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The reconfiguration problem (DPSR) in electrical distribution systems is a critical area of research, aimed at optimizing the operational efficiency of these networks. Historically, this problem has been approached through a variety of optimization methods. Regarding mathematical models, a key challenge identified in these models is the formulation of equations that ensure the radial operation of the system, along with the nonlinear equations representing Kirchhoff's laws, the last often necessitating complex relaxations for practical application. This paper introduces an alternative representation of system radiality, which potentially surpasses or matches the existing methods in the literature. Our approach utilizes a more intuitive and compact set of equations, simplifying the representation process. Additionally, we propose a linearization of the current calculation in the power flow model typically used to solve DPSR. This linearization significantly accelerates the process of obtaining feasible solutions and optimal reconfiguration profiles. To validate our approach, we conducted rigorous computational comparisons with the results reported in the existing literature, using a variety of test cases to ensure robustness. Our computational results demonstrate a considerable improvement in computational time. The objective functions used are competitive and, in many instances, outperform the best reported results in the literature. In some cases, our method even identifies superior solutions. [ABSTRACT FROM AUTHOR]

Fuzzy logic is becoming one of the most-influential fields of modern mathematics with applications that impact not only other sciences, but society in general. This newly found interest in fuzzy logic is in part due to the crucial role it plays in the development of artificial intelligence. As a result, new tools and practices for the development of the above-mentioned field are in high demand. This is one of the issues this paper was composed to address. To be more specific, a sizable part of fuzzy logic is the study of fuzzy connectives. However, the current method used to generalize them is restricted to the use of basic automorphisms, which hinders the creation of new fuzzy connectives. For this reason, in this paper, a new method of generalization is conceived of that aims to generalize the fuzzy connectives using polynomial automorphism functions instead. The creation of these automorphisms is achieved through numerical analysis, an endeavor that is supported with programming applications that, using mathematical modeling, validate and visualize the research. Furthermore, the automorphisms satisfy all the necessary criteria that have been established for use in the generalization process and, consequently, are used to successfully generalize fuzzy connectives. The result of the new generalization method is the creation of new usable and flexible fuzzy connectives, which is very promising for the future development of the field. [ABSTRACT FROM AUTHOR]

In the realm of cementitious materials, integrating nanoclay shows promise in enhancing properties relevant to additive manufacturing. This paper presents a novel mathematical model that combines simple empirical dissolution/nucleation Avrami-like kinetics with a thixotropic kinetics equation. To analyze the initial exothermic peak, two sets of the calculation parameter function are built to describe the exothermic rate as a function of time, following an exponential pattern. This allows for the prediction of the changes in cumulative heat and heat rate during hydration, considering different concentrations of nanoclay. In the rheological aspect, the relationship between shear stress, shear rate, and time is modeled as a combination of exponential dependencies. This enables the prediction of the variations in shear stress with one variable while holding the other constant (either time or shear rate). By integrating these aspects, this model effectively describes both the first exothermal peak and the rheological behavior during cement hydration with the inclusion of nanoclay. Validated against experimental results, these models demonstrate good accuracy (overall below 3% error), reliability, and applicability. The findings offer valuable insights into the thermal and rheological aspects of concrete printing, enabling informed design decisions for both scientific and industrial applications. [ABSTRACT FROM AUTHOR]

The paper presents a review of models that can be used to describe dynamics of lung cancer growth and its response to treatment at both cell population and intracellular processes levels. To address the latter, models of signaling pathways associated with cellular responses to treatment are overviewed. First, treatment options for lung cancer are discussed, and main signaling pathways and regulatory networks are briefly reviewed. Then, approaches used to model specific therapies are discussed. Following that, models of intracellular processes that are crucial in responses to therapies are presented. The paper is concluded with a discussion of the applicability of the presented approaches in the context of lung cancer. [ABSTRACT FROM AUTHOR]

In this paper, we construct a more realistic mathematical model to study toxoplasmosis dynamics. The model considers two discrete time delays. The first delay is related to the latent phase, which is the time lag between when a susceptible cat has effective contact with an oocyst and when it begins to produce oocysts. The second discrete time delay is the time that elapses from when the oocysts become present in the environment to when they are able to infect. The main aim in this paper is to find the conditions under which the toxoplasmosis can disappear from the cat population and to study whether the time delays can affect the qualitative properties of the model. Thus, we investigate the impact of the combination of two discrete time delays on the toxoplasmosis dynamics. Using dynamical systems theory, we are able to find the basic reproduction number R 0 d that determines the global long-term dynamics of the toxoplasmosis. We prove that, if R 0 d < 1 , the toxoplasmosis will be eradicated and that the toxoplasmosis-free equilibrium is globally stable. We design a Lyapunov function in order to prove the global stability of the toxoplasmosis-free equilibrium. We also prove that, if the threshold parameter R 0 d is greater than one, then there is only one toxoplasmosis-endemic equilibrium point, but the stability of this point is not theoretically proven. However, we obtained partial theoretical results and performed numerical simulations that suggest that, if R 0 d > 1 , then the toxoplasmosis-endemic equilibrium point is globally stable. In addition, other numerical simulations were performed in order to help to support the theoretical stability results. [ABSTRACT FROM AUTHOR]

