows that the right-hand side of (14) does not exceed
the dtttfC
kt
m
0
,2 (the constant C doesn’t depend on m ). Then
we can write
dtttfCtt
k
m
t
mmmm
0
2
0
22
,22 . (15)
Due to (14) we get const
0
dttf
kt
.
From (15) it follows that 22
mom Ct .
The last expression implies that
const tm , (16)
(where this constant doesn’t depend on m ).
Returning to (15) we obtain
const tm , (17)
(As in the previous case, to express (16) the given constant also depends
on the index m ).
It follows that Ttk , and from inequalities(16) and (17) we get that
for m the values m ― are limited, that is, belong to a limited set in
Математичне та комп’ютерне моделювання
104
p
k LHtL 1
0;,0 .
3. Going to the limit. In accordance with the Dunford-Pettis theorem
[10], the space p
k LHtL 1
0;,0 (accordingly 2;,0 LtL k is
adjoint to p
k LHtL 1
0
1 ;,0 (and accordingly to 21 ;,0 LtL k , and
therefore, from sequency m possible to extract sequency , that
d weakly in p
k LHtL 1
0;,0 , (18)
that is
p
k
t
m
t
LHtLqdttqtdttqt
kk
1
0
1
00
;,0,,, . (19)
Furthermore, from (16), in particular, follows, that values m are
limited in, which implies that the sequence m belongs to a limited set in
1
0H .
However, known that enclosures 1
0H in 2L are compact (Rel-
lich-Kondrashov theorem [7]). Thus, we can assume that the sequence
, that is chosen from the sequence m , is satisfies condition
d strong in 2L and almost everywhere addition to (18) and (19).
We pass to limit (11) considering that m . Let j is fixid and
j . Then, by (11) we have
jtfta
t
td
jjj 1,,,, , (20)
However, by (19)
jj aa ,, d weakly in ktL ,0
and, thus
j
d
j dt
d
dt
td
,, ktD ,0 .
From (20) we can obtain that
jjdj
d tfa
t
d ,,,
,
And this is true for any fixed j . This, taking into account the density
of the basis, this implies that
pLHtfa
t
d 1
0d
d ,,,, .
Серія: Технічні науки. Випуск 9
105
As previously was assumed dtg , , it can be concluded that
the conditions of existence are obtained.
Thus, due to the proof of theorem 1 we obtain conditions for the exis-
tence of solutions of equation (1) with initial data (2) and boundary (3)
conditions. It is not known whether these results provide a unique solution.
Let us prove it. MM represent generalized as such (without losing never-
theless the loss of generality):
tMftMA
t
tM
,,
,
, (21)
kMRM ; ktt ,0 ; dtM , ;
MtM
Mt
,, 00
; (22)
0,
tM , (23)
where M ― randomly taken point, the coordinates of which satisfy the
state vector of the system.
Then the following theorem is true.
Theorem 2. The problem's solution (21)–(23), which is continuous
in the closed region Q with the boundary of by variable ktt ,0 , and,
moreover, by the coordinates of the point M ― is single.
Proof of theorem 2. Let us tM ,1 и tM ,2 ― is the two solu-
tions, which satisfy conditions of theorem 2, and 21 . Show that
0, tM in region Q will satisfy the proof of an uniqueness of the so-
lution (1)–(3).
For proof of theorem 2 we will use the first Green's formula [11] for
function 21 . The result is (assuming that operator A ― hyperbolic)
1 2 1 2
1 2
1 2 1 2 1 2 ,
Q Q
Q Q
A d A d
d d d
(24)
where functions 0 M ; 0 M are continuous in the region
Q . For the problem of the form (21)–(23) Green's formula looks
QQQ
dddA 2121 . (25)
Obviously that function 21 is a solution of the homogeneous
problem
Математичне та комп’ютерне моделювання
106
tMA
t
tM
,
,
, (26)
0,
0
t
tM , 0,
M
tM . (27)
Seeing tA , then from (25) we obtain
QQQ
ddd
t
. (28)
Integrating the identity (28) in the time variable t in the interval
kt,0 and using the identity 00, M , obtain
kk t
Q
k
t
Q
k
Q
k dtdtMdtdtMdtM
00
,,, . (29)
Since the right-hand side of (28) is nonpositive, and the left side — a
non-negative, then
0,
Q
k dtM .
