Justification of conclusions and proposals. Topic: reliability and practical significance of scientific results


Traditionally, scientific knowledge has been defined as reliable knowledge. Such knowledge must have an unshakable justification. But what is the rationale for this? This problem it is all the more important that scientific research as such is the process of developing new scientific knowledge, one of the types cognitive activity. Necessary component research is the analysis and synthesis of the results obtained. Correct interpretations and justification of research results allow us to correctly formulate new facts and laws, verify the correctness of initial hypotheses, etc.

In development scientific research can be distinguished two interconnected process: On the one side, search and discovery of new truths in science, on the other hand, their justification. The contrast between these contexts arose after science moved from the accumulation, systematization and generalization of factual material to its theoretical analysis and explanation. Previously, natural science was limited to establishing the simplest patterns in nature and the discovery of empirical laws; later, to explain them, it was necessary to move on to the discovery of more essential and universal theoretical laws. Empirical laws can be discovered through observation and experimentation using the methods of induction. However, with the help of such procedures it is impossible to discover theoretical laws, because they are laws about unobservable objects and therefore do not contain empirical concepts. The practice of scientific research has convincingly demonstrated the correctness of this thesis. In this regard, there is a radical revision of previous ideas about the process of scientific research and criticism begins of the possibility of the existence of a special logic of discovery and the question of ways and methods of substantiating scientific knowledge is proletarianized.

Rationale is a procedure for presenting certain convincing arguments or arguments by virtue of which any statement or concept should be accepted as true. Justification usually includes a whole series of mental actions relating not only to the position under consideration, but also to that system of statements, that theory, constituent element which it is.

Highlight general and comparative rationale.

General scheme or structure, the absolute justification is as follows: "A must be accepted by virtue of C", where A is the position being justified and C is the justification. Structure of comparative reasoning: “It is better to accept A than B because of C.” for example, the statement “We must accept that the sky is in normal conditions blue, since direct observation speaks in favor of it, is an absolute justification. The expression “It is better to accept that the sky is blue than to accept that it is red, based on the principles of atmospheric physics” is a comparative justification for the same statement “The sky is blue.” Comparative justification is sometimes also called rationalization: in conditions where absolute justification is unattainable, comparative justification represents a significant step forward in improving knowledge, in bringing it closer to the standards of rationality. It is obvious that comparative justification is not reducible to absolute justification.

In general, there are two main and most general strategies justification knowledge. Unlike fallibizism, which substantiates knowledge by refutation, conventionalism(Latin conventio - agreement) believes that the basis scientific theories arbitrary agreements (conventions) lie and their choice is regulated by considerations of convenience, simplicity, usefulness, and so on - criteria not related to the concepts of the theory itself. The founder of conventionalism is J.A. Poincaré - characterized the axiom systems of various mathematical theories as agreements that are outside the field of truth or falsity. The preference of one system of axioms over another is due to the principle of convenience. Poincaré considered the postulates of geometry as useful agreements, emphasizing that, along with such agreements, there are also useless agreements.

Let us consider in more detail the most important methods used to substantiate acquired knowledge - proof, refutation, confirmation, explanation, interpretation, justification.

Proof- a logical procedure in which an expression with unknown meanings is derived from statements whose truth has already been established. The structure of the proof: thesis (this is an expression whose truth is established), arguments (statements with the help of which the truth of the thesis is established), additional assumptions (additional expressions that are used in the course of evidence), demonstration. Example: proof of the theorem. Proof can be: direct (the thesis follows from the evidence found), indirect (they go in a roundabout way, using false statements), apagogical (proof by contradiction), disjunctive (truth is established by eliminating all contradictions).

Refutation– establishes the falsity of the thesis. There are two varieties:

By evidence of antithesis(first the antithesis is formulated, i.e. a statement opposite to the thesis, and then the truth of the antithesis is established).

- establishing the falsity of the investigation, arising from the thesis (an assumption about the truth of the thesis, from which a corollary is drawn, and then the falsity of the corollary is proven) - this is called reduction to absurdity.

