1,255 research outputs found
Competence amplification of correctness result verification in mathematical disciplines
The ability to verify the correctness and effectiveness of the result is an important competence for all areas of training. Checking the correctness of the decision should be a mandatory final stage of solving mathematical problems. On the example of differentiation and integration of functions shown that when tested using simple numerical algorithms that can be implemented using the basic features package Excel. Assimilation of natural competence easier to implement with the help of numerical methods, which are fixed in the process of constant testingΠ£ΠΌΠ΅Π½ΠΈΠ΅ ΠΎΡΡΡΠ΅ΡΡΠ²Π»ΡΡΡ ΠΏΡΠΎΠ²Π΅ΡΠΊΡ ΠΊΠΎΡΡΠ΅ΠΊΡΠ½ΠΎΡΡΠΈ ΠΈ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΠΎΠ³ΠΎ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ° ΡΠ²Π»ΡΠ΅ΡΡΡ Π²Π°ΠΆΠ½ΠΎΠΉ ΠΊΠΎΠΌΠΏΠ΅ΡΠ΅Π½ΡΠΈΠ΅ΠΉ Π΄Π»Ρ Π²ΡΠ΅Ρ
Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠΉ ΠΏΠΎΠ΄Π³ΠΎΡΠΎΠ²ΠΊΠΈ. ΠΡΠΎΠ²Π΅ΡΠΊΠ° ΠΏΡΠ°Π²ΠΈΠ»ΡΠ½ΠΎΡΡΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π΄ΠΎΠ»ΠΆΠ½Π° ΡΠ²Π»ΡΡΡΡΡ ΠΎΠ±ΡΠ·Π°ΡΠ΅Π»ΡΠ½ΡΠΌ Π·Π°Π²Π΅ΡΡΠ°ΡΡΠΈΠΌ ΡΡΠ°ΠΏΠΎΠΌ ΡΠ΅ΡΠ΅Π½ΠΈΡ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ Π·Π°Π΄Π°ΡΠΈ. ΠΠ° ΠΏΡΠΈΠΌΠ΅ΡΠ΅ Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈ ΠΈΠ½ΡΠ΅Π³ΡΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΡΠ½ΠΊΡΠΈΠΉ ΠΏΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΠΏΡΠΈ ΡΠ΅ΡΡΠΈΡΠΎΠ²Π°Π½ΠΈΠΈ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡΡΡΡ ΠΏΡΠΎΡΡΡΠ΅ ΡΠΈΡΠ»Π΅Π½Π½ΡΠ΅ Π°Π»Π³ΠΎΡΠΈΡΠΌΡ, ΠΊΠΎΡΠΎΡΡΠ΅ ΠΌΠΎΠΆΠ½ΠΎ ΡΠ΅Π°Π»ΠΈΠ·ΠΎΠ²Π°ΡΡ Ρ ΠΏΠΎΠΌΠΎΡΡΡ Π±Π°Π·ΠΎΠ²ΡΡ
Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠ΅ΠΉ ΠΏΠ°ΠΊΠ΅ΡΠ° Excel. Π£ΡΠ²ΠΎΠ΅Π½ΠΈΠ΅ Π΅ΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎΠ½Π°ΡΡΠ½ΡΡ
ΠΊΠΎΠΌΠΏΠ΅ΡΠ΅Π½ΡΠΈΠΉ Π»Π΅Π³ΡΠ΅ ΡΠ΅Π°Π»ΠΈΠ·ΠΎΠ²Π°ΡΡ Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΡΠΈΡΠ»Π΅Π½Π½ΡΡ
ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ², ΠΊΠΎΡΠΎΡΡΠ΅ Π·Π°ΠΊΡΠ΅ΠΏΠ»ΡΡΡΡΡ Π² ΠΏΡΠΎΡΠ΅ΡΡΠ΅ ΠΏΠΎΡΡΠΎΡΠ½Π½ΠΎΠ³ΠΎ ΡΠ΅ΡΡΠΈΡΠΎΠ²Π°Π½ΠΈ
Methods of predicting relapsing hemorrhage.
In this article the authors presented their own original methods for predicting ulcerous gastroduodenal bleeding defended by Patent of Ukraine. The implementation of these procedures led to substantial lowing of recurrent hamorrhage rate β more than twice. All methods have pathogenetic foundation and are based on ulcerogenesis mechanisms revealed during the longlasting complex clinical and experimental research. In such a way surgeons obtain some possibilities of early diagnostics of bleeding relapses and adequate treatment and effective hemorrhage prevention accordingly.