The variation analysis is a key tool for ensuring the high quality assembly in the process of developing the technology for manufacturing of aircraft parts. One of the main factors in variations is the deviations in the positioning procedure. This paper is devoted to the development of an approach that allows taking into account the variations during positioning and merging it with the special algorithm of contact problem solving. The impact of varied boundary conditions is incorporated into an additional vector of forces that can be interpreted as reactions to the shift of supports. The obtained results are illustrated with a case of wing-to-fuselage assembly. [ABSTRACT FROM AUTHOR]

Breast cancer ranks among the most prevalent malignancies affecting the female population and is a prominent contributor to cancer-related mortality. Mathematical modeling is a significant tool that can be employed to comprehend the dynamics of breast cancer progression and dissemination and to formulate novel therapeutic approaches. This paper introduces a mathematical model of breast cancer that utilizes the Caputo–Fabrizio fractal-fractional derivative. The aim is to elucidate and comprehend the intricate dynamics governing breast cancer cells and cytotoxic T lymphocytes in the context of the fractional derivative. The derivative presented herein offers a broader perspective than the conventional derivative, as it incorporates the intricate fractal characteristics inherent in the process of tumor proliferation. The significance of this study lies in its contribution to a novel mathematical model for breast cancer, which incorporates the fractal characteristics of tumor development. The present model possesses the capability to investigate the impacts of diverse treatment strategies on the proliferation of breast cancer, as well as to formulate novel treatment strategies that exhibit enhanced efficacy. [ABSTRACT FROM AUTHOR]

This paper explores the concept of Generalized Roughness in LA-Semigroups and its applications in various mathematical disciplines. We highlight the fundamental properties and structures of Generalized Roughness, examining its relationships with Fuzzy Lie Algebras, Order Theory, Lattice Structures, Algebraic Structures, and Categorical Perspectives. Moreover, we investigate the potential of mathematical modeling, optimization techniques, data analysis, and machine learning in the context of Generalized Roughness. Our findings reveal important results in Generalized Roughness, such as the preservation of roughness under the fuzzy equivalence relation and the composition of roughness sets. We demonstrate the significance of Generalized Roughness in the context of order theory and lattice structures, presenting key propositions and a theorem that elucidate its properties and relationships. Furthermore, we explore the applications of Generalized Roughness in mathematical modeling and optimization, highlighting the optimization of roughness measures, parameter estimation, and decision-making processes related to LA-Semigroup operations. We showcase how mathematical techniques can enhance understanding and utilization of LA-Semigroups in practical scenarios. Lastly, we delve into the role of data analysis and machine learning in uncovering patterns, relationships, and predictive models in Generalized Roughness. By leveraging these techniques, we provide examples and insights into how data analysis and machine learning can contribute to enhancing our understanding of LA-Semigroup behavior and supporting decision-making processes. [ABSTRACT FROM AUTHOR]

This paper describes a mathematical model of an autowave process in a cell with a ferrocolloid. The model is a system of differential coupled equations of the second order and differs from the previously presented model in terms of its original boundary conditions. The mathematical modeling of autowaves presented in this work constitutes an innovative approach, since the characteristics of the wave process are not initially included in the model but the model demonstrates a wave motion. A 2D solution of the model, which shows the correctness of the described mechanism of the autowave process, i.e., the recharging of magnetic particles in dense near-electrode layers formed near the electrodes under the influence of an electric field, is obtained. The propagation of single and phase autowaves is demonstrated in a computer experiment. [ABSTRACT FROM AUTHOR]

This work focuses on the methods of creating in-fiber devices, such as sensors, filters, and scatterers, using the fiber fuse effect. The effect allows for the creation of structures in a fiber core. However, it is necessary to know exactly how this process works, when the plasma spark occurs, what size it reaches, and how it depends on external parameters such as power and wavelength of radiation. Thus, this present study aims to create the possibility of predicting the consequences of optical breakdown. This paper describes a mathematical model of the optical breakdown initiation in a fiber core based on the thermal conductivity equation. The breakdown generates a plasma spark, which subsequently moves along the fiber. The problem is solved in the axisymmetric formulation. The computational domain consists of four elements with different thermophysical properties at the boundaries of which conjugation conditions are fulfilled. The term describing the heat source in the model is determined by the wavelength of radiation and the refractive indices of the core and the shell and also includes the radiation absorption on the released electrons during the thermal ionization of the quartz glass. The temperature field distributions in the optical fiber are obtained. Based on the calculations, it is possible to estimate the occurrence times of various phase states inside the fiber, in particular, the plasma spark occurrence time. [ABSTRACT FROM AUTHOR]

The compaction of asphalt mixture is crucial to the performance of the pavement. However, the mix design (i.e., porosity, aggregate size distribution, binder content), which is based on compaction results, remains largely empirical. It is difficult to relate the aggregate size distribution and the asphalt binder properties to the compaction curve in both the field and laboratory compaction of asphalt mixtures. In this paper, the author proposes a simple mathematical model from the perspective of granular physics to predict the compaction of asphalt mixtures. In this model, the compaction process is divided into two mechanisms: (i) viscoplastic deformation of an ordered granular-fluid assembly, and (ii) the transition from an ordered system to a disordered system due to particle rearrangement. This model could take into account both the viscous properties of the asphalt binder and the grain size distributions of the aggregates, where the viscous deformation is calculated with a proposed governing equation and the particle rearrangement effect is solved using simple DEM simulations. This model is calibrated based on the Superpave gyratory compaction tests in the pavement lab, and the R-squares of model predictions are all above 0.95. The model results are compared with experimental data to show that it can provide good predictions for the experiments, suggesting its potential for enhancing the design of asphalt mixtures. [ABSTRACT FROM AUTHOR]

The paper presents a solution to the problem related to the reconstruction of parameters in the mathematical model of bacterial colony patterns in a domain with symmetry. The inverse problem consists of determining the value of the diffusion coefficient of active bacteria. The model describing the distribution of active bacteria in a given region, as well as the concentration of the substrate over time is considered. Such a model consists of a system of partial differential equations with appropriate initial-boundary conditions. The finite element method was used to solve the direct problem. However, the Fibonacci search method was used to minimize the functional description of the error of the approximate solution. [ABSTRACT FROM AUTHOR]

In this paper, we construct a generalized epidemiological mathematical model to study toxoplasmosis dynamics, taking into consideration both cat and mouse populations. The model incorporates generalized proportions for the congenital transmission in the mouse and cat populations, along with the oocysts available in the environment. We focus on determining the conditions under which toxoplasmosis can be eradicated. We conduct a stability analysis in order to reveal the dynamics of toxoplasmosis in the cat and mouse populations; moreover, we compute the basic reproduction number R 0 , which is crucial for the long-term behavior of the toxoplasmosis disease in these populations as well as the steady states related to both populations. We find that vertical transmission in the cat population is essential, and affects the basic reproduction number R 0 . If full vertical transmission is considered in the mouse population and R 0 < 1 , we find that all solutions converge to the limit set comprised by the infinitely many toxoplasmosis-free-cat steady states, meaning that toxoplasmosis would vanish from the cat population regardless of the initial conditions. On the other hand, if R 0 > 1 , then there is only one toxoplasmosis-endemic steady state. When full vertical transmission is not considered in the mouse population, then a unique toxoplasmosis-free equilibrium exists and toxoplasmosis can be eradicated for both the cat and mouse populations. This has important public health implications. Numerical simulations are carried out to reinforce our theoretical stability analysis and observe the repercussion of some parameters on the dynamics. [ABSTRACT FROM AUTHOR]

Fifth-generation (5G) New Radio (NR) systems are expected to support multiple traffic classes including enhanced mobile broadband (eMBB), ultra-reliable low-latency communications (URLLC), and massive machine-type communications (mMTC) at the same air interface. This functionality is assumed to be implemented by utilizing the network slicing concept. According to the 3rd Generation Partnership Project (3GPP), the efficient support of this feature requires statistical multiplexing and, at the same time, traffic isolation between slices. In this paper, we formulate and solve a mathematical model for a class of Radio Access Network (RAN) slicing algorithms that simultaneously include resource reservation and a priority-based service discipline allowing us to incur fine granularity in the service processes of different traffic aggregates. The system is based on a queueing model and allows parametrization by accounting for the specifics of wireless channel impairments. As metrics of interest, we utilize K-class session drop probability, K-class session pre-emption probability, and system resource utilization. To showcase the capabilