Mathcad Prime Research Articles

Postsurgical pain intensity in children on the VAS and FLACC scale across various analgesic techniques. Mathematical prediction as a component of justification

Nowadays, in pediatric practice, the Visual Analogue Scale (VAS) and the Face, Legs, Activity, Cry, Consolability (FLACC) scale are effective for assessing postsurgical pain. The modern concept of pain management includes a multimodal approach, including regional analgesia techniques. The aim of the study was to present a mathematical model to assess the efficacy of regional analgesia techniques in managing postsurgical pain intensity on the VAS and FLACC scale up to the fifth day of the study and predict the behaviour of the experimental data function up to day 87 following surgery using the autoregressive probability model. Materials and Methods. 89 patients operated on the anterior abdominal wall were divided into 3 groups depending on the type of anesthesia. The assessment of pain management quality and the presence of acute pain was conducted using the VAS and FLACC scale on days 1, 2, 3, and 5 post-operatively in all children. The ‘predict’ function in РТС MathCad Prime 7.0. software was used to automate calculating predictions based on the Burg method. Results. Studying the efficiency of the proposed treatment using regional analgesia techniques versus conventional analgesia enabled the prediction of varying postsurgical pain intensities on the VAS and FLACC scale based on their mathematical models, with coefficient of determination R2=0.9876, R2= 0, 9827, R2=0.9952 for the FLACC scale and R2=0.9868, R2=0,915, R2=0.9774 for the VAS. Conclusions. The use of regional analgesia techniques in children undergoing anterior abdominal wall surgery has been confirmed to be associated with a significant reduction in postsurgical pain intensity to the fifth day of observation and predicted to remain so up to day 87

MATHEMATICAL PREDICTION OF CHANGES IN THE LEVELS OF CD40-CD40L TRANSMEMBRANE PROTEIN SYSTEM ACROSS DIFFERENT ANALGESIA TECHNIQUES IN CHILDREN

The impact of the CD40-CD40L on the development of non-communicable neurological conditions is determined by abnormal CD40 expression and may be detrimental to nervous tissue function. Pain is one of the earliest psychophysical functions to develop. Postoperative complications causing pain should be addressed immediately. Regional analgesia techniques can speed up children’s recovery and reduce the need for opioids. They can also lower the incidence of postoperative nausea and vomiting, respiratory complications, and postsurgical pain intensity.The aim of this study was to present a mathematical model that predicts changes in CD40-CD40L levels in children who underwent surgery under various analgesic modalities within the fi rst fi ve days postoperatively. The autoregressive probability model was used to predict the behavior of the experimental data function within 29 days after surgery.Material and Methods. The children were divided into three groups. Group I consisted of 33 children who underwent anterior abdominal wall surgery under general anesthesia with morphine. Group II comprised 27 children who underwent anterior abdominal wall surgery under general anesthesia with the transversalis fascia plane block (TFPB). Group III included 27 children who underwent anterior abdominal wall surgery under general anesthesia with the TFPB, combined with the quadratus lumborum block 4 (QLB-4) via a single injection. The serum CD40L levels were evaluated using the immunoenzymatic assay method. The autoregressive model method based on the Burg algorithm was used to predict the behavior of the experimental data function. To automate the calculation of predictions based on the Burg method, the ‘predict’ function in РТС MathCad Prime 7.0 software was used. All clinical and laboratory studies were conducted in accordance with the World Medical Association Declaration of Helsinki ‘Ethical Principles for Medical Research Involving Human Subjects’. The study is a fragment of the research project of the Department of Children Diseases of Postgraduate Medical Education Faculty, Ivano- Frankivsk National Medical University «Health Status and Adaption of Children from the Precarpathian Region with Somatic Diseases, Their Prevention» 2021-2026, state registration number 0121U111129.Results. On the fi fth day after surgery, the serum CD40-CD40L levels were highest in children who received conventional opioid analgesia. There was no signifi cant diff erence observed between children in the TFPB and TFPB+QLB groups. On the 29th day after surgery, the predicted CD40-CD40L levels were lowest in children who received conventional opioid analgesia combined with the TFPB+QLB.Conclusions. The fi ndings obtained confi rmed the positive eff ect of combined analgesia using opioids and regional nerve block TFPB+QLB in children who received anterior abdominal surgery on suppressing immune mechanisms of pain syndrome involving the CD40-CD40L signaling system.