Optimization of complex functions and the algorithm for exact geometric search for complex roots of a polynomial
The paper describes an application for visualization of four-dimensional graphs of a complex variable function. This application allowed us to construct an exact geometric algorithm for finding the real and complex roots of a polynomial on the same plane. A graph of an n-th order polynomial on the real plane allows us to define geometrically all the real roots. Number of real roots varies from 0 to n. The rest of the roots are complex and not determined by the graph. In the article, in addition to the graph of the basic polynomial, two auxiliary graphs are constructed, which allow us to represent all complex roots on the same real plane. Realization of this method is considered in detail for the solution of a cubic polynomial. In this case the method has exceptional features in comparison with polynomials of other degrees. We also propose an algorithm for constructing auxiliary functions for the general case of a polynomial of order n which have exact formulas for polynomials with order n β€ 10. The algorithm for the first time builds the exact hodograph of poles for the control systems with feedback. We generalize the concepts of stationary and extremal points to the case of a complex function. The absence of the possibility of comparing the complex values of the objective function is compensated by an analysis of the behavior of the stationary point under small perturbations of the polynomial by linear functions. Optimality criteria are proposed using complex trajectories of stationary points. Β© 201
A nonstationary form of the range refraction parabolic equation and its application as an artificial boundary condition for the wave equation in a waveguide
The time-dependent form of Tappert's range refraction parabolic equation is
derived using Daletskiy-Krein formula form noncommutative analysis and proposed
as an artificial boundary condition for the wave equation in a waveguide. The
numerical comparison with Higdon's absorbing boundary conditions shows
sufficiently good quality of the new boundary condition at low computational
cost.Comment: 12 pages, 9 figure
The quality of geometric objects constraints and the duality gap in semi-infinite linear programming