It follows the function , 0kM t for arbitrary 0kt . Thus, theo-
rem 2 is proved.
4. Conclusion.
For the class of processes and devices of primary processing of crude
hydrocarbons, the generalized mathematical model in the form of partial
differential equations, characterized by the presence of restrictions on the
state functions and control variables. Given these characteristics of the
generalized MM, the qualitative study is carried out, which resulted in the
theorem proving the existence and uniqueness of solutions of equations
defining the generalized MM.
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Сформульовано і доведено теореми існування та єдиності розв’язків
систем рівнянь з частинними похідними, які становлять собою узагальне-
ну математичну модель процесів і апаратів первинної переробки сирих
вуглеводнів. Узагальнення дає змогу застосувати принцип уніфікації та
типізації щодо розробки методу чисельної реалізації математичних моде-
лей класу процесів (апаратів) первинної переробки сирих вуглеводнів, а
доведення відповідних теорем (суть ― якісний аналіз) забезпечує корек-
тність застосування узагальненої моделі в прикладних задачах математи-
чного моделювання досліджуваних процесів (апаратів).
Ключові слова: математична модель, узагальнений математич-
ний опис, системи рівнянь з частинними похідними, теореми існуван-
ня та єдиності розв’язків.
Отримано: 19.11.2013
UDC 004.942
V. A. Fedorchuk, Dr. of Technical Sciences, Professor,
O. I. Mahovych, postgraduate student
Kamianets-Podilsky National Ivan Ohienko University,
Kamianets-Podilsky
CREATING A COMPUTER MODEL FOR THE DIAGNOSTIC
SYSTEM OF DIESEL GENERATOR
Mathematical model of a diesel generator, which includes an
integral operator, is considered. Investigated the stability of the
computational algorithm.
Key words: diesel generator, integral model, the stability of
numerical implementation.
Introduction. When you are using a diesel generator for energy sup-
ply of the uninterrupted technological processes an important task is to
ensure reliable operation of the diesel engine. One way to improve the
© V. A. Fedorchuk, O. I. Mahovych, 2013
80-84.pdf
А. Я. Бомба*, д-р техн. наук, професор,
Ю. В. Турбал**, канд. фіз.-мат. наук
*Рівненський державний гуманітарний університет, м. Рівне,
**Національний університет водного господарства та природокористування, м. Рівне
математичне моделювання ПРОЦЕСУ РУХУ солітона в анізотропноМУ пружноМУ тілІ змінної густини
Ключові слова: анізотропія, рівняння руху, солітон, закон Гука, рівняння в частинних похідних.
Список використаних джерел:
Key words: anisotropy, crystal system, the motion equations, solitary wave, Hooke's law.
А. А. Верлань, канд. техн. наук
Национальный технический университет Украины «КПИ», г. Киев.
ОБ ОРГАНИЗАЦИИ СТРУКТУРЫ ИСТОЧНИКОВ ЭЛЕКТРОПИТАНИЯ С ЗАЩИТОЙ И АВТОМАТИЗИРОВАННОЙ СИСТЕМОЙ КОНТРОЛЯ
Ключевые слова: автоматизированные системы контроля, вторичного источника электропитания.
Список использованной литературы:
Key words: automated control systems, secondary power supply.
Д. А. Верлань*, аспірант,
К. С. Чевська**, асистент
*Київський національний університет імені Тараса Шевченка, м. Київ,
**Кам’янець-Подільський національний університет імені Івана Огієнка, м. Кам’янець-Подільський
ОЦІНКА ПОХИБОК РОЗВ’ЯЗАННЯ ІНТЕГРАЛЬНИХ РІВНЯНЬ ВОЛЬТЕРРИ ІІ РОДУ ЗАСОБАМИ ІНТЕГРАЛЬНИХ НЕРІВНОСТЕЙ
Ключові слова: інтегральні рівняння, інтегральні нерівності.
Список використаних джерел:
Key words: integral equations, integral inequalities.
А. П. Власюк*, д-р техн. наук, професор,
Т. А. Дроздовський**, аспірант
Математичне моделювання зміни напружено-деформованого стану ґрунтового масиву при нагнітанні в нього в’яжучого розчину в одновимірній постановці
Ключові слова: математична модель, напружено-деформований стан, вільна межа, числовий розв’язок, метод скінченних різниць, в’яжучий розчин, нагнітання.
1. Постановка задачі
2. Математична модель задачі
3. Розв’язок задачі
3.1. Розв’язок задачі нагнітання
3.2. Розв’язок задачі НДС
3.2.1. Аналітичний розв’язок задачі
Розв’язок задачі (16), (17) має вигляд
3.2.2. Числовий розв’язок задачі
4. Результати числових експериментів
Висновки
Key words: mathematical model, stress strain state, free boundary, numerical solution, finite difference method, binding fluid, injecting.
А. П. Громик*, канд. техн. наук,
І. М. Конет**, д-р фіз.-мат. наук, професор
* Подільський державний аграрно-технічний університет, м. Кам’янець-Подільський,
**Кам’янець-Подільський національний університет імені Івана Огієнка, м. Кам’янець-Подільський
МОДЕЛЮВАННЯ КОЛИВНИХ ПРОЦЕСІВ У НАПІВОБМЕЖЕНОМУ Кусково-одноріднОМУ КЛИНОВИДНОМУ ПОРОЖНИСТОМУ ЦИЛІНДРІ
Ключові слова: моделювання, коливний процес, гіперболічне рівняння, початкові та крайові умови, умови спряження, інтегральне перетворення, функція впливу, функція Гріна.
Список використаних джерел:
Key words: modelling, oscillating, hyperbolic equation, initial and boundary conditions, conditions of conjugation, integral transformation, the influence function, Green's function.
O. A. Diachuk*, Ph. D. of Technical Sciences,
N. L. Kostyan**, Senior Teacher,
A. A. Sytnik***, Ph. D. of Technical Sciences,
F. A. Halmuhametova****, Senior Teacher
*Institute for Economics and Forecasting UNAS, Kyiv,
**Kyiv National University of Technologies and Design, Kyiv,
***Cherkassy state technological university, Cherkassy, Ukraine,
****Tashkent State Technical University, Tashkent
The method and algorithms for identification of dynamic objects on basis of integral equations
Key words: dynamic objects, models, identification algorithms, Volterra integral equations, automatic control systems.
References:
Ключові слова: динамічні об'єкти, моделі, алгоритми ідентифікації, інтегральні рівняння Вольтерра, автоматичні системи управління.
М. М. Каримов*, д-р техн. наук, профессор,
Ю. О. Фуртат**, аспирант,
С. М. Сагатова*, студент
*Ташкентский государственный технический университет, г. Ташкент, Узбекистан,
**Институт проблем моделирования в энергетике им. Г. Е. Пухова НАН Украины, г. Киев
ИСПОЛЬЗОВАНИЕ МОДЕЛИ УЧАЩЕГОСЯ В СИСТЕМАХ ОБУЧЕНИЯ НА ОСНОВЕ ТЕСТОВ
Ключевые слова: модель учащегося, дистрактор, машинный тьютор, эротематический диалог.
Список использованной литературы:
Key words: student model, distractor, machine tutor, erotematic dialog.
В. П. Марценюк, д-р техн. наук, професор,
З. В. Майхрук, асистент
Тернопільський державний медичний університет імені Івана Яковича Горбачевського, м. Тернопіль
Побудова оптимального керування біфуркацією в моделі Ходжкіна-Хакслі на основі принципу максимуму
Ключові слова: модель Ходжкіна-Хакслі, оптимальне керування, принцип максимуму.
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| id | nasplib_isofts_kiev_ua-123456789-86404 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 2308-5916 |
| language | English |
| last_indexed | 2025-12-07T16:12:56Z |
| publishDate | 2013 |
| publisher | Інститут кібернетики ім. В.М. Глушкова НАН України |
| record_format | dspace |
| spelling | Polozhaenko, S.A. 2015-09-16T17:57:00Z 2015-09-16T17:57:00Z 2013 The qualitative analysis of mathematical models of processes and devices of the crude hydrocarbons preprocessing on the basis of the models general concept / S.A. Polozhaenko // Математичне та комп'ютерне моделювання. Серія: Технічні науки: зб. наук. пр. — Кам’янець-Подільський: Кам'янець-Подільськ. нац. ун-т, 2013. — Вип. 9. — С. 99-107. — Бібліогр.: 11 назв. — англ. 2308-5916 https://nasplib.isofts.kiev.ua/handle/123456789/86404 004.942 Theorems of existence and uniqueness of the decision of system of the equations in the private derivatives, representing the generalized mathematical model of processes and devices of preprocessing of crude hydrocarbons are formulated and proved. Generalization gives the chance to apply the principle of unification and typification when developing a method of numerical realization of mathematical models of a class of processes (devices) of preprocessing of crude hydrocarbons, and the proof of the corresponding theorems (an essence ― the qualitative analysis) provides a correctness of application of the generalized model in applied problems of mathematical modelling of studied processes (devices). Proofs of the formulated theorems are strict, logically true and are consistently executed within terms of the functional analysis. Practical applicability of theorems of existence and uniqueness of the decision as component of the qualitative analysis, is defined by possibility of research on their basis of adequacy of algorithmic means of mathematical modelling of a studied class of processes (devices). Сформульовано і доведено теореми існування та єдиності розв’язків систем рівнянь з частинними похідними, які становлять собою узагальнену математичну модель процесів і апаратів первинної переробки сирих вуглеводнів. Узагальнення дає змогу застосувати принцип уніфікації та типізації щодо розробки методу чисельної реалізації математичних моделей класу процесів (апаратів) первинної переробки сирих вуглеводнів, а доведення відповідних теорем (суть ― якісний аналіз) забезпечує коректність застосування узагальненої моделі в прикладних задачах математичного моделювання досліджуваних процесів (апаратів). en Інститут кібернетики ім. В.М. Глушкова НАН України Математичне та комп'ютерне моделювання. Серія: Технічні науки The qualitative analysis of mathematical models of processes and devices of the crude hydrocarbons preprocessing on the basis of the models general concept Article published earlier |
| spellingShingle | The qualitative analysis of mathematical models of processes and devices of the crude hydrocarbons preprocessing on the basis of the models general concept Polozhaenko, S.A. |
| title | The qualitative analysis of mathematical models of processes and devices of the crude hydrocarbons preprocessing on the basis of the models general concept |
| title_full | The qualitative analysis of mathematical models of processes and devices of the crude hydrocarbons preprocessing on the basis of the models general concept |
| title_fullStr | The qualitative analysis of mathematical models of processes and devices of the crude hydrocarbons preprocessing on the basis of the models general concept |
| title_full_unstemmed | The qualitative analysis of mathematical models of processes and devices of the crude hydrocarbons preprocessing on the basis of the models general concept |
| title_short | The qualitative analysis of mathematical models of processes and devices of the crude hydrocarbons preprocessing on the basis of the models general concept |
| title_sort | qualitative analysis of mathematical models of processes and devices of the crude hydrocarbons preprocessing on the basis of the models general concept |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/86404 |
| work_keys_str_mv | AT polozhaenkosa thequalitativeanalysisofmathematicalmodelsofprocessesanddevicesofthecrudehydrocarbonspreprocessingonthebasisofthemodelsgeneralconcept AT polozhaenkosa qualitativeanalysisofmathematicalmodelsofprocessesanddevicesofthecrudehydrocarbonspreprocessingonthebasisofthemodelsgeneralconcept |