SYSTEM ANALYSIS OF TECHNOLOGICAL PROCESSES

The article discusses ways to solve engineering problems in the study of technological processes using methods of system analysis. The essence of this method is to study the technology as a cybernetic system with an assessment of the" reactions” of this system to external influences formed during an active experiment. At the same time, optimization problems are solved analytically. Analytical optimization is based on two main principles. The regression equations obtained as a result of processing experimental data and testing statistical hypotheses are models that adequately describe real processes. Each of these equations is an algebraic function of several variables, to which methods of mathematical analysis are applicable, including the study of extremums of functions in partial derivatives. The next step is to develop a process algorithm and develop computer programs that allow you to select the composition and predict the properties of the product. As an engineering interpretation, it is possible to construct optimized nomograms that allow solving both direct and inverse problems; that is, predicting the result or selecting technological factors. The research methods described in the article are implemented in the study of technologies of cellular concrete, foam concrete, cement-polymer concrete and products made of mineral wool and foam glass. As an example, the article considers the optimization of the selection of the composition of fine-grained concrete reinforced with chopped glass fiber. The implementation of the developed method allowed us to determine the optimal value of the determining parameters, including the consumption of fiber and plasticizer, as well as to form a method for studying the properties of products.

Helium-like ions in d-dimensions: analyticity and generalized ground state Majorana solutions

Non-relativistic Helium-like ions (−e, −e, Ze) with static nucleus in a d−dimensional space (d > 1) are considered. Assuming r−1Coulomb interactions, a 2-parametric correlated Hylleraas-type trial function is used to calculate the ground state energy of the system in the domain Z ≤ 10. For odd d = 3, 5, the variational energy is given by a rational algebraic function of the variational parameters whilst for even d = 2, 4 it is shown for the first time that it corresponds to a more complicated non-algebraic expression. This twofold analyticity will hold for any d. It allows us to construct reasonably accurate approximate solutions for the ground state energy E0(Z, d) in the form of compact analytical expressions. We call them generalized Majorana solutions. They reproduce the first leading terms in the celebrated 1Z expansion, and serve as generating functions for certain correlation-dependent properties. The (first) critical charge Zc vs d and the Shannon entropy S(d)r vs Z are also calculated within the present variational approach. In the light of these results, for the physically important case d = 3 a more general 3-parametric correlated Hylleraas-type trial is used to compute the finite mass effects in the Majorana solution for a three-body Coulomb system with arbitrary charges and masses. It admits a straightforward generalization to any d as well. Concrete results for the systems e− e− e+, H+2 and H− are indicated explicitly. Our variational analytical results are in excellent agreement with the exact numerical values reported in the literature.

USING A SIXTEEN-CHANNEL EEG RECORDING COMPLEX TO DETECT VARIOUS CHANGES IN THE ELECTRICAL ACTIVITY OF THE BRAIN FOR FURTHER INTERPRETATION

Проведена апробация изготовленного по материалам открытого проекта шестнадцатиканального мобильного комплекса регистрации электроэнцефалограммы (ЭЭГ). Аппаратно-программный комплекс регистрации ЭЭГ позволяет проводить регистрацию неинвазивным способом 16-ти монополярных ЭЭГ каналов, содержащих биоэлектрические сигналы головного мозга человека. Все составные элементы комплекса регистрации конструктивно расположены на шлеме-основе из твердого пластика. Шлем надевается на голову и удерживает на себе до 32-х вкручивающихся штырьковых электродов, платы электронного устройства регистрации и обработки сигналов, радиопередатчики, аккумуляторные батареи. Регистрируемые сигналы ЭЭГ в режиме реального времени передаются по радиоканалу (стандарт Wi-Fi) на ЭВМ для последующей обработки. Сигналы ЭЭГ, полученные в ЭВМ, подаются в пакет прикладных программ MATLAB для последующей обработки. Сигналы ЭЭГ в ЭВМ формируются в виде стандартных цифровых отсчетов и, соответственно, могут быть переданы в любую программу обработки данных. Сигналы ЭЭГ должны быть подвергнуты математической обработке для выявления определенных состояний головного мозга и формирования паттернов ЭЭГ, служащих ориентирами при подготовке управляющих сигналов на внешние исполнительные устройства. При математической обработке полученных сигналов был проведен анализ частотного состава ЭЭГ, проведены специальные преобразования сигналов и вспомогательные операции для идентификации необходимых паттернов ЭЭГ сигналов. В первую очередь была проведена фильтрация полученных сигналов полосовым фильтром и алгебраической функцией вейвлета Добеши 8-го уровня. Затем были собраны контрольные образцы мозговой деятельности при выполнении трех типов активностей. Обнаружена корреляция между экспериментами и контрольными образцами. Сделанные наработки могут быть использованы для упрощения установки входных параметров искусственных нейронных сетей, применяемых для обработки и анализа сигналов ЭЭГ We carried out the approbation of a sixteen-channel mobile EEG registration complex made based on the materials of an open project. The hardware and software complex for EEG registration allows for non-invasive registration of 16 monopolar EEG channels containing bioelectric signals of the human brain. All the components of the registration complex are structurally located on a helmet-based made of hard plastic. The helmet is put on the head and holds up to 32 screw-in pin electrodes, boards of an electronic device for recording and processing signals, radio transmitters, and batteries. The recorded EEG signals are transmitted in real time via a radio channel (Wi-Fi standard) on a computer for subsequent processing. The EEG signals received in the computer are fed into the MATLAB application software package for subsequent processing. The EEG signals in the computer are formed in the form of standard digital samples and, accordingly, can be transmitted to any data processing program. EEG signals should be subjected to mathematical processing to identify certain states of the brain and form EEG patterns that serve as guidelines for the preparation of control signals to external actuators. During the mathematical processing of the received signals, we analyzed the frequency composition of the EEG, special signal transformations and performed auxiliary operations to identify the necessary EEG signal patterns. First of all, we filtered the received signals by a bandpass filter and an algebraic function of the Daubechy wavelet of the 8th level. Then, we collected control samples of brain activity when performing three types of activities. We found a correlation between the experiments and the control samples. It can be developed to be used to simplify the installation of input parameters of artificial neural networks used for processing and analyzing EEG signals

IDENTIFICATION OF STUDENT ERRORS IN SOLVING DERIVATIVE PROBLEMS IN SMA NEGERI 3 PALANGKA RAYA

This study aims to find out: (1) students' mistakes in solving problems derived from algebraic functions, and (2) the causes of studenterrors. This research is qualitative descriptive research, conducted in October until November 2020. The subjects in this study were 37 students of grade XI MIPA 3 SMA Negeri 3 Palangka Raya. Next, 3 students are selected for the interview, to find out why the student made a mistake. The instrument in this study consists of 5 test questions in the form of descriptions used to determine the type of mistakes made by students. Based on the results of the study, the types of mistakes made by students solve the problem of AlgebraIc Function Derivatives are: errors in facts, concepts, operations and principles Factors that cause students to make mistakes in solving problems derived from algebraic functions based on aspects of errors in understanding facts, concepts, operations and principles that contain students' knowledge of materials that have been learned from simple to difficult then students' memories of the concept of limits, root concepts and concepts of inverse , lack of ability to understand students to the material that has been studied such as understanding the concept of limit, root concept and concept of inverse. lack of ability to decipher material or apply material that has been studied in new situations and concerns the use of rules or principles such as applying the concept of limit, root concept, inverse concept and operating numbers.

Modulation Instability Analysis of a Nonautonomous (3+1)-Dimensional Coupled Nonlinear Schrödinger Equation

We investigate the modulation instability (MI) analysis of a nonautonomous (3+1)-dimensional coupled nonlinear Schrödinger (NLS) equation with time-dependent dispersion and phase modulation coefficients. By employing standard linear stability analysis, we obtain an explicit expression for the MI gain as a function of dispersion, phase modulation, perturbation wave numbers and an initial incidence power. The nonautonomous coupled NLS equation is found to be modulationally unstable for the same sign of dispersion and phase modulation coefficients. This equation is modulationally stable for zero dispersion and or phase modulation coefficients. But non-zero dispersion coefficient, it is modulationally stable/unstable on distinct bandwidth of wave numbers. The trigonometric, exponential, algebraic function of time and constant have been chosen as test functions for dispersion and phase modulation to find the effect on the MI analysis. The effect of focusing and defocusing medium on the MI analysis has also been investigated. The MI bandwidth in the focusing medium is found to be larger than defocusing medium. It is found that the modulation instability of the equation can be managed by proper choice of the dispersion and phase modulation parameters.

An Error Analysis of Students’ Difficulties in Differential Calculus

This study aims to describe the types of mistake and causes of the XI grade students of SMA Negeri 31 Jakarta TP. 2019/2020 made a mistake in solving the problem of an algebraic function derivative application. The method of this research is a qualitative descriptive study. The data was obtained by conducting tests and interview online. The respondents were drawn from 6 XI class in SMA Negeri 31 Jakarta. Each student's work was analyzed to describe the types of mistakes using the Newman analysis procedure, then an interview was conducted to describe the factors that caused students to make mistakes. Based on the results of the study, it can be concluded that the types of mistakes found when students solve problems in the application of algebraic function derivatives are 1) reading mistakes, that is, incorrectly writing the functions listed in the questions, 2) mistakes in understanding, in the form of misinterpreting what is known and asked about, 3) transformation mistakes, in the form of students' inability to choose procedures to solve problems appropriately, 4) process skill mistakes, in the form of incomplete student work, miscalculation, 5) conditioning mistakes, in the form of students' inability to show the final answer. The contributing factors are that students do not understand the derivative application material of algebraic functions, students are in a hurry to solve the problems, different types of questions given are different from the questions exemplified by the teacher, and rarely make conclusions at the end of the answer. Keywords: analysis of mistakes, newman procedure, application of derivative algebraic functions.