A Synthesis Method of Open-Chain Coupled Serial Linkage Mechanism Fusing Trajectory and Posture

In order to meet the motion characteristics requirements of multi-objective fusion of execution components, a synthesis method of open-chain coupled serial linkage mechanism fusing trajectory and posture is proposed. According to periodic change characteristics of the execution component trajectory and posture of the linkage mechanism, the motion characteristics equation including trajectory and posture information is established by using Fourier series. The harmonic parameters of the link trajectory and posture are calculated according to the principle of discrete Fourier transform. The complex vector theory is applied to determine the functional relationship between the harmonic parameters of the trajectory and posture and the independent variable of the linkage mechanism, and furthermore the motion synthesis equation of the open-chain linkage mechanism fusing trajectory and posture information is established. The linkage mechanism parameters are calculated using Mathcad Prime software. The single-degree-of-freedom open-chain coupled serial linkage mechanism fusing trajectory and posture information is obtained by using a noncircular gear planetary gear train to couple the connection points of the linkage mechanism. The correctness of the method is verified through an example.

Influence of parameters of a screw dispenser on its dosing accuracy

BACKGROUND: Strict observance of the number of individual components in the total mass of the feed mixture is necessary in the production of compound feeds. In this aspect, the process of components dosing, performing automatically in modern conditions, has a special role. The paper considers the process of feed components dosing with a screw dispenser, which has a number of advantages over other types of dispensers when supplying bulk feed components. However, its main disadvantage is low accuracy due to the presence of a certain amount of free-falling material. The paper describes theoretical studies that help to adjust the operation of screw dispensers in further. AIMS: Defining the influence of the design features and operating mode of the dispenser, as well as the physical and mechanical properties of the feed components on the mass of the attachment. METHODS: The mathematical methods based on physical laws are used in the study. The Mathcad Prime 6.0 computer mathematics system was used for conducting the computational experiment. RESULTS: As a result of the conducted research, the dependence of the amount of the free-falling material on the height of the fall, the material supply and the velocity of the material particles hovering has been studied. At the same time, it was found that with an increase in the height of the fall, the amount of material in the fall increases exponentially. When dosing components with different physical and mechanical properties at fixed values of the material supply and the fall height, a greater number of free-falling components with a lower soaring speed are observed. CONCLUSIONS: The study is reasonable to use when weighing small appendages up to 500 g for various kinds of additives. The obtained results of the study will help to adjust the dispenser control program.

Application of Thermodynamic Models to Predict the Solubility of Biologically Active Substances

Introduction. The choice of solvents for the processes of extraction of biologically active substances from natural raw materials, the processes of purification of natural and synthesized substances by extraction, crystallization and dissolution methods is an important problem of the modern pharmaceutical industry, because a large number of experiments must be performed to determine the optimal solvent or mixture of solvents. To reduce the cost of developing and optimizing the extraction and purification of substances stages, it is proposed to use thermodynamic models at the stage of preliminary solubility assessment. The article investigates predicting the solubility of pharmaceutical substances issue on the example of the technology for isolating hesperidin and glycyrrhizic acid from plant materials.Aim. Theoretical determination of the dissolving power of various solvents with respect to hesperidin and glycyrrhizic acid.Materials and methods. The PMUNIFAC and NRTL-SAC thermodynamic models were used to predict solubility. The solubility calculation for the NRTL-SAC model was performed using Aspen Properties V14 software, and for the PMUNIFAC model using PTC Mathcad Prime V6. To evaluate the results obtained using thermodynamic models, a number of experiments were carried out, the object of which was the peel of an orange (dried flavedo and albedo, the degree of grinding is 0.2–0.5 mm, the moisture content is 8 %). The quantitative content of hesperidin was determined by direct spectrophotometry at a wavelength of 290 nm. Statistical data processing was performed using Minitab v20 software (Minitab Inc., USA), differences were considered statistically significant at p < 0.05.Results and discussion. On the basis of thermodynamic models, the prediction of the solubility of hesperidin and glycyrrhizic acid was made. It has been shown that the solubility can be assessed both in the presence of solubility data according to the NRTL-SAC model, and in their complete absence according to PMUNIFAC. The correspondence of the theoretically calculated data to the experimental data confirms the correctness of the calculations of thermodynamic models. The results of the calculations are evaluated and solvents are recommended that can be used in the technology of isolating hesperidin and glycyrrhizic for the stages of degreasing, extraction and crystallization with the antisolvent.Conclusion. Using the NRTL-SAC and PMUNIFAC thermodynamic models, the dissolving power of various solvents with respect to hesperidin and glycyrrhizic acid was determined. From the calculation results, a list of solvents was built, ranked by the solubility of the studied substances in them. The resulting list can be used in the development of an industrial technology for the isolation and purification of hesperidin and glycyrrhizic acid. It is shown that the NRTL-SAC and PMUNIFAC models have good prospects for quantitative prediction of the solubility of active substances.