With the help of refutation, a negative result is achieved. But it wears positive character: Narrows the search for the true position.

Confirmation- This is another type of justification. Playing special role in the presence of hypotheses (positions whose truth needs to be proven). Confirmation and proof differ in that when proving, the complete truth of the expression being proven is established, and when confirming theoretical positions, only partial truth is established. It is also important that what is being confirmed and what is being confirmed are at the same level of cognition. This method is not suitable if theoretical principles are confirmed by empirical data, because different levels knowledge.

If confirmation serves to strengthen a certain thesis in terms of its truth, then objection aimed at weakening it. Objections are divided into direct (the shortcomings of the thesis are revealed through its consideration) and indirect (directed not against the thesis itself, but against the arguments given in support of it).

Explanation– another method of substantiating research results. Explanations are divided into object-based (i.e., revealing the essential characteristics of a phenomenon; for example, the explanation will be the answer to the question of why a magnetic field is formed around a conductor) and subjective (the activity of the subject is taken into account). Subjective explanation takes into account that the same fact can receive different explanations depending on historical context, activities, conditions, etc.

Interpretation- attributing some meaningful meaning or meaning to the symbols and formulas of a formal system. As a result, the formal system turns into a language that describes a particular subject area. Classic example interpretation can be served by finding a model (a fragment of reality), the properties of which were described by Lobachevsky’s geometry. It took a lot of time to find a field of activity in which this theory could be applied (surfaces of negative curvature).

Justification– the term is applied in relation to some practical action(practical or mental). To justify an action means to bring some value consideration in its favor, i.e. a statement about what we should strive for, what is our duty, preference, ideal. Justification, as a rule, or rather arguments are accompanied by the words “good”, “bad”, “equal”, “obligatory”. The lack of justification makes any statement unfounded and, as a rule, represents an empty, declarative attempt to create the impression of meaningfulness, content and scientific character of the proposed concept.


TOPIC 4. RELIABILITY AND PRACTICAL SIGNIFICANCE OF SCIENTIFIC RESULTS

4.1. Assurance Guidelines scientific results

Reliability is the second “pillar” on which a scientific result is based. Let us highlight in the Regulations of the Higher Attestation Commission those places that contain reliability requirements. Paragraph 32 states: “New ways to solve problems proposed by the author must be strictly reasoned and practically evaluated in comparison with known solutions...”. In paragraph 66, where we're talking about O public protection, it is indicated that “At the same time, the reliability and the validity of all conclusions and recommendations of a scientific and practical nature contained in the dissertation"(emphasis added by the authors). Even 20 years ago the need was pointed out “during the examination of dissertations Special attention pay attention to the reliability of the applicant’s conclusions, results and recommendations contained in his work" .

In the “Regulations of the Higher Attestation Commission of Ukraine” the term “reliability” is not used. Instead, it speaks of “the scientific validity of the results...” (paragraph 13). But in the “Regulations on the Specialized Council” the official opponent is obliged (clause 3.6) to establish in his review “the degree of validity of scientific positions, conclusions and recommendations formulated in the dissertation, their reliability and novelty...”. Thus, reliability is not the degree of scientific validity of the result. How to separate these concepts?

Credibility, i.e. sufficient fidelity, this is proof that the named result (law, pattern, set of facts, possibility, etc.) is fulfilled Always for a named class of objects under named conditions.

Validity scientific result is the presence of convincing evidence of its reliability.

^ 4.2. Methods for proving reliability

As an example, let's see whether some of the provisions given in Lecture 3 meet the reliability requirement. Let's take Ohm's law. From life experience we know that for a homogeneous electrical circuit always I = U/R, while the 20/80 principle is questionable. We are not sure of its reliability.