The paper considers the model of geometric object constraints defined by feasible set of semi-infinite linear programming problem (SILP). Quality geometric method for analyzing SILP duality relations based on the use of the conical hull of the system constraints coefficients is proposed. A relation between presence of the duality gap and nonclosure of the conical hull boundary of points in a multidimensional space is established. An SILP example with three variables illustrates that problems with the duality gap are not exotic. The possibility of applying the system MATLAB for numerical quality analysis of geometrical objects constraints is under discussion. We put forward a hypothesis that the duality gap of SILP adversely affects on the quality of geometric objects constraints.Π Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΡΡΡ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΎΠ³ΡΠ°Π½ΠΈΡΠ΅Π½ΠΈΠΉ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΎΠ±ΡΠ΅ΠΊΡΠ°, Π·Π°Π΄Π°Π²Π°Π΅ΠΌΠ°Ρ Π΄ΠΎΠΏΡΡΡΠΈΠΌΡΠΌ ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²ΠΎΠΌ ΠΏΠΎΠ»ΡΠ±Π΅ΡΠΊΠΎΠ½Π΅ΡΠ½ΠΎΠΉ Π·Π°Π΄Π°ΡΠΈ Π»ΠΈΠ½Π΅ΠΉΠ½ΠΎΠ³ΠΎ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ (ΠΠ±ΠΠ). ΠΡΠ΅Π΄Π»Π°Π³Π°Π΅ΡΡΡ ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅Π½Π½ΡΠΉ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠΏΠΎΡΠΎΠ± Π°Π½Π°Π»ΠΈΠ·Π° ΡΠΎΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΠΉ Π΄Π²ΠΎΠΉΡΡΠ²Π΅Π½Π½ΠΎΡΡΠΈ ΠΠ±ΠΠ, ΠΎΡΠ½ΠΎΠ²Π°Π½Π½ΡΠΉ Π½Π° ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠΈ ΠΊΠΎΠ½ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΎΠ±ΠΎΠ»ΠΎΡΠΊΠΈ ΠΊΠΎΡΡΡΠΈΡΠΈΠ΅Π½ΡΠΎΠ² ΡΠΈΡΡΠ΅ΠΌΡ ΠΎΠ³ΡΠ°Π½ΠΈΡΠ΅Π½ΠΈΠΉ. Π£ΡΡΠ°Π½Π°Π²Π»ΠΈΠ²Π°Π΅ΡΡΡ ΡΠ²ΡΠ·Ρ Π½Π°Π»ΠΈΡΠΈΡ ΡΠ°Π·ΡΡΠ²Π° Π΄Π²ΠΎΠΉΡΡΠ²Π΅Π½Π½ΠΎΡΡΠΈ Ρ Π½Π΅Π·Π°ΠΌΠΊΠ½ΡΡΠΎΡΡΡΡ Π³ΡΠ°Π½ΠΈΡΡ ΠΊΠΎΠ½ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΎΠ±ΠΎΠ»ΠΎΡΠΊΠΈ ΡΠΎΡΠ΅ΠΊ Π² ΠΌΠ½ΠΎΠ³ΠΎΠΌΠ΅ΡΠ½ΠΎΠΌ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅. ΠΠ° ΠΏΡΠΈΠΌΠ΅ΡΠ΅ ΠΠ±ΠΠ Ρ ΡΡΠ΅ΠΌΡ ΠΏΠ΅ΡΠ΅ΠΌΠ΅Π½Π½ΡΠΌΠΈ ΠΏΠΎΠΊΠ°Π·ΡΠ²Π°Π΅ΡΡΡ, ΡΡΠΎ Π·Π°Π΄Π°ΡΠΈ Ρ ΡΠ°Π·ΡΡΠ²ΠΎΠΌ Π΄Π²ΠΎΠΉΡΡΠ²Π΅Π½Π½ΠΎΡΡΠΈ Π½Π΅ ΡΠ²Π»ΡΡΡΡΡ ΡΠΊΠ·ΠΎΡΠΈΡΠ΅ΡΠΊΠΈΠΌΠΈ. ΠΠ±ΡΡΠΆΠ΄Π°Π΅ΡΡΡ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΡ ΡΠΈΡΡΠ΅ΠΌΡ MATLAB Π΄Π»Ρ ΡΠΈΡΠ»Π΅Π½Π½ΠΎΠ³ΠΎ Π°Π½Π°Π»ΠΈΠ·Π° ΠΊΠ°ΡΠ΅ΡΡΠ²Π° ΠΎΠ³ΡΠ°Π½ΠΈΡΠ΅Π½ΠΈΠΉ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΎΠ±ΡΠ΅ΠΊΡΠΎΠ². ΠΡΠ΄Π²ΠΈΠ³Π°Π΅ΡΡΡ Π³ΠΈΠΏΠΎΡΠ΅Π·Π° ΠΎΠ± ΠΎΡΡΠΈΡΠ°ΡΠ΅Π»ΡΠ½ΠΎΠΌ Π²Π»ΠΈΡΠ½ΠΈΠΈ ΡΠ°Π·ΡΡΠ²Π° Π΄Π²ΠΎΠΉΡΡΠ²Π΅Π½Π½ΠΎΡΡΠΈ Π·Π°Π΄Π°ΡΠΈ ΠΠ±ΠΠ Π½Π° ΠΊΠ°ΡΠ΅ΡΡΠ²ΠΎ ΠΎΠ³ΡΠ°Π½ΠΈΡΠ΅Π½ΠΈΠΉ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΎΠ±ΡΠ΅ΠΊΡΠΎΠ²
Formalization of OLAP-cubes and relational databases with the algebra of sets