RESEARCH OF OPTIMAL TECHNOLOGICAL SEQUENCES IN THE ORGANIZATION OF CONSTRUCTION PRODUCTION

The article discusses some problems of economics and organization of construction, which can be solved by linear programming using PTC Mathcad Prime, Excel Microsoft365 and data ranking. The authors analyzed the literature, which presents the existing optimization methods in various industries and the field of construction production. Shows the basic principles of using linear programming in various software tools. The authors analyzed in detail the comparison of different methods for the selection of optimal technological sequences. Examples of solving optimization problems in construction production by means of linear programming and data ranking method are presented. To solve the problem, the technology of applying the mixture to a vertical surface was used. Namely: cleaning the facade, plastering the surface, painting the surface. Three technologies were considered. For applying to a vertical surface using standard equipment are scaffolding, ladders and cradles. The process flow consists of the following processes: This is surface preparation. It can be performed in three ways: manual cleaning, sandblasting apparatus, hydrojetting. The next process is the technology of plastering the surface. At this stage, two options are considered: manual plastering and mechanized plaster application. Next, you perform a surface grouping process. This process can be performed either manually or using a pulvelizer. And the last process is painting the surface. Considered manual painting or mechanized device. The next step was to analyze the possibilities of each of the optimization search methods and provide recommendations for their possible application in solving similar problems. Created a mathematical model that can be scaled to implement optimization search in groups of technological sequences with different methods of work. Conclusions were also made regarding the use of the presented methods in solving similar problems of construction production.This article may be an analog for calculating not only the mechanization processes, but it may become a meeting for automating the construction processes.

Research of the dynamics of the process of excavating the soil with the additional slope board of the bulldozer on the caterpillar track

The purpose of the research is to determine the conditions for maintaining the course stability of the bulldozer on the caterpillar track (hereinafter referred to as the term "caterpillar") in the process of excavating the soil with the slope board. The paper presents mathematical model of the process of operation of the caterpillar bulldozer with the slope board, taking into account its main parameters: 1) parameters of the slope board and its installation angles; 2) parameters of the base machine; 3) dynamic parameters of the bulldozer with the slope board; 4) parameters of the soil. Based on the developed model, using the computer modelling method in Mathcad Prime 3.0 program, a hodograph of the maximum force applied on the slope board of the caterpillar bulldozer was built, which made it possible to determine the maximum allowable force applied on the slope board, taking into account the retention of the course stability.

Ecological plasticity and stability of cabbage crop ptoductivity as affected by method of sowing