How is authenticity confirmed? Verification! Verification (from lat. erus– true and facio- I do) is the repeatability of the result under the same conditions with many checks on many objects. In many cases it is necessary to check for test cases, i.e. when limited conditions. Although practice is indeed the best criterion of truth, it is not always possible to check a scientific result for accuracy using the verification method. This method is mainly suitable for physical and chemical phenomena. For example, why do scientists still not recognize the phenomena of telepathy, clairvoyance, and telekinesis as objectively existing? Because, as noted in his book “Parapsychology” by Prof. C. Hanzel, none of the parapsychological phenomena described in the literature meets the requirement of reproducibility, that is, repeatability of the result under the same conditions.

What are the methods for proving authenticity? They can be combined into three groups:


  • analytical;

  • experimental;

  • confirmation by practice.
Analytical methods the most “powerful”. Their essence is proof of a result (theorem, formula, law) through mathematical transformations. Methods are used when the applicant manages to construct mathematical model the phenomenon under study, for example, describe the flow of liquid, heating of a body, change in strength, market mechanism, conflict in a group, etc. Let us give an interesting example of analytical proof of the reliability of a speculative conclusion. In 1968, Dr. Benjamin Spock, one of the organizers of the movement against the Vietnam War, was summoned to district court Boston, where he was charged with conducting illegal activities, preventing the implementation of the law on military service in practice. Spock's lawyers questioned the fairness of the procedure used to determine the jury because there were no women among the jurors. The latter was of no small importance, since worldwide famous book Spoke about caring for babies is on the table for millions of mothers. The question was whether it was by chance that the jury consisted of only men, or whether the reason lay in deliberate discrimination against women.

Let's first get acquainted with the jury selection procedure. This procedure consists of three stages. In the first step, the court clerk randomly selects the names of 300 potential jurors. At the second stage, about 30 people are again selected at random from these 300, and summonses are issued to them. Before the trial begins, 12 people are selected from among them, who perform the corresponding functions. The question arose, is it a reliable coincidence that all 12 people were men? To prove unreliability, samples of the jury pools in the Spock case and in other cases were statistically processed. It is interesting that the proportion of women in the population of Boston is slightly higher than the proportion of men. Therefore, we have the right to expect at least 150 women at the first stage. Calculations showed that the chances of getting a sample of 12 jurors at the third stage from only men with a random selection from the population of Boston are astronomically small - 1 in 10 18 (for comparison: there are 5  10 9 people living on Earth).

The essence experimental methods verification of reliability consists in reproducing the phenomenon under study on a physical, digital or analogue model and comparing theoretical and experimental results. In this case, the question of errors always arises, taking into account real conditions and number of experiments.

Upon confirmation scientific result practice it is necessary for the provisions derived in theory to coincide with the phenomena observed in practical situations. For example, if the active operator model implies that when preparing machine media the number of errors and the processing time of a given amount of information are correlated and jointly distributed according to the normal law, then in the practice of the computer center for data preparation operators, the specified parameters (the number of errors and processing time) must always be jointly distributed according to the normal law.

The reliability and validity of scientific research results are ensured by:


  • taking into account a representative number of factors influencing the solution of a scientific problem;

  • using initial data obtained from practice, as well as on semi-natural models and proven mathematical (or physical) models;

  • a well-founded choice of basic assumptions and limitations accepted as initial ones when formulating the formulation of scientific problems;

  • the use of modern, proven scientific and methodological (mathematical) apparatus, the correct choice of general and specific indicators and criteria used, as well as the mathematical models used and developed;

  • combination theoretical research with a large amount of experimental research.
Reliability and validity are confirmed by:

  • results of mathematical and (or) physical modeling, data from laboratory experiments, full-scale (semi-natural) tests;

  • high convergence of theoretically (analytically) obtained results with experimental data, as well as with the results of full-scale tests and (or) practical implementation;

  • convergence of modeling results with available experimental data;

  • obtaining from newly developed general scientific principles (conclusions, recommendations, models, dependencies, etc.) widely known private scientific results;

  • results of experimental design developments, experience in the practical implementation of proposals;

  • results of tests (military, testing grounds, government, etc.) of the proposed technical and organizational solutions;

  • the fact that the results obtained have a clear physical interpretation and do not contradict known (published) data.
^ 4.4. What can be implemented?

