Mathematical Calculations Research Articles

Prospect of developing a hydrogenic deposit Semizbay

Relevance. The fact that hydrogenic deposits are developed using combined technologies, and the criteria for combining technologies have not been sufficiently developed. Aim. To select the optimal method of deposit development, taking into account the characteristics of the uranium ores composing it. Objects. The Semizbai sandstone deposit, which lies in loose sedimentary rocks, is localized within a 36 km long section with a width of 10 km. Methods. Analysis of the theory and practice of field development, finding dependencies between operational indicators, modeling, methods of mathematical statistics, technical and economic calculations and approbation of some provisions. Results. The authors have given characteristic of systems for developing hydrogenic deposits and substantiated the necessity of combining metal extraction technologies by leaching with traditional technologies in the conditions of the deposit. Alternative technologies for metal leaching using interacting wells and with metal leaching in a pile are detailed. The mechanism and differences in the conditions of uranium leaching in a quicksand array and in a heap was clarified. The authors have carried out comparative characteristic of alternative options for field development, indicating, among other things, their advantages and disadvantages. It was determined that leaching parameters depend on speed and efficiency of opening new reaction areas with a different mechanism for removing uranium from mineral particles. It is proved that the efficiency of the development of hydrogenic deposits is increased by combining the processes of borehole hydro extraction of ores and heap leaching of metals. The authors proposed the model of decision-making sequence with an arbitrary source of information based on the criterion of discounted profit from mining. Conclusions. The results of the study may be in demand when revaluing reserves, modernizing systems for the development and optimization of methods for managing the quality of mining products. The recommended methods of monitoring the combined development of hydrogenic deposits contribute to increasing the completeness of subsurface use.

An Extremely Close Vibration Frequency Signal Recognition Using Deep Neural Networks

This study proposes the utilization of an optical fiber vibration sensor for detecting the superposition of extremely close frequencies in vibration signals. Integration of deep neural networks (DNN) proves to be meaningful and efficient, eliminating the need for signal analysis methods involving complex mathematical calculations and longer computation times. Simulation results of the proposed model demonstrate the remarkable capability to accurately distinguish frequencies below 1 Hz. This underscores the effectiveness of the proposed image-based vibration signal recognition system embedded in DNN as a streamlined yet highly accurate method for vibration signal detection, applicable across various vibration sensors. Both simulation and experimental evaluations substantiate the practical applicability of this integrated approach, thereby enhancing electric motor vibration monitoring techniques.

THE TRAVELING WAVE SOLUTIONS OF THE CONFORMABLE TIME-FRACTIONAL ZOOMERON EQUATION BY USING THE MODIFIED EXPONENTIAL FUNCTION METHOD

The present study focuses on the acquisition of traveling wave solutions associated with the conformable time-fractional Zoomeron equation through the utilization of the modified exponential function method (MEFM). The solution functions derived from mathematical computations encompass hyperbolic, trigonometric, and rational functions. Various graphical representations, such as 2D, 3D, contour graphs, and density graphs, are utilized to visually depict the distinct features of the solution functions derived from the determination of suitable parameters.

Effect of active and passive techniques used in thromboembolic prophylaxis on venous flow velocity in the post-procedure period.

Studies have shown that using mechanical thromboembolic prophylaxis methods speeds up venous flow and decreases stasis. These studies examine the post-intervention period of 1-10min. The length of the effect of procedures to raise venous flow velocity cannot be determined by clinical trials. To apply mathematical techniques to estimate how long mechanical thromboembolism prophylaxis procedures will increase venous flow rate. In the survey, we examined 25 persons (poststroke patients), with an average age of 57.2 ± 6.3 years. Regarding the proportion of genders, 13 (52%) participants were male and 12 (48%) female. The peak venous blood flow velocity was measured with a HADECO BIDOP ES-100V II type Doppler ultrasound device, using an 8MHz head, in the femoral vein, at the level of the hip joint. We estimated the change of the venous blood flow velocity from the available sampled data using the method of least squares. For the calculations, we used Microsoft Excel, version Mac Excel 2019. The decrease in peak venous flow velocity can be approximated by a logarithm function. Mathematical calculations show that after active thromboembolic prophylaxis interventions, resting venous flow velocity is restored at 26.8min on the intact limb and 85.1min on the hemiparetic side. Resting flow velocity is restored in 131.9min after passive mobilization of the hemiparetic side and in 137.7min after the consensual effect. An elementary mathematical function can be used to estimate the time to recovery of peak venous flow velocity to resting state from measurements taken 15min after the intervention. Active and passive mechanical thromboembolic prophylaxis after the intervention has a longer-term effect on venous flow velocity.

Analysis of the shear stresses in a filling line of parenteral products: The role of sterilizing filters

This study investigates the impact of shear stress on protein-based parenteral drug products, particularly during the filling process, with a focus on the filtration unit. A 3D computational replica of a real sterilizing filter was developed using a stochastic geometry generation methodology, able to replicate realistic values of permeability, porosity, and pore size distribution. Computational Fluid Dynamics simulations were employed to analyze fluid dynamics within the filtration unit. The evolution of shear stress for massless tracers was examined to assess average shear stress in the sterilizing filtration unit. The results provide insights into shear stress dynamics and suggest potential scale-down strategies for industrial applications. The presented analysis is novel compared to most estimations of shear stress in sterilizing filtration units, which generally rely on mathematical calculations.

A panel discussion on AI for science: the opportunities, challenges and reflections.

Artificial intelligence (AI) tools are changing the way we do science. AlphaFold basically solved the conundrum of protein structure prediction; DeepMD greatly improved the efficiency and accuracy of molecular simulations; and the emerging large language models such as ChatGPT are opening up more possibilities for scientific applications. In this panel, five experts from China and the US discussed the concept, development, bottlenecks and opportunities of AI for Science (AI4S), as well as their understanding of the relationship between AI and science. Roberto Car Professor at Department of Chemistry, Princeton University, USA Weinan E Professor at School of Mathematical Sciences, Peking University, China; AI for Science Institute, Beijing, China David Srolovitz Professor at Department of Mechanical Engineering, University of Hong Kong, China Han Wang Professor at the Institute of Applied Physics and Computational Mathematics, Chinese Academy of Sciences, China Linfeng Zhang (Chair) Chief scientific officer of DP Technology, China; AI for Science Institute, Beijing, China.

Influence of the DC frequency limit controller on the frequency characteristics of the multi-area asynchronous interconnected power grid with renewable energy integration

To systematically analyze the impact of the DC frequency limit controller (FLC) configuration scheme on the frequency characteristics of asynchronous interconnected power grids with renewable energy integration, a comprehensive frequency analysis model for three-area asynchronous interconnected power grids including the FLC is proposed. The model is based on the SFR model considering renewable energy integration and includes a simplified model of the DC FLC. A rigorous validation of the rationality and stability of the model is achieved through detailed mathematical calculations and pole-zero analysis. Taking the local power grids as an example, the established model is used to study the difference between single- and double-sided configuration of the DC FLC, the relationship between the increase in the renewable energy penetration rate and the frequency characteristics of each regional power grid, and the influence of DC FLC configuration on the maximum acceptance ratio of renewable energy. Through data comparison and theoretical analysis, the influence of FLC configuration on the frequency characteristics of each region of the asynchronous power grid under renewable energy integration is obtained. The results show that the configuration of a bilateral FLC on the DC line has more advantages in alleviating the complementary power disturbance at both ends and obvious limitations on the non-complementary power disturbance at both ends. Compared with the configuration of the bilateral FLC, the configuration of a unilateral FLC on the weak grid has a larger proportion of renewable energy acceptance. When the DC FLC power transmission capacity is sufficient, the weak grid and the adjacent two asynchronous grid DC tie lines are configured with a single-sided FLC, and the weak grid is theoretically connected to the renewable energy penetration rate of up to 100%.

How to Protect Copyright Data in Optimization of Large Language Models?

Large language models (LLMs) and generative AI have played a transformative role in computer research and applications. Controversy has arisen as to whether these models output copyrighted data, which can occur if the data the models are trained on is copyrighted. LLMs are built on the transformer neural network architecture, which in turn relies on a mathematical computation called Attention that uses the softmax function. In this paper, we observe that large language model training and optimization can be seen as a softmax regression problem. We then establish a method of efficiently performing softmax regression, in a way that prevents the regression function from generating copyright data. This establishes a theoretical method of training large language models in a way that avoids generating copyright data.

Evaluating the impact of material service life on embodied energy of residential villas in the United Arab Emirates

PurposeRecently, there has been a shift toward the embodied energy assessment of buildings. However, the impact of material service life on the life-cycle embodied energy has received little attention. We aimed to address this knowledge gap, particularly in the context of the UAE and investigated the embodied energy associated with the use of concrete and other materials commonly used in residential buildings in the hot desert climate of the UAE.Design/methodology/approachUsing input–output based hybrid analysis, we quantified the life-cycle embodied energy of a villa in the UAE with over 50 years of building life using the average, minimum, and maximum material service life values. Mathematical calculations were performed using MS Excel, and a detailed bill of quantities with >170 building materials and components of the villa were used for investigation.FindingsFor the base case, the initial embodied energy was 57% (7390.5 GJ), whereas the recurrent embodied energy was 43% (5,690 GJ) of the life-cycle embodied energy based on average material service life values. The proportion of the recurrent embodied energy with minimum material service life values was increased to 68% of the life-cycle embodied energy, while it dropped to 15% with maximum material service life values.Originality/valueThe findings provide new data to guide building construction in the UAE and show that recurrent embodied energy contributes significantly to life-cycle energy demand. Further, the study of material service life variations provides deeper insights into future building material specifications and management considerations for building maintenance.

Retracted: Considering Computational Mathematics IGHG3 as Malignant Melanoma Is Associated with Immune Infiltration of Malignant Melanoma.

[This retracts the article DOI: 10.1155/2022/4168937.].

Mathematical formulation and computation of the dynamics of blood flow, heat and mass transfer during MRI scanning

Computational modeling of arterial blood flow, heat and mass transfer during MRI scanning is studied. The flow is assumed to be unsteady, in-compressible, and asymmetric. Mathematical formulation considers the presence of stenosis, joule heating viscous dissipation and chemical reaction. The explicit finite difference scheme is used to numerically solve the model equations. The MATLAB software was used to plot the graphical results. The study reveals that, during MRI scanning, both radial and axial velocities diminish with increase in the strength of magnetic fields. Besides, the study found that, Eckert number and Hartman number enhance the blood’s temperature and the same, diminishes with increase in Prandtl and Reynolds numbers. Concentration profile is observed to decline with increase in chemical reaction parameter, Schmidt number and Reynolds number. Soret number on the other hand, is observed to positively influence the concentration.

Justification of range limits of root spray angle of an adaptive spraying device

BACKGROUND: Oscillations of the sprayer field boom in the transverse-vertical plane causes a decrease in the quality of the technological operation. This is especially true in relation to the operation of small-sized single-support barrow-type sprayers. One of the possible solutions to compensate the effect of transverse oscillations of the boom on the quality of spraying is the use of adaptive sprayers with a variable root angle of the spray jet, responding to the position taken by the sprayer in relation to the surface being treated. AIM: Justification of the necessary limits for changing the spray angles of an adaptive sprayer for a single-support spraying device. The novelty of the research lies in the fact that insufficient attention is paid to the implementation of technologies using means of small-scale mechanization, unlike industrial agricultural machinery. METHODS: A prototype of a single-support boom motor sprayer was used as the study object. The field experiment was carried out at the experimental area of the Oryol State Agrarian University. Data acquisition on the deviation of the sprayer from the vertical axis was carried out using a specially developed angle gauge. A spreadsheet processor in the Microsoft Excel environment was used to perform mathematical processing of the decrypted experimental data. The study of the obtained analytical dependencies was carried out in the environment of the Mathcad 14.0 mathematical calculation system. RESULTS: It has been experimentally found that the maximum deviations of the sprayer from the vertical can be up to 30° during operation. At the same time, the average amplitude of the transverse operating oscillations of the boom of a single-support barrow-type boom sprayer ranges from +11° to -18°. The amplitude of the transverse oscillations of a single-support sprayer depends on the operator’s skills and the unit motion velocity. Balancing the sprayer is important due to the moment of force caused by the weight of the one-sided field boom. A formula for calculation of the spray width of one sprayer, taking into account the geometric parameters of a single-support sprayer, as well as its inclination angle in the transverse-vertical plane, has been derived. An analytical relationship that makes it possible to calculate the required limits of the root angle of the spray jet of an adaptive sprayer, taking into account the installation distance of the sprayer relative to the vertical plane passing through the support point of the sprayer, has been obtained. The values of the root spray angles for the deflectors of adaptive sprayers, with the sprayer oscillations amplitude from -18° to +11° in the transverse-vertical plane, were found. CONCLUSIONS: The practical value of the study lies in the potential of using the formula to determine the range limits of root spray angles when designing and developing adaptive sprayers.

Digitalization of Physics Teaching: Using Computer Models and Animations

The article analyzes current trends in the introduction of information technologies into the physics teaching process – the use of computer modeling and visualization to improve the efficiency of mastering complex physical material by students. The relevance of the work is due to the importance of using innovative digital teaching tools in the context of the rapid modernization of education. Using the example of modeling the discharge of a capacitor through a resistor, the technique of creating mathematical computer models with software implementation in Python and graphical visualization using Matplotlib is examined in detail. Various approaches to computer animation (multi-screen, fragmentary, elemental, figurative) are considered for presenting dynamic systems. Specific examples of animation of physical processes are given. The systematic technique of developing interactive electronic posters for teaching physics is highlighted. Methodological recommendations for the use of computer models in different types of lessons and at different stages of the educational process are formulated. The materials of the article are addressed to physics teachers, methodologists and specialists in the field of modern educational technologies. The article provides a methodological rationale for the feasibility of introducing information and communication technologies into physics teaching, analyzes various approaches to computer modeling and visualization, and examines specific examples and stages of creating animation and modeling tools for schoolchildren.

Исследование способа измерения артериального давления ёмкостным интегрированным датчиком

A method of wireless measurement of blood flow parameters is investigated using an implantable passive capacitive sensor and an external reader. This device is designed to measure the parameters of blood flow in the human body, through the installation of a passive capacitive sensor and inductive coupling with an external reader device. The method of wireless measurement is based on the connection of resonant circuits at an operating frequency of 10 MHz. The mathematical calculation of the device circuit is presented. The result of the calculation was the dependence of the output voltage of the external reader on the change of capacitance in the implanted passive sensor. The values of the potential sensitivity of the device are obtained. The manufactured layout of the device and its parameters are presented. The mock-up allowed to investigate the dependences of the coupling factor of the circuits when using coils of an external reader of different sizes. Also the measurement of the output voltage of the external reader from the value of the passive sensor capacitance was made. The value of real sensitivity of the device layout was measured.

PREDICTION OF TEMPERATURE DISTRTBUTION INFLEXIBLE PAVEMENTS

In the present study, finite difference method is proposed to use for the development of Mathematical model for the prediction of the pavement temperature distribution (PPTD) in flexible pavement.To simpli$ the mathematical calculation, Visual Basic language was selected to perform a progam that has a capability fc.: the Prediction of Pavement Temperature as a function of depth and time. To test its accuracy, the program was applied to predict the pavement temperature distribution on specific location in section (R12) from the Expressway No.l in Iraq. The output of this program appears to be in good agreement with the (R12) observed data. Therefore the program can be recognized for use in the prediction of the asphaltic pavement temperature distribution

An improved algorithm for the estimation of the root mean square value as an optimal solution for commercial measurement equipment

This paper demonstrates that direct changes in the algorithm for the estimation of the root mean square value of a voltage signal of an arbitrary waveform can lead to improved performances and lower measurement uncertainty of commercially available instruments without requiring any upgrade of their existing hardware. The research conducted and presented here is an original contribution to the development of estimation techniques and mathematical models for measurement oriented purposes regardless of the number of samples in the given period relying on mathematical calculation of the equal complexity as in the methods already in use. The theoretical approach examines the problem of numerical integration focusing on modified Simpson's 1/3 rule and modified Simpson's 3/8 rule used for the purpose of the estimation of the root mean square value when a small number of samples per period is available. It highlights the limitations of Simpson's 1/3 rule and Simpson's 3/8 rule, and shows that the newly proposed algorithm is optimal with respect to measurement accuracy and precision even in cases when the ratio of the sampling frequency and the signal's fundamental frequency is low. All theoretical results have been validated experimentally.

Clinical and economic analysis of the application of the method of three-dimensional reconstruction of lung tissue in the practice of tuberculosis institution

Background. The use of clinical and economic analysis in practical healthcare allows for a more rational use of the resources allocated by the state and contributes to the achievement of optimal indicators in terms of the quality of disease identification and the effectiveness of its treatment.
 Aim. To conduct a clinical and economic analysis of the prospects for introducing the 3D lung reconstruction method into tuberculosis practice, which is used to correct the level of adherence, reduce the severity of symptoms of anxiety and depression, and increase the effectiveness of chemotherapy.
 Materials and methods. In this scientific work, the results of treatment (more than 90 people) of newly diagnosed patients with destructive pulmonary tuberculosis, which were observed in the Nizhny Novgorod Regional Clinical Tuberculosis Dispensary, were used. The patients were divided into two groups. For the 1st group of patients, tactile lung models were made, among them a questionnaire was conducted using the MMAS-4 questionnaire and the HADS scale. For patients of the 2nd group, lung models were not made, and no survey was conducted. Each group was assessed the effectiveness of chemotherapy. Clinical and economic analysis of the cost of introducing the method of three-dimensional lung reconstruction into tuberculosis practice was carried out on the basis of two evaluation criteria «cost – effectiveness» and «cost-effectiveness increment» with additional mathematical calculations of the necessary indicators. The results obtained were compared with the existing known method of increasing adherence to tuberculosis treatment - the issuance of food packages.
 Results. Based on the results of the study, it was proved that the use of tactile models of the lungs in phthisiatric practice is more than 8 times cheaper than the method of issuing food kits with, in fact, comparable results of treatment effectiveness. If there is a need to increase the effectiveness of the treatment of tuberculosis patients by increasing the subsidy of food packages, the cost of one additional percent of efficiency is not economically viable.
 Conclusion. The clinical and economic analysis of the prospects for introducing the method of three-dimensional lung reconstruction into phthisiatric practice presented in the paper looks promising, which is confirmed by the performed mathematical calculations and comparisons, and can be recommended for use in the routine practice of phthisiatricians to correct the level of adherence of tuberculosis patients to chemotherapy, reduce the severity symptoms of anxiety and depression, as well as an increase in the effectiveness of treatment.

Quantifying distortion in time-correlated single photon counting: a universal parameter.

One major drawback of the classic time-correlated single photon counting (TCSPC) technique is pileup-related distortion. To keep it under a reasonable level, the maximum count rate has to be reduced, posing a serious limitation to the overall measurement speed. This means that there is an intrinsic trade-off between speed and distortion: either count rate is raised, but distortion is worsened, or distortion is minimized at the expense of speed. In both cases, it is impossible to precisely evaluate the degree of distortion introduced. Here comes our new, to the best of our knowledge, figure of merit, which is able to provide a numerical estimate of the distortion whatever the signal shape is, marking a real turning point in the way of doing TCSPC. In this article, this new parameter will be defined and its effectiveness will be demonstrated by means of mathematical computations.

Classification of optical coherence tomography images using deep machine learning methods

Backgraund. Optical coherence tomography (OCT) is a modern high-tech and informative method for detecting pathology of the retina and preretinal layers of the vitreous body. However, the description and interpretation of the research results require high qualifications and special training of an ophthalmologist, and significant time expenditure for the doctor and the patient. At the same time, the use of mathematical models based on artificial neural networks (ANN- models) currently makes it possible to automate many processes associated with image processing. Therefore, solving problems associated with automating the process of classifying OCT images based on ANN models is actual.
 Aims. To develop architectures of mathematical (computer) models based on deep learning of convolutional neural networks (CNN) for classification of OCT images of the retina. To compare the results of computational experiments conducted using Python tools in the Google Colaboratory with single-model and multi-model approaches and evaluate classification accuracy. To make conclusions about the optimal architecture of ANN models and the values of the hyperparameters used.
 Materials and methods. The original dataset, which was anonymized OCT images of real patients, included more than 2000 images obtained directly from the device in a resolution of 1920 × 969 × 24 BPP. The number of image classes is 12. To create the training and validation data sets, a subject area of 1100 × 550 × 24 BPP was “cut out.” Various approaches were studied: the possibility of using pretrained CNNs with transfer learning, techniques for resizing and augmenting images, as well as various combinations of hyperparameters of ANN-models. When compiling the model, the following parameters were used: Adam optimizer, categorical_crossentropy loss function, accuracy metric. All technological processes with images and ANN-models were carried out using Python language tools in Google Colaboratory.
 Results. Single-model and multi-model principles for classifying OCT images of the retina are proposed. Computational experiments on automated classification of such images obtained from a DRI OCT Triton 3D tomograph using various ANN model architectures showed an accuracy of 98-100% during training and validation and 85% during an additional test, which is a satisfactory result. The optimal architecture of the ANN model - a six-layer convolutional network - was selected and the values of its hyperparameters were determined.
 Conclusions. The results of deep training of convolutional neural network models with various architectures, their validation and testing showed satisfactory classification accuracy of retinal OCT images. These developments can be used in decision support systems in the field of ophthalmology.

Mathematical digital quantum computation by means of much more logical skills

We expand Deutsch’s algorithm for determining the mappings of a logical function using four orthogonal states. Using this, we propose a parallel computation for all of the combinations of values in variables of a logical function using sixteen orthogonal states. As an application of our algorithm, we demonstrate two typical arithmetic calculations in the binary system. We study an efficiency for operating a full adder/half adder by quantum-gated computing. The two typical arithmetic calculations are (1+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(1+1)$$\\end{document} and (2+3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(2+3)$$\\end{document}. The typical arithmetic calculation (2+3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(2+3)$$\\end{document} is faster than that of its classical apparatus which would require 43=64\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4^3=64$$\\end{document} steps when we introduce the full adder operation. Another typical arithmetic calculation (1+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(1+1)$$\\end{document} is faster than that of its classical apparatus which would require 42=16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4^2=16$$\\end{document} steps when we introduce only the half adder operation.