Purpose. To establish the peculiarities of the formation of ecological plasticity and productivity stability of winter cabbage crops as affected by the components of agricultural technology, specifically the width of the rows and the application rates of mineral fertilizers.
 Methods. The research was carried out in the years 2018–2021 in the Chernihiv region at the Nizhyn Agricultural Technical Institute of the National University of Life and Environmental Sciences of Ukraine). Conventional methods were used in the research. The field experiment design provided for the cultivation of typhoon variety ‘Orakam’ under different methods of sowing (width between rows of 15, 30 and 45 cm) and rates of mineral fertilizers (without fertilizers, N80P60K60 and N120P90K90). Parameters of ecological stability (b) and plasticity (W) of seed yield and energy yield from biomass were calculated according to the Eberhard-Russell method using the Mathcad Prime 3.1 software.
 Results. The lowest stability of both seed yield (0.55–0.79) and energy yield from biomass (0.55–0.81) was noted in the treatments without fertilizers, while with N80P60K60 and N120P90K90 it was almost twice as high (1.03–1.33 and 0.97–1.32, respectively). At the same time, within all three fertilization backgrounds, a clear tendency of decreasing crop productivity stability along with increasing row width was observed. In particular, the highest coefficient of stability of seed yield in the experiment (1.33) was obtained on the background of N80P60K60 at a row spacing of 15 cm, at the same time as the row spacing increased to 30 and 45 cm, it decreased to 1.19 and 1.05, respectively. As for the plasticity parameters of the productive indicators, they were approximately at the same level in all treatments.
 Conclusions. The best conditions for the formation of high seed yield and total energy yield from the biomass of typhoon variety ‘Orakam’ were provided at a row width of 15 and 30 cm and the application of mineral fertilizers N80P60K60 and N120P90K90. In this case, the formation of crop productivity demonstrated a high level of plasticity. In general, intensive cultivation conditions contributed to the full realization of the crop biological potential and effective utilization of fertilizers.

Development of the Turbulent Diffusion Model of Fine Suspended Substances in the Lower Atmosphere Layer

A promising direction for solving the problem of air pollution by fine substances is the use of numerical modeling in the development of mathematical models of the transport of pollutants in the atmosphere. An urgent problem in applying mathematical models with numerical algorithms and software is constructing a qualitative model that would meet both the physical parameters and fulfill all the optimal conditions of numerical analysis. The main objective of this study was to develop an algorithm of a mathematical model based on the equation of distribution of impurities in a turbulent medium. That allows considering the simultaneous influence of wind speed, turbulence of atmospheric air, pollution parameters, direction, and wind force on the size of scattering zones. The unique feature of the study is the use of the coordinate splitting equation of impurities distribution in a turbulent environment with subsequent normalization and parameterization of conditions. Finding integrands functions in the calculation algorithm allows obtaining a stable computational algorithm of the proposed propagation model of fine suspended particles. The solution of the function implemented in the Mathcad Prime 7 software. Distributions of concentrations and their levels for various values of turbulence of atmospheric air and dangerous wind speed are received. The most significant number of fine particles is at a distance of up to 4 km from the emission source. Still, there is also the transfer of contaminants at more than 5 km (up to 57 % of the initial emission concentration). The model has convenient software and algorithmic software, the time of calculation of graphic visualizations up to 20 minutes on medium-power computers. The obtained mathematical model can use in systems of forecasting man-caused load on the environment for the prompt solution of environmental problems.

The application of the orthogonal decomposition method for the algebraic solver separator

The method which is valid for improving the transmission of information and a clean separation of signal and noise is suggested in [1]. The basis of the proposed new way of developing the theory and methods of communication is the rejection of the probabilistic method for evaluating noisy signals according to the maximum likelihood rule. This method contains the mathematical procedure for absolutely accurate separation, as well as proving the absence of any fundamental theoretical limits [2,3] on the effectiveness of communications, including the absence of channel capacity limitations [4]. This approach includes the fundamentally new concept and the technical aspects of implementing telecommunication systems and uses systems of linear algebra equations (SLAE) to filter signals from noise. The SLAE matrix is the linear algebraic matrix (LSM) that separates and extracts the true values of informative signal parameters. Such a SLAE always has the solution, but obtaining this solution sometimes requires a particular method to be used, because its matrix is not always square, but can be rectangular as well. Therefore, the method of the orthogonal decomposition is proposed in this paper. For obtaining the matrices of orthogonal decomposition the Gram–Schmidt process, which is suitable for matrices of any size and composition, can be used. The method of solving a SLAE includes full description of solution and acceptable for matrices of any size. The example of solving the SLAE with a small matrix is presented in the paper. The MathCad Prime has been implemented for a bigger matrix. The implementation includes the functions that can be used in any other programming language. The solution has minimal norm and acceptable for linear algebraic matrices that separate signal and noise.

Mechanical projects: dimensioning of shafts with correction for keyway and bearing support

This article goes through several steps in order to deliver a reliable result, according to the ASME method, of a shaft dimensioning, aiming to automate the calculation memorial process for shaft projects. The design steps are: stress diagrams, fatigue and geometry analysis (if necessary); correction due to discontinuity (if any); shaft diameter correction due to keyway (if any); and correction due to manufacturer’s selected bearing support (adopting SKF models). In this way, the article aims, in order to comply with the literature and standards, to dimension transmission shafts. The results of the exercises solved in the book Projeto de Máquinas: Uma abordagem integrada will be used as a reference. The developed program aims to meet both professional and academic demands by optimizing the calculations to obtain the diameter of a shaft. In addition, the project is justified by the fact that it allows several changes for a better understanding, either for a designer or for a student. The software used to automate the processes and obtain the results will be Mathcad Prime 5.0 from PTC Enterprise. At the end of the article, along with the results and conclusion, there are examples of design problems solved by the program, along with their explanations and comparisons with the results obtained in the Norton’s book.

A REFINED METHOD FOR ANALYTICAL MODELING OF THE PROCESSES OF SPREADING VIRUS SOFTWARE TO ASSESS THE SECURITY OF INFORMATIZATION OBJECTS

Task. The purpose of writing this article is to improve the security of information in information systems. Model. The article proposes an improved method for analytical modeling of the process of spreading virus software in information systems in relation to the features of a special class of attacks implemented by the family of virus software - ransomware. Conclusions. The proposed method makes it possible to analytically calculate the intensity of infection of hosts of a protected information system with various types of virus software and use the obtained characteristics as initial data for the final assessment of the information security risk on the protected informatization object. Value. Modeling in the environment of the mathematical package PTC Mathcad Prime 7 showed the applicability of the proposed approach for analytical threat modeling.

Dynamics of the Rolling Stock and the Choice of Parameters of Vibration Dampers

Modern railway rolling stock should meet requirements regarding comfort (maximum travel speed with minimum vibrations of wagons, noiselessness of movement, etc.).To eliminate the influence of dynamic loads, rolling stock is equipped with vibration dampers. The objective of the work is to select the parameters of the vibration dampers of rolling stock, depending on its characteristics, to ensure the due indicators of comfort and safety of transportation of passengers and goods by rail. To achieve this objective, applied methods of mathematical modelling were based on numerical programming of operation of dynamic systems. The indicators of vibration dampers are evaluated according to the results of studies of the dynamics of the rolling stock (in particular, of vibration protection rates).Assessment of dynamic state of the rolling stock implies application of methods of mathematical and physical modelling, which include the development of a physical and mathematical model, a calculation algorithm, and computer programming. The study of the mathematical model by numerical methods makes it possible to carry out a multifactorial experiment using a large number of input parameters (factors) and to select the characteristics of vibration dampers that are optimal for the conditions under consideration.To solve dynamic problems, the harmonic perturbation model, which is the most widespread, was specified in the form of a sinusoid with a period corresponding to the rail length.A quantitative assessment of the vibration process (frequency, amplitude) makes it possible to identify the main processes occurring in the system under consideration under various types of external load. The introduced assumptions related to rigidity, mobility and geometric immutability of the system allow determining the methods for obtaining a mathematical model and considering the vibrations as flat ones.The equations were solved in MathCad Prime 4.0 package using the Runge–Kutta method with automatic step selection. The subsequent study of the properties of the dynamic system was carried out by changing the resistance parameter of dampers of the first stage of spring suspension, while recording the values of the amplitude of the vibrations of the system and the period.The analysis of the results has shown that the vibration period of the body and bogies under any changes in the resistance parameter of the damper remains unchanged, while rational parameters of resistance of axle box dampers have been revealed for specified indicators. Hydraulic vibration dampers with the revealed parameters used on rolling stock help to reduce wear and damageability of running gears, improve ride comfort and traffic safety, as well as to reduce repair and maintenance costs.

Design interaction diagrams for reinforced concrete circular columns following ACI 319-19

The procedure for creating interaction diagrams for reinforced-concrete circular crosssections, based on ACI 318-19, is described in thepaper. The algorithm is generated based on mathematical tools Mathcad Prime. The author would like to introduce algorithms to thecompany designs, engineers build an evaluation method column bearing capacity of the circular cross-section. The obtained results are compared with a conventional method (ie, the computer software SP‐Column). The obtained results are promising, as the values obtained by the Interaction Charts and the conventional method appear to be in good agreement.

Improvement of method for estimation of parameters of contact interaction of billet with roll tool in lines of continuous electric pipe-welded mills

A technique for calculating the parameters of the shape of the boundary and areas of contact indentations of a pipe billet with a roller tool of a forming mill, in which the boundaries of the shape of the contact indentation are described by rectilinear lines, and the shape is modeled by triangles on the plane of the pipe billet, is investigated. The results of an experiment on fixing the contact sections of a tubular billet with initial dimensions of 160×1.5×1800 mm from steel 09G2S with rolls in the section of open pass are presented. As a result of the experiment, the contact areas of the pipe billet with the lower and upper rolls were fixed. The boundary of the experimental contact areas are curved arcs. Comparison of the experimental data with the technique showed that the parameters of the boundaries of the contact area according to the technique lead to an overestimation of the values by 30-40 % compared to the experimental data. On the basis of experimental data, the development of the existing technique for determining contact areas is presented, in which the boundaries are defined in the form of arcuate curves. The boundaries of the entry contact sections for the lower and upper rolls are determined by the equations of exponential approximation. Taking into account the equations of the boundaries of the sections, a method is presented for determining the areas of contact sections of a pipe billet on the surfaces of the lower and upper rolls, the results of which do not exceed 6 % of the experimental data. The engineering mathematical software PTC Mathcad Prime 6.0 was used to calculate and construct the areas of contact areas.

CO2 Removal Using Adsorption Onboard A Floating Production Storage and Offloading (FPSO) Vessel

Offshore operations gas purification has always been limited to the marketable associated value of the gas where purification would either be onsite or sent to surface facilities for treatment. CO2 and H2S removal and gas sweetening in remote offshore locations is for the most part non-existent and CO2 is either being released into the atmosphere, within the acceptable operation limit of the platform, or being captured using conventional techniques with physical solvents such as in the selexol, rectisol, or sulfinol processes. Approximately 429.61 kg of CO2 exists in a 42-gallon barrel of distillate fuel oil and a CO2 coefficient of 0.0549 kg exists in 1 cubic foot of gas thereby emphasizing the need for an engineering solution on floating production storage and offloading (FPSO) units [1]. With strict regulation on greenhouse gases, it is increasingly paramount to utilize engineering measures to provide a contingency plan in mitigating carbon footprint with emerging novel technologies. The purpose of this study is to retrofit an existing FPSO with a CO2 capture plant; the efficiency of the capture plant, its capture capacity, and energy requirement based on experimental data will be thoroughly investigated during the scale up procedure. The research proceedings will require the use of a plethora of simulation suites which include Autodesk Fusion 360 for plant design. Further simulation will be carried out with numerical suites using Mathcad Prime 3.0 to study the scale up procedure from experimental to industrial sized adsorption unit complete with dimensions, energy requirement, capture capacity, and thermal values. The FPSO in figure 1 above presented by (Araujo et al., 2016) indicates the availability of a capture plant as part of the process train on an FPSO. Efficiency loss contribution to the system may be deduced but also it is relevant to note the custom nature of the FPSO design being independent in its operation mode compared to other profiles. The availability of the stage compressors, dehydration units, and steam generation plant as part of the FPSO operation aid in minimising the need for additional equipment for the adsorption plant, however investigation has to be made on the redirecting of processes to serve the additional components highlighted above. Primary results have shown a low tendency for dual adsorption from the initial kinetic stoichiometric balance which could also be due to the force field parameters and charges affecting the active sites. For the current concept the fixed bed experimental model from the Research and Innovation Centre on CO2 and H2 is scaled up numerically to a fixed bed height of 6.56 feet, and filled with precipitated silica impregnated with PEI solution pressurized with CO2 inflow rated at 13 lb/hr at a fixed 1.2 Bar 60°C. The operational nature of the FPSO will be modified to account for the changes requested in gas sweetening and capture programs or enhanced oil recovery. Results from the simulation will also assist in providing a tangible and relatable understanding to the complexity of solid sorption technology integration within existing processing plants. The findings of this study will help comprehend the viability of an integrated adsorption plant within an existing process train. The efficiency of the plant operation for an oil production offshore facility with associated gas or for a standalone gas field will be addressed using a feasibility study conducted for the purpose of sustainable offshore operations.

Ensuring the operating modes of the seeding apparatus specialized equipment

The subjects of the research are the process of sowing seeds with a seeding apparatus and the indicators of quality of their distribution in a row. The goal is to substantiate a rational technological process of distributing row crops seeds in a row with a pneumatic seeding apparatus. Special equipment was used in the system of ensuring the revolutions of the seeding disc, sucking seeds to its holes, pneumatic transport of seeds after separation from the opening of the seeding disc for contact interaction with the receiving platform of the sensor of the number of seeds and its settling in the collector. The novelty of the research lies in the use of an acoustic sensor for a single registration of the sowed seeds with a short time interval, which makes it possible to assess the quality of the operation of the sowing device by the standard deviation of seeds from a given seeding rate in their normal distribution in accordance with the law of numbers. The operating mode of the pneumatic seeding apparatus from specialized equipment as part of the test bench was carried out as an example of sowing sunflower seeds with a seeding rate of 3 seeds/linear meter for the conventional seeder speed of 9 km/h. The data obtained with different time intervals between the registered seeds in WAV format by the PTC Mathcad Prime software was represented by classical distributed seeds in graphical form and data in tabular form. The quality indicators of seeds for sowing and their class distribution in a row by rational operating modes of the seeding apparatus, assessed by specialized equipment when applying the law of large numbers, are the basis of scientific research on predicting the yield of row crops.

Optimum Design of a Ring-Shaped Clip Gauge

The optimisation methodology was applied to design a specific geometry for a ring-shaped clip gauge as a quasi-static displacement measurement. The gauge was designed to maximise sensitivity under various types of constraints, including working range, strength, and installation. The analytical expressions of the ring gauge’s responses and constraints were derived to formulate an optimisation problem. The optimal solution was determined by an optimisation solver in the MathCAD Prime 4 program. The sensitivity of the objective function with respect to the parameters in the optimisation problem evaluated at the optimal solution was also determined. The sensitivity and linearity of the designed ring gauge is in the range of commercial gauges. The accuracy of the ring gauge was better than 0.1%, complying with ASTM standard E1820. Performance of the ring gauge, i.e. its linearity, hysteresis, and repeatability, was better than the DCB gauge reproduced from the standard. Applying the ring gauge to a tensile test with a cracked specimen yielded an accurate displacement measurement. Limitations of the analytical formulation are highlighted and recommendations for improving the formulation are discussed.

Sampling method for evaluation and control of industrial product quality

The article develops a sampling method to control and evaluate the quality of industrial products. The method allows for a comprehensive quality evaluation at designing and controlling industrial product manufacture. The method is based on a set of mathematical and statistical models of forming a sampling frame of industrial product parameters. It takes into account the factors of the company’s external and internal environment, control over decision making process (DMP), quality evaluation by a sum of partial indicators of ten groups. The method developed is automated with the help of the software MathCad Prime. The industrial approbation of the method showed its efficiency for the solution of production tasks related to the evaluation and control of industrial product quality at various stages of product and manufacturing life cycles.

Computational design applied to equilibrium-staged and rate-based absorption processes

Simulators are of great interest in Chemical Engineering because they facilitate process optimization and help evaluate different solutions through the so-called �what-if� approach. They include the most advanced thermodynamical models and complete libraries for the calculation of physicochemical properties and estimation of phase equilibria data which are successfully integrated in the process design. Moreover, simulators allow addressing both stationary and batch operations. For this reason, their use in the design of Industrial Chemistry processes has gained much acceptance in the last decades. Even so, simulations should be accompanied by another computational tool which allows the professionals to implement specific algorithms which relate inputs and outputs, so as to get the most out of the computing power. We herein exemplify how Aspen Plus and Mathcad Prime software packages were successfully integrated in a case study on the removal of carbon disulphide by contact with a paraffinic oil in an absorption tower. This absorption operation was studied in both trayed and packed columns. Regarding the first contact type, i.e. trays, Mathcad�s powerful programming tool and graphical interface enabled to corroborate and to better understand the effect of temperature on the number of theoretical stages previously observed with Aspen Plus.