Mathematical formalization of OLAP-cubes is developed. Dimensions of cube and Cartesian products are supplied with an algebra of sets and measure. These sets are involved in queries. Operations projection and cross section are consistent with the algebra of dimension. Relational connections between dimensions realized with the help of index maps on the works of these dimensions. We introduce three types of index maps to the dimension corresponding to the three types of relational ties. It is shown that the relational database is an OLAP-cube with the corresponding index maps, and can be written by one formula. As an example the analytical processing of the questionnairesΠΡΠ΅Π΄Π»Π°Π³Π°Π΅ΡΡΡ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΡΠΎΡΠΌΠ°Π»ΠΈΠ·Π°ΡΠΈΡ OLAP-ΠΊΡΠ±ΠΎΠ², Π² ΠΊΠΎΡΠΎΡΠΎΠΉ ΡΠ°Π·ΠΌΠ΅ΡΠ½ΠΎΡΡΠΈ ΠΊΡΠ±Π° ΠΈ ΠΈΡ
Π΄Π΅ΠΊΠ°ΡΡΠΎΠ²ΡΠ΅ ΠΏΡΠΎΠΈΠ·Π²Π΅Π΄Π΅Π½ΠΈΡ ΡΠ½Π°Π±ΠΆΠ°ΡΡΡΡ Π°Π»Π³Π΅Π±ΡΠΎΠΉ ΠΏΠΎΠ΄ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ² ΠΈ ΠΌΠ΅ΡΠΎΠΉ. ΠΡΠΈ ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²Π° ΡΡΠ°ΡΡΠ²ΡΡΡ Π² Π·Π°ΠΏΡΠΎΡΠ°Ρ
. ΠΠΏΠ΅ΡΠ°ΡΠΈΠΈ ΠΏΡΠΎΠ΅ΠΊΡΠΈΠΈ ΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΡ ΡΠΎΠ³Π»Π°ΡΡΡΡΡΡ Ρ Π°Π»Π³Π΅Π±ΡΠ°ΠΌΠΈ ΡΠ°Π·ΠΌΠ΅ΡΠ½ΠΎΡΡΠ΅ΠΉ. Π Π΅Π»ΡΡΠΈΠΎΠ½Π½ΡΠ΅ ΡΠ²ΡΠ·ΠΈ ΠΌΠ΅ΠΆΠ΄Ρ ΡΠ°Π·ΠΌΠ΅ΡΠ½ΠΎΡΡΡΠΌΠΈ ΡΠ΅Π°Π»ΠΈΠ·ΡΡΡΡΡ Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΠΈΠ½Π΄Π΅ΠΊΡΠ½ΡΡ
ΠΎΡΠΎΠ±ΡΠ°ΠΆΠ΅Π½ΠΈΠΉ Π½Π° ΠΏΡΠΎΠΈΠ·Π²Π΅Π΄Π΅Π½ΠΈΡΡ
ΡΡΠΈΡ
ΡΠ°Π·ΠΌΠ΅ΡΠ½ΠΎΡΡΠ΅ΠΉ. ΠΠ²ΠΎΠ΄ΡΡΡΡ ΡΡΠΈ ΡΠΈΠΏΠ° ΠΈΠ½Π΄Π΅ΠΊΡΠ½ΡΡ
ΠΎΡΠΎΠ±ΡΠ°ΠΆΠ΅Π½ΠΈΠΉ Π½Π° ΡΠ°Π·ΠΌΠ΅ΡΠ½ΠΎΡΡΠΈ, ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΡΡΡΠΈΠ΅ ΡΡΠ΅ΠΌ ΡΠΈΠΏΠ°ΠΌ ΡΠ΅Π»ΡΡΠΈΠΎΠ½Π½ΡΡ
ΡΠ²ΡΠ·Π΅ΠΉ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΡΠ΅Π»ΡΡΠΈΠΎΠ½Π½Π°Ρ Π±Π°Π·Π° Π΄Π°Π½Π½ΡΡ
ΡΠ²Π»ΡΠ΅ΡΡΡ OLAP-ΠΊΡΠ±ΠΎΠΌ Ρ ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΡΡΡΠΈΠΌΠΈ ΠΈΠ½Π΄Π΅ΠΊΡΠ½ΡΠΌΠΈ ΠΎΡΠΎΠ±ΡΠ°ΠΆΠ΅Π½ΠΈΡΠΌΠΈ ΠΈ ΠΌΠΎΠΆΠ΅Ρ Π±ΡΡΡ Π·Π°ΠΏΠΈΡΠ°Π½Π° ΠΎΠ΄Π½ΠΎΠΉ ΡΠΎΡΠΌΡΠ»ΠΎΠΉ. Π ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΏΡΠΈΠΌΠ΅ΡΠ° ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΡΡΡ Π°Π½Π°Π»ΠΈΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΎΠ±ΡΠ°Π±ΠΎΡΠΊΠ° Π°Π½ΠΊΠ΅Ρ
Competence amplification of information technologies interaction in educational process an example of Microsoft Excel application
Nowadays the ability to provide programs interaction, which are written on different programming languages and between different applications, is important competence for training area βComputer Science and Engineeringβ. In this report, interaction between Java-applications and Excel spreadsheet is considered, especially popular in education field. The necessity of this interaction was caused to automate the use of the service Solver in Excel to solve the optimization