You can implement all theoretical and practical results, which may have independent meaning. The subject of implementation can be a model, method, method, technology, algorithm, program, methodology, business game, etc. This, as they say, in general case. And for each specialty it is advisable to think in advance possible forms use of the dissertation results. For example, the results of a dissertation in the specialty 05.13.06 " Automated systems management and progressive information Technology» can be used as:


  • research tool current system production management;

  • method (technique) for designing functional or supporting parts of an automated control system;

  • block (element) of the functional part of the automated control system;

  • functional block of the supporting part of the automated control system;

  • fragment of CAD ACS;

  • element of regulatory and methodological support at any level (enterprise standard, RTM, OST, etc.);

  • basics of university lecture courses and IPK;

  • material for practical classes, laboratory work, educational business games, coursework and diploma design.
I will give other examples of the implementation of the results of dissertations in the specialty 05.01.04 “Ergonomics”.

S. M. Andreev, based on the results of his master’s thesis on the topic “Assessing the level of vocational training flight personnel during initial training" (Kharkov, 1999) introduced:


  • mathematical model of cadet learning, which displays gradual qualitative changes And mutual influence in the totality of knowledge, skills and abilities of the pilot, on the one hand, and training tools, on the other hand;

  • regression model of a parameter characterizing a cadet’s ability to learn depending on a number of factors;

  • diagram of decision-making on the advisability of training a cadet in flight training profiles.
Yashchun T.V., based on the results of his candidate’s dissertation on the topic “Assessing the quality of educational and cognitive activities in the student-computer system” (Kharkov, 2000), introduced:

  • qualimetric multifactorial regression self-organizing model of student interaction with the learning environment based on the method of group accounting of arguments;

  • technology mental self-regulation student of his educational and cognitive activities while studying the fundamentals of computer science.
Migal G.V., based on the results of her candidate’s dissertation on the topic “Development of a method for identifying the state of fatigue of the operator of the “man - technology - environment” system” (Kharkov, 2000), introduced:

  • differential measuring probes – electrodes and multifunctional sensors for precise definition location of biologically active points of the skin and measurement of their new parameters;

  • evolutionary-entropy model of information and energy exchange in the human body;

  • a method for express diagnostics of operator fatigue, which does not require the operator to be taken away from work.
These various examples are given here in order to show the applicant the truly limitless possibilities of implementing the results of dissertations.

^ 4.5. Signs of practical significance of a PhD thesis

The USSR Higher Attestation Commission discussed the issue of formal signs practical significance of candidate's dissertations. A generally accepted list of such signs has not yet been developed either then or now, but for certain groups of specialties expert advice developed requirements. Thus, for agro-industrial specialties, the following were considered signs of practical significance of Ph.D. dissertations in the USSR:

A) practical use research results at at least one enterprise (farm, plant, factory), confirmed by an appropriate document indicating the achieved effectiveness;

B) solution competent authority(headquarters of the ministry, regional agro-industrial association) on the completeness of the research and further practical use of its results;

C) inclusion of research materials in government and industry standards, in the design and development plan, their use in design and design work, confirmed by relevant documents;

D) approved in in the prescribed manner normative and technical documentation, in the development of which the applicant took part either as an executor or as a responsible executor;

D) engineering calculation method approved by the lead design or research organization;

E) methodological development, carried out based on research results and approved by the scientific council of this institute;

G) decision of the scientific and technical council of the ministry (state committee, departments of academies of sciences) on the significance of research results for science, technology, production and on ways of practical use of the work performed, o further development research in this direction;

H) a reasoned conclusion of a specialized council that published works and copyright certificates for inventions and discoveries should be considered the implementation of research results with an assessment of their significance for science and technology.

^ 4.7. Implementation of research results. Acts of implementation

4.7.1. Signs of implementation. One of complex issues The question is what is considered the implementation of research work. The signs of implementation are to some extent close to the signs of the practical significance of dissertations, but one should always remember: implementation is primary, and practical significance is secondary. Section 4.4 talked about the variety of subjects for implementing dissertation results. But these items are, as it were, an intermediate product, and the national economy is interested in the final product: new equipment, technology, materials. In relation to new technology in one of regulatory documents it is clearly stated that research work is considered implemented if its results are used in the development of:


  • samples new technology, prospects for their development, recommendations for design;

  • Technical specifications for the creation of new and modernization of existing samples;

  • Terms of reference for carrying out new R&D, as well as new promising fundamental and exploratory research;

  • test methods and criteria for evaluating samples and complexes of new equipment, documentation for the manufacture of instruments and equipment;

  • information releases, manuals, reference books, manuals, manuals, instructions and other documents for new technology.

^ 4.7.2. Organizational forms of implementation. In paragraph 33 of the Regulations of the Higher Attestation Commission it was said: “ The dissertation (or appendices to it) must provide information confirming the implementation or practical use in the national economy of the scientific results obtained by the author, or considerations for the specific implementation and use of scientific findings».

In chapter " Practical significance results obtained" of the document "Basic requirements for dissertations and abstracts" says:

"It is necessary to give brief information on the implementation of the research results, indicating the names of the organizations in which the implementation was carried out, forms of implementation and details of reporting documents".

Implementation of research results – mandatory requirement for all dissertations, and the results of implementation should be fully reflected in the texts of the dissertation and abstract. In order for this to be done, implementation must be carried out within the framework of generally accepted organizational forms. Experience shows that two schemes for implementing scientific results are used. The traditional way is through ministries, departments and their parent enterprises, and a shorter and more effective way, in which direct access to interested enterprises is carried out during a theoretical search. Subsequent work is being carried out with these enterprises.

Most perfect form organizing implementation work - concluding an agreement for the transfer of scientific and technical achievements and providing assistance in the use of borrowed best practices.

More simple and sufficient effective method implementation is the conclusion of an agreement on creative collaboration: in this case, the graduate student acts as the main, and sometimes even the only performer of the work. Usually standard forms agreements on creative collaboration contain special clauses with deadlines for the implementation of transferred research results, which determines the subsequent receipt of documents on implementation. For many years, at the Ukrainian Correspondence Polytechnic Institute, the university standard STV – 001 – 82 “Procedure for concluding, formalizing and implementing an agreement on scientific and technical cooperation” was in force, which can now be used as a guiding document.

The qualitative nature of the relationship between time, cost and complexity of implementation is shown in.


  • ^ Qualitative nature of the relationship between time, cost and complexity of implementation
You can also indicate other repeatedly tested forms of organizing implementation work. If a graduate student participates in self-supporting and state budget research work at an enterprise, then it is always possible to highlight the part of the work performed directly by this graduate student. Upon completion of the dissertation, certificates of implementation can be issued for it. It should be taken into account that materials from unfinished research cannot be included in the dissertation. If it is impossible to do without them, then it is necessary to stipulate at the beginning of the work the admissibility of publishing these materials. This should be reflected in the research contract.

Typically, implementation is formalized by an act signed by representatives of the organizations that transfer and use the implemented materials. It is approved by the management of the implementing enterprise. The act must indicate the specific results of the dissertation work used in experimental design or other types of work of the implementing organization, as well as the effect of implementation, not only the technical effect (reducing development time or reducing the likelihood of design errors, etc.), but also the amount annual economic effect.

To reflect the personal contribution of the applicant to the implemented works, the author repeatedly used following form: in the part of the implementation act where the essence of the innovation was described, the authors of the development for each part were indicated overall result. For example, an automated set of tasks for monitoring the fulfillment of contractual obligations was introduced. The act indicated a team of authors of 5 people. A graduate student took part in resolving issues of ensuring reliability. He developed an organizational and software complex for training quality management primary documents. The act reflected this fact and indicated his last name.

4.7.3. Types of effect taken into account when assessing research and development work and reflected in implementation acts. Distinguish the following types effect taken into account when assessing research and development work:

scientific and technical, which is understood as the expansion of knowledge about nature, society and thinking, characterized by the identification of new facts, connections, patterns, laws, the development of fundamentally new methods, devices and substances,

economic effect, which is understood as saving all production resources (living labor, materials, capital investments), received national economy, ultimately resulting in increased productivity social labor and growth of national income;

social effect, which is understood as strengthening the social homogeneity of society - erasing class differences, significant differences between city and countryside, mental and physical labor, comprehensive development and bringing together all nationalities, improving the nature and conditions of work, its protection, safety precautions, increasing the degree of its mechanization and automation, increasing standard of living population, improvement living conditions, growth and improvement of the use of free time, improvement of health care and public education, expansion of opportunities for comprehensive spiritual development of the individual, protection and improvement of the natural environment;

pedagogical effect, which means improving the quality of educational and cognitive activity (in particular, academic performance), reducing the time required to develop skills, consolidating skills, increasing motivation for learning, etc.

^ 4.7.4. Where in the dissertation to describe the results of implementation. The author recommends last chapter make a special paragraph “Characteristics of the implementation of the results obtained”, in which provide the following information:


  • objects of implementation (where it was implemented);

  • content of implementation (what was implemented);

  • forms of implementation (in what form it was implemented);

  • achieved effect (what has changed);

  • what confirms the implementation (acts of implementation).
Complete the paragraph with a summary table. Include the same table in the presentation.

determined by the adopted methodology and research methodology, a comprehensive analysis of the results of the functioning of the penal system in the conditions of its reform. In general, the study is based on the works of scientists in the field of law, management,

sociology, psychology and economics, which determined its complex nature. During the dissertation research, more than 450 employees of the penal system were interviewed using a specially designed questionnaire, taking into account a representative sample (their attitude towards the ongoing reform), and the main indicators characterizing the personnel potential of the system were studied. The formulated conclusions and proposals are based on a comprehensive analysis of legal acts regulating the activities of the penal system, international legal standards, historical experience reforming penitentiary system. The author’s personal professional experience was also used in preparing the work. long time served in territorial institutions and penitentiary authorities, and for the last five years as the head of the Main Directorate for the Execution of Punishments of the Ministry of Justice of Russia.

Testing and implementation of research results. The main results of the study were used and implemented in the preparation of the Concept for reforming the penal system for the period until 2005, Government Resolution Russian Federation dated August 29, 2001 No. 636 “On the Federal target program criminal reform executive system Ministry of Justice of the Russian Federation for 2002-2006".

Certain provisions of the dissertation were used in the preparation of reform concepts and programs specific directions activities of the penal system ( educational work with convicts, legal support, organization of work with personnel, enterprise development correctional institutions, educational and scientific activities

of the penal system). Many of the author’s ideas were implemented in the preparation of legislative and regulatory acts aimed at improving the procedure and conditions for applying measures of criminal procedural restraint in the form of detention, humanizing the procedure and conditions for serving sentences in the form of imprisonment, and introducing new types of punishments.

One of the forms of testing and implementation of the results of the research was the author’s speeches at international events! plh and Russian scientific and scientific-practical conferences, as well as publications on the research topic. The dissertation materials are used in educational process V educational institutions Penal system of the Ministry of Justice of Russia, Academy of Management of the Ministry of Internal Affairs of Russia in preparation management personnel but the course Theoretical basis management in law enforcement sphere" And academic disciplines: “Organization of management in the penal system”, “Operational investigative activities”.

Structure and scope of the dissertation. The dissertation consists of an introduction, two chapters, a conclusion, a list of references and applications.

More on the topic Validity and reliability of research results:

  1. Gelovani V. A., Britkov V. B., Dubovsky S. V.. USSR and Russia in the global system (1985-2030): Results of global modeling, 2009
  2. Gorbunova E.M., Larionova M.V.. ANALYSIS OF RISKS AND POTENTIAL OPPORTUNITIES OF RUSSIAN EDUCATION IN THE CONDITIONS OF ACCESSION TO THE WTO, 2007
  3. Surikov I. E.. Essays on historical writing in classical Greece, 2011
  4. Andrey Nikolaevich Sakharov. Historical portraits. 1762–1917. Catherine II – Nicholas II, 1997

Feedback from an official opponent on the dissertation

___________________________________
Full Name
_________________________________________________________________________
title of dissertation
for competition scientific degree candidate (doctor) technical sciences by specialty(s) ________________________________________________________________
code and name of the specialty in accordance with the nomenclature of scientific specialties

Relevance of the topic

The relevance of the topic chosen by the dissertation author is beyond doubt. The subject of the dissertation research, in my opinion, is... Questions... remain difficult to research, because... Currently, there is a well-known contradiction between... This gives grounds to assert that scientific problem, formulated in the dissertation, ... is relevant. The solution to this problem will allow (implications for the branch(es) of science) ...

Degree of validity of scientific statements, conclusions and recommendations

(assessment of the validity of the results in the dissertation by the author from the opponent’s point of view)

The author quite correctly uses well-known scientific methods substantiation of the obtained results, conclusions and recommendations. The author has studied and critically analyzed the well-known achievements and theoretical positions of other authors... ... on issues... The list of used literature contains... titles.
For analysis... the author creates a methodology (model)... that allows us to identify patterns...
The author finds an explanation for the fact..., with which one can agree, however, it is known from the works... that...
To confirm the theoretical provisions, the author conducts experimental studies, the purpose of which is to establish a connection between...
Similar results were obtained experimentally in the works..., but the conditions for obtaining them did not take into account the influence of factors... Taking these factors into account explains the discrepancies in the values...
The validity of the results put forward by the applicant is based on the consistency of experimental data and scientific conclusions. Thus, it was experimentally established that... A similar result was obtained when calculating the values...
The reliability of experimental data is ensured by using modern means and research methods. The provisions of the theory are based on well-known achievements of fundamental and applied scientific disciplines... mathematics and mathematical statistics, ... In his work, the dissertation author competently uses mathematical apparatus..., correctly introduces new concepts...

Assessment of novelty and reliability

(opponent’s assessment of the novelty and reliability of the results)

The dissertation author put forward the following as new scientific results...:
In general, the results obtained by the author are new scientific knowledge... branch (junction of branches) of knowledge. However, in my opinion, the applicant’s conclusion about... This, in particular, is evidenced by the following fact...
Also, it is premature to talk about the sufficient validity of the position indicating... Similar results were obtained in studies..., however, they showed that...
The results presented for defense are consistent (not consistent) with the data obtained... The well-known model obtained... allows one to obtain the results..., but without taking into account...
Credibility theoretical results work is confirmed by experimental data presented in well-known works...
The main results of the dissertation were published in... printed works, they were repeatedly discussed at various conferences and symposiums and received the approval of leading experts.
The reliability..., in particular, is evidenced by the examination of data carried out...

Comments on the dissertation work as a whole

1. The research did not reflect the question... .
2. The conclusion about... is questionable.
3. There is an inaccurate presentation the following points... .
4. Some results are descriptive in nature (p. ...) and can be shortened without much damage.
The noted shortcomings reduce the quality of the research, but they do not affect the main theoretical and practical results of the dissertation.

Conclusion

The dissertation is a completed research work completed by the author independently at a high scientific level. The work presents scientific results that allow them to be qualified as... (one of the points of the attribute that determines the nature of the dissertation results). The results obtained by the author are reliable, the conclusions and conclusions are justified.
The work is based on a sufficient number of initial data, examples and calculations. It is written clearly, competently and neatly presented. For each chapter and the work as a whole, completed clear conclusions.
The abstract corresponds to the main content of the dissertation.
The dissertation work meets the requirements of the Regulations for the Award of Academic Degrees", and its author (Last Name First Name Patronymic) deserves to be awarded the academic degree of candidate (doctor) ... of science in the specialty(s) ...

Official opponent _______________________
I certify the signature of the official opponent:
Academic Secretary of the University ___________
Official seal
date

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