What is Kantian Philosophy of Mathematics? An Overview of Contemporary Studies
This review of contemporary discussions of Kantian philosophy of mathematics is timed for the publication of the essay Kant’s Philosophy of Mathematics. Volume 1: The Critical Philosophy and Its Roots (2020) edited by Carl Posy and Ofra Rechter. The main discussions and comments are based on the texts contained in ...
A transcendental analysis of mathematics: The constructive nature of mathematics
... focuses on both the human method of cognition in general [CPR, B 25] and certain types of cognition aimed at justifying their objective significance. This article aims to explicate Kant’s understanding (resp. justification) of the abstract nature of mathematical knowledge (cognition) as the “construction of concepts in intuition” (see: “to construct a concept means to exhibit a priori the intuition corresponding to it”; [CPR, A 713/В 741], which is “thoroughly grounded on definitions, ...
A look in the past and the problems of modern mathematical education
This article considers the features of mathematical education in Russia in the 18th-19th centuries. The focal point is the significance of children’s physical activity for the development of spatial perception and mathematical thinking. The author makes recommendations on the development ...
Kant and new mathematics 100 years later
Cassirer’s critique of Russell’s philosophy of mathematics and the Neo-Kantian philosophy of science and mathematics as a whole is of special relevance in the context of modern mathematics and mathematical physics. The fact that the modern standard axiomatic architecture of mathematical theories does ...
A transcendental analysis of mathematics: The abstract nature of mathematical knowledge
... focuses on both the human method of cognition in general [CPR, B25] and certain types of cognition aimed at justifying their objective significance. This article aims to explicate Kant’s understanding (resp. justification) of the abstract nature of mathematical knowledge (cognition) as the “construction of concepts in intuition” (see: “to construct a concept means to exhibit a priori the intuition corresponding to it”; [CPR, A713/В 741], which is “thoroughly grounded on definitions, axioms,...
Kant, Gödel, and the problem of synthetic a priori judgements
Debates over Kant’s famous postulate about the existence of synthetic a priori judgements in mathematics, formulated in the Critique of Pure Reason, have been raging for over two centuries. On the one hand, it was fiercely criticised by neo-positivists in the early 20th century. On the other hand, Kant’s ideas on constructive nature of mathematics ...
Portfolio optimization in the case of an exponential utility function and in the presence of an illiquid asset
... reduction is consistent with the boundary condition. This reduction represents a significant simplification of the original problem.
1. Bordag L. A. Geometrical properties of differential equations. Applications of Lie group analysis in Financial Mathematics. Singapore, 2015.
2. Bordag L. A., Yamshchikov I. P. Lie group analysis of nonlinear Black-Scholes models // Ehrhardt M., Günther M., ter Maten E. J. W. (eds.). Novel Methods in Computational Finance. Springer, 2017. P. 109—128.
3. Bordag ...
Possible applications of the resources of the Mathematica programming environment to solving mathematical problems
This article describes possible applications of the resources of the Mathematica programming environment (version 184.108.40.206) in teaching mathematics as a means of the automatic control of initial data input, input data generator, and a means to improve the visibility of mathematical problem solving. The author offers examples of Mathematica codes for each case and identifies the sequence ...
About various approaches on visualizations for classical mathematic models
Various visualization methods for classical mathematic models, including statistical graphics, 2D and 3D animation are reviewed, and possible means of realization for such animations are suggested.
1. Худенко В. Н. Об использовании анимации в преподавании ...
On the mathematical modeling of the space of mental images
This article stresses the need to use a mathematical model of the space of mental images in psychology, medicine, and other sciences. The author identifies the relation between such space and the space-time of physics. The article shows opportunities for structuring the space and introducing ...
Mathematical model for feeling hope
A mathematical model, which determines composition and structure of human feelings was created. It was shown that each feeling can be shown in the shape of a wreath from sequentially arising emotions. The mathematical model for feeling hope was built and ...
Mathematical modeling of a injury of a backbone
A plenty of proceedings of various disciplines fundamental and applied science is devoted to studying of vertebral damage. The special role in studying this pathology is played with methods of mathematical modelling since allow to predict development of adverse deformations of a backbone and to optimize methods of elimination of these damages. Using mathematical model three-vertebra a complex the algorithm of surgical treatment of typical spinal ...
The implementation of creative developmental function of mathematics at a higher education institution
This article presents the preconditions and individual concepts of the development of creative mathematical training at a higher education institution.