task. This problem was solving within writing of course work βJDOM-functions usage for work with scientific data in XML-files on Java programming languageβ. As a result of the work the program was written in Java, interacting by means of XML-files with Excel spreadsheet and calling the service Solver by means of the vbs-scriptΠ Π½Π°ΡΡΠΎΡΡΠ΅Π΅ Π²ΡΠ΅ΠΌΡ ΡΠΌΠ΅Π½ΠΈΠ΅ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΡΡ Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΠ΅ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌ, Π½Π°ΠΏΠΈΡΠ°Π½Π½ΡΡ
Π½Π° ΡΠ°Π·Π½ΡΡ
ΡΠ·ΡΠΊΠ°Ρ
ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ, ΠΈ ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ
ΠΏΡΠΈΠ»ΠΎΠΆΠ΅Π½ΠΈΠΉ ΡΠ²Π»ΡΠ΅ΡΡΡ Π²Π°ΠΆΠ½ΠΎΠΉ ΠΊΠΎΠΌΠΏΠ΅ΡΠ΅Π½ΡΠΈΠ΅ΠΉ Π΄Π»Ρ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΠΏΠΎΠ΄Π³ΠΎΡΠΎΠ²ΠΊΠΈ Β«ΠΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΊΠ° ΠΈ Π²ΡΡΠΈΡΠ»ΠΈΡΠ΅Π»ΡΠ½Π°Ρ ΡΠ΅Ρ
Π½ΠΈΠΊΠ°Β». Π Π΄ΠΎΠΊΠ»Π°Π΄Π΅ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π»ΠΎΡΡ Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΠ΅ Java-ΠΏΡΠΈΠ»ΠΎΠΆΠ΅Π½ΠΈΠΉ ΠΈ ΡΠ°Π±Π»ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ° Excel, ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎ ΠΏΠΎΠΏΡΠ»ΡΡΠ½ΠΎΠΌ Π² ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°ΡΠ΅Π»ΡΠ½ΠΎΠΌ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅. ΠΠ΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΡ Π΄Π°Π½Π½ΠΎΠ³ΠΎ Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΡ Π±ΡΠ»Π° Π²ΡΠ·Π²Π°Π½Π° Ρ ΡΠ΅Π»ΡΡ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΠ·Π°ΡΠΈΠΈ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΡΠ΅ΡΠ²ΠΈΡΠ° Β«ΠΠΎΠΈΡΠΊ ΡΠ΅ΡΠ΅Π½ΠΈΡΒ» Π² Excel Π΄Π»Ρ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°ΡΠΈ ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ. ΠΠ°Π½Π½Π°Ρ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ° ΡΠ΅ΡΠ°Π»Π°ΡΡ Π² Ρ
ΠΎΠ΄Π΅ Π½Π°ΠΏΠΈΡΠ°Π½ΠΈΡ ΠΊΡΡΡΠΎΠ²ΠΎΠ³ΠΎ ΠΏΡΠΎΠ΅ΠΊΡΠ° Β«ΠΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ JDOM-ΡΡΠ½ΠΊΡΠΈΠΉ Π΄Π»Ρ ΡΠ°Π±ΠΎΡΡ Ρ Π½Π°ΡΡΠ½ΡΠΌΠΈ Π΄Π°Π½Π½ΡΠΌΠΈ Π² XML-Π΄ΠΎΠΊΡΠΌΠ΅Π½ΡΠ°Ρ
Π½Π° ΡΠ·ΡΠΊΠ΅ JavaΒ». Π ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ ΡΠ°Π±ΠΎΡΡ Π±ΡΠ»Π° Π½Π°ΠΏΠΈΡΠ°Π½Π° ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ° Π½Π° ΡΠ·ΡΠΊΠ΅ Java, Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΡΡΡΠ°Ρ ΠΏΠΎΡΡΠ΅Π΄ΡΡΠ²ΠΎΠΌ XML-ΡΠ°ΠΉΠ»ΠΎΠ² Ρ ΡΠ°Π±Π»ΠΈΡΠ½ΡΠΌ ΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠΎΠΌ Excel ΠΈ ΠΎΠ±ΡΠ°ΡΠ°ΡΡΠ°ΡΡΡ ΠΊ ΡΠ΅ΡΠ²ΠΈΡΡ Β«ΠΠΎΠΈΡΠΊ ΡΠ΅ΡΠ΅Π½ΠΈΡΒ» ΡΠ΅ΡΠ΅Π· vbs-ΡΠΊΡΠΈΠΏ
Limit cycles of orthogonal projection onto the set of the most remote
The problem of finding the limit polygonal cycles of orthogonal projection onto the most remote set in the plane is discussed. As a simplest case we have considered projections onto the remote side of the triangle. A criterion of existence and analytical formulas for limit triangular cycles is described. We construct the set of initial points of the sequence converging to the triangular cycle. The examples of limit polygonal cycles are presented. Numerical calculations are performed.Π Π°ΡΡΠΌΠΎΡΡΠ΅Π½Π° Π·Π°Π΄Π°ΡΠ° Π½Π°Ρ
ΠΎΠΆΠ΄Π΅Π½ΠΈΡ ΠΏΡΠ΅Π΄Π΅Π»ΡΠ½ΡΡ
ΠΌΠ½ΠΎΠ³ΠΎΡΠ³ΠΎΠ»ΡΠ½ΡΡ
ΡΠΈΠΊΠ»ΠΎΠ² ΠΏΡΠΈ ΠΎΡΡΠΎΠ³ΠΎΠ½Π°Π»ΡΠ½ΠΎΠΌ ΠΏΡΠΎΠ΅ΠΊΡΠΈΡΠΎΠ²Π°Π½ΠΈΠΈ Π½Π° Π½Π°ΠΈΠ±ΠΎΠ»Π΅Π΅ ΡΠ΄Π°Π»Π΅Π½Π½ΠΎΠ΅ ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²ΠΎ ΠΈΠ· ΠΊΠΎΠ½Π΅ΡΠ½ΠΎΠ³ΠΎ Π½Π°Π±ΠΎΡΠ° Π²ΡΠΏΡΠΊΠ»ΡΡ
ΠΊΠΎΠΌΠΏΠ°ΠΊΡΠ½ΡΡ
ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ² Π½Π° ΠΏΠ»ΠΎΡΠΊΠΎΡΡΠΈ. Π ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΏΡΠΎΡΡΠ΅ΠΉΡΠ΅Π³ΠΎ ΡΠ»ΡΡΠ°Ρ ΠΏΠΎΡΡΡΠΎΠ΅Π½Ρ ΠΏΡΠ΅Π΄Π΅Π»ΡΠ½ΡΠ΅ ΡΠΈΠΊΠ»Ρ ΠΏΡΠΎΠ΅ΠΊΡΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π½Π° Π½Π°ΠΈΠ±ΠΎΠ»Π΅Π΅ ΡΠ΄Π°Π»Π΅Π½Π½ΡΡ ΡΡΠΎΡΠΎΠ½Ρ ΡΡΠ΅ΡΠ³ΠΎΠ»ΡΠ½ΠΈΠΊΠ°. ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Ρ ΠΊΡΠΈΡΠ΅ΡΠΈΠΉ ΡΡΡΠ΅ΡΡΠ²ΠΎΠ²Π°Π½ΠΈΡ ΠΈ Π°Π½Π°Π»ΠΈΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠΎΡΠΌΡΠ»Ρ Π΄Π»Ρ ΠΏΡΠ΅Π΄Π΅Π»ΡΠ½ΡΡ
ΡΡΠ΅ΡΠ³ΠΎΠ»ΡΠ½ΡΡ
ΡΠΈΠΊΠ»ΠΎΠ². ΠΠΏΠΈΡΠ°Π½ΠΎ ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²ΠΎ Π½Π°ΡΠ°Π»ΡΠ½ΡΡ
ΡΠΎΡΠ΅ΠΊ ΠΏΠΎΡΠ»Π΅Π΄ΠΎΠ²Π°ΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ, ΡΡ
ΠΎΠ΄ΡΡΠ΅ΠΉΡΡ ΠΊ ΡΡΠ΅ΡΠ³ΠΎΠ»ΡΠ½ΠΎΠΌΡ ΡΠΈΠΊΠ»Ρ. ΠΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Ρ ΠΏΡΠΈΠΌΠ΅ΡΡ ΠΌΠ½ΠΎΠ³ΠΎΡΠ³ΠΎΠ»ΡΠ½ΡΡ
ΡΠΈΠΊΠ»ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΠΎΠ½ΡΡΡΠΎΠ². ΠΡΠΎΠ²Π΅Π΄Π΅Π½Ρ ΡΠΈΡΠ»Π΅Π½Π½ΡΠ΅ ΡΠ°ΡΡΠ΅ΡΡ Π΄Π»Ρ ΡΡΠ΅ΡΠ³ΠΎΠ»ΡΠ½ΠΈΠΊΠΎΠ²
Germanium Detector with Internal Amplification for Investigation of Rare Processes
Device of new type is suggested - germanium detector with internal
amplification. Such detector having effective threshold about 10 eV opens up
fresh opportunity for investigation of dark matter, measurement of neutrino
magnetic moment, of neutrino coherent scattering at nuclei and for study of
solar neutrino problem. Construction of germanium detector with internal
amplification and perspectives of its use are described.Comment: 13 pages, latex, 3 figures, report at NANP-99, International
Conference on Non-Accelerator Physics, Dubna, Russia, June 29- July 3, 1999.
To be published in the Proceeding
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