Креативно ориентированная математическая подготовка в вузе: монография. Калининград,...
Practical classes in mathematics as a means to develop the research competence in students of technical universities
... competence in technical university students in accordance with the requirements of relevant federal state educational standards. The authors focus on the preparedness of future engineers to conduct technical experiments, whose important component is the mathematical processing of experimental data and performance of simulation experiments. It is proposed to develop such skills during practical classes in mathematics considered as a means to develop research competences.
1. Артищева Е. К....
Examples of the mathematical model of the management company
The article discusses Two mathematical models of housing and utilities services organization as an example of a managing company are considered. The first model is based on balance equations of the organization. It takes into account and systematizes income and expenses of a managing ...
An analysis of mathematical models of the stress state of the outer shell of the roller one-way clutches
The outer shell is an important constructive element of roller one-way clutches. Currently, for the calculation of the stress state of the outer shell using the mathematical models obtained based on the essential assumptions. In the article the analysis is carried out and recommendations about use of design mathematical models are made. It is established that at change of number of wedging rollers in a range ...
Numerical model operation of the mass transfer of the disperse phase of aerosol in nonlinear wave fields for axisymmetric quasithree-dimensional geometrical statement
The article describes numerical modelling of fluctuations of an aerosol column in pipes at resonant frequencies. The author suggests a mathematical model of dynamics of the heterogeneous medium-mix with approximately equal component mass fractions. The mathematical model suggests the solution of a dynamics equation system for each of the mix component. The carrier medium is a viscous,...
Efficient algorithms for computing superelliptic curves
Represents basics algorithms of arithmetics superelliptic curves and optimal parameters superelliptic curve suitable for cryptography.
1.Koblitz N. Elliptic curve cryptosystems // Mathematics of Computation. 1987. № 48 (177). P. 203–209.
2. ANSI X9.63 Public Key Cryptography for the Financial Services Industry: El-liptic Curve Key Agreement and Key Transport Schemes. Working Draft - Ver-sion 2.0. 1998.
3. Galbraith S. D.,...
An analysis of mathematical models of the deformation state of the outer shell of the roller one-way clutches
The outer shell is an important component influencing on the working capacity of roller one-way clutches. The analysis is carried out and recommendations about use of mathematical models for calculation of deformation of outer shell are made. It is established that at change of number of wedged rollers in a range from 3 to 7 there is a nonlinear decrease of value of a radial deformation, and in a range from 7 to 30 ...
Mathematical modelling of filtration processes of moisture in heavy soils
A mathematical model of filtration of moisture in heavy soils. The transfer of a film of moisture on the surface took into account.
1. Hallaire M. Le potential efficace de l’eau dans le sol en regime de dessechement // L’eau et production vegetale....
Mathematical simulation in road-building
Mathematical models for an estimation of quality of road-building materials are considered. The mathematical model of the modern asphalt-concrete factory with several asphalt-mixing installations is constructed. The technique of definition of reliability ...
On the dynamics of mathematical information forms in training of air navigation students on
This article deals with the role of mathematical information in teaching. The author emphasizes the need for the development of informational and activity mobility. The author offers an excerpt from students’ individual work triggering the activity component of informational mobility....
The methodological and mathematical implementation of the integrated controlling theory
... to the innovative concept of managing modern industrial enterprises as economic systems, namely, integrated controlling. The author presents a methodological framework for the implementation of the integrated controlling theory. Possible uses of the mathematical apparatus in studying integrated controlling are shown. Static and dynamic characteristics of integrated controlling as a complex system are described. A mathematical model of such system is constructed.
1. Акимова И. В., Ермолаева ...
A review of the existing generalizations of the Deuring Reduction Theorem
... Pairing-Friendly Abelian Varieties over Non-prime Fields // Pairing-Based Cryptography–Pairing 2009, Lecture Notes in Comput. Sci., vol. 5671. Springer, 2009. P. 52—65.
2. Blake C. A Deuring criterion for abelian varieties // Bulletin of the London Mathematical Society. Dec. 2014. Vol. 46, issue 6. P. 1256.
3. Bradford J. Commutative Endomorphism Rings of Simple Abelian Varieties over Finite Fields. Ph. D. Thesis, University of Maryland, 2012.
4 Clark P. L. Bounds for torsion on abelian varieties ...
A Lax pair for the (1+3) nonlinear equation
Integral systems with four independent variables have special signifi-cance in mathematics and physics. The discovery of inverse scattering method played an important role in reconsidering the place of integrable systems of nonlinear partial differential equations in mathematical sciences. The search for a systematic approach to ...
Multiple-factor mathematical models of heterogeneous metasystems
Nonlinear mathematical modeling of physical processes in heterogeneous metasystems with bubble or a solid-state filler allows to receive the parities convenient for numerical calculations and comparison of theoretical results with the data of experiments. For creation ...
The computer simulation of tsunami wave breaking against a steep shore
... atmosphere above it are considered as an integral continuous environment. At the water-air surface, the density changes abruptly from ρ = ρwater = 1000 kg/m3 for water to ρ = ρair = 1.2 kg/m3 for air. The solution to model equations is generalised. The mathematical mechanism
of equation solving suggests automatic smoothing of density in the area of wave breaking and formation of a thin fluid layer with an intermediate density.
1. Пелиновский Е. Н. Гидродинамика волн цунами....
The modelling of postmortem heat transfer and estimating the time of death
This article analyses different mathematical models of the process of postmortem heat transfer in an adult cadaver based on postmortem temperature dynamics. A model of heat transfer in a newborn cadaver presented as a finite cylinder is examined in detail. An important factor in constructing ...
A mathematical model of conversion of GaAs substrate into thin GaNxAs1-x films obtained by nitridation of porous GaAs substrate
A mathematical model of conversion of GaAS substrate into thin GaNxAs1-x films obtained by nitridation of porous GaAs substrate are presented. The technologic conditions influence on GaNxAs1-x parameters are discussed. The comparative analysis of both experimental ...
Problems of modeling of the working processes of a stationary plasma engine
Today in creation of mathematical models of the stationary plasma thruster (SPT) a certain advance is noticeable, but all these models are based on empirical laws with a possibility of application to concrete type of the engine. The paper considers the possibility of constructing ...
Non-standard problems in competence-based mathematics teaching
The authors analyse various types of non-standard tasks, identifies their main characteristics related to the formation of cognitive competence in mathematical education. The article explores ways of solving heuristic, research, and creative problems. A comprehensive approach to the definition of the nonstandard task is proposed. The proposed structure of the problem is based on the following scheme: ...
A mathematical simulation and a numerical investigation of dynamics of intramolecular tautomerny transformation without considering processes of a proton relaxation. Part I. A description of a mathematical model
... Балтийского федерального университета им. И. Канта. Вып. 10. С. 79—93.
7. Ландау Л. Д., Лифшиц Е. М. Квантовая механика. М., 1963.
Kvitko G., Kuzin E., Latyshev К., Shott D.
mathematical model, hydrogen binding, proton, Schrödinger equation, adiabatic model potentials, statistical operator, probability of tautomerny transformation.
Anagrammatic structures in the semiotic aspect
... article considers the functional features and deep cognitive foundations of ana¬grammatic structures in verbal texts. The traditional perspective on the phenomenon is defined as a general sign-based one: anagrammatic structures are examined in music and mathematics. It is concluded that anagrams are special cognitive universals; anagrammatic structures are possible in semiotic codes with a linear organisation; one of the key functions of anagrams is cognitive – linear texts are perceived as a whole
Kant’s transcendentalism and concept of the thing in itself
... Kantovskiiy sbornik [The Kantovsky sbornik], no. 2 (48). P. 10—25.
31. Katrechko, S. L. 2014b, Transcendental'nyiy analiz matematicheskoiy dejatel'nosti: abstraktnye (matematicheskie) ob"ekty, konstrukcii i dokazatel'stva [Transcendental analysis of mathematical activity: abstract (mathematical) objects, structures and proofs], in: Dokazatel'stvo: ochevidnost', dostovernost' i ubeditel'nost' v matematike (Proceedings of the Moscow Seminar on the Philosophy of Mathematics). M. : «LIBROKOM», P. 86—120....
Optimization of Repeatability Injured Backbone with the Help of Rigid Laminas on the Basis of a Mathematical Model of a Three-Vertebra System
... высоких технологий в промышленности». СПб., 2008. С. 161.
Sedov R., Orlov S., Bobarykin N.
Modeling of human’s three-vertebra system and optimisation of fixation constructions // The International Conference Mathematical modeling and computational physics.
Sedov R. L., Orlov S. V., Latishev K. S.
mathematical modelling, the ordinary differential equations, numerical methods, optimization, biomechanics.
Formal models of a system of automated generation of programming tests
Formal approaches to creation of algorithms implemented in automated tests generation system are considered. Structure of a software system of programming tests generation is presented. Problem statements and mathematical models for some modules of the system are described.
1. Алсынбаева Л. Г. Система автоматизированной генерации тестовых заданий // Программные продукты и системы....
One method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid
... Pt. 2. Vol. 45.
2. Kato T. Quasi-linear equations of evolution, with applications to partial differential equastions // Journal of Functional Analysis. 1972. Vol. 9. P. 296.
3. Kato T. Spectral theory and differential equastions // Lecture Notes in Mathematics / ed. W.N. Everitt. Berlin, 1975. Vol. 448. P. 25.
4. Constantin P., Wu J. The inviscid limit for non-smooth vortivity // Indiana University Mathematics Journal. 1996. № 1. P. 45.
5. Wu J. J. The Inviscid Limit of the Complex Ginzburg-Landau ...
A dynamic visualizations of mathematic models of the singular points of hydrodynamics analytic functions
Dynamic visualizations for mathematic models for potentially stable flows of ideal incompressible liquid have been built using special points of analytic functions.
1. Голубева О. В. Курс механики сплошных сред. М., 1972.
2. Лойцянский ...
The efficiency of applying electronic education technologies at the final stage of preparation for the Unified State Exam in mathematics
Through the case of general educational institutions of the Kaliningrad region, the authors consider the methods for increasing the level of students’ preparation for the Unified State Examination in mathematics through using the system of distance learning for training and monitoring the level of preparation. The authors describe the approach, which makes it possible not only to present the content and function of computer-assisted testing, but also ...
Formalization and solving optimal control technological complexes
Results of development of mathematical methods and statement of problems of optimum control of a set of the interconnected trajectories–technologies of continuous technological processes and creations of numerical methods of their decision are given.
1. Красовский ...
Determination of suitability of network intrusion detection rules and their mathematical evaluation
... parameters of damaged packets is investigated. To assess the suitability of the rules for detecting network attacks and their subsequent control, a method for upgrading the component composition of intrusion detection systems has been redesigned. A method of mathematical evaluation of the suitability of the rules for detecting network attacks is considered.
Podtopelny V. V., Vetrov I. A.
risk, information system, network attack, network intrusion, module
Application of the mathematical modelling and simulation methods to the study of didactic systems
Didactic systems relate to poorly structured and poorly formalizable objects that function under conditions of uncertainty and lack of information about the state of the student, the teaching methods used, etc. The article considers the application of mathematical and computer modeling methods for the study of didactic systems and various approaches to the construction of mathematical and computer models of the student. The following models are discussed: linear and nonlinear learning models; multicomponent ...
Mathematical processing of measurements results in a laboratory practical work
The problems connected to a technique of mathematical processing of measurements results in a laboratory practical work are considered. The purpose of measurements results processing is optimization of procedure of random error calculation.
1. Зайдель А. Н. Ошибки измерений ...
Analytic philosophy: a historico-critical survey
... Analytic Philosophy. N. Y., 1949.
13. Pap A. Analytische Erkenntnistheorie. Wien, 1955.
14. Quine W. V. O. Two Dogmas of Empiricism. Reprinted // Quine W. V. O. From a Logical Point of View. Cambridge (Mass.), 1953.
15. Ramsey F. P. The Foundations of Mathematics and Other Logical Essays. L., 1931.
16. Ramsey F. P. Notes on Philosophy, Probability and Mathematics / ed. by Galavotti M. C. Napoli, 1991.
17. Rescher N. The Coherence Theory of Truth. Oxford, 1973.
18. Rorty R. Philosophy and the Mirror ...
The role of individual work in the development of creative competency in bachelors of education (The case of the Basics of Mathematical Information Processing course )
... indi-vidual work of students (IWS) in the formation of creative competence and the requirements for its organization, contributing to the formation of creative competence are identified. The case of organizing individual work when studying the Basis of Mathematical Information Processing is examined.
1. Пичкова Л. С. Организация самостоятельной работы студентов как фактор формирования профессионально значимых ...
About one training course of mathe-matical modeling
A program of the general course of mathematical modeling coordinated with modeling of transport flows is submitted.
1. Гасников А., Дорн Ю., Прохоров А., Швецов В. Как бороться с пробками? // Троицкий вариант. 2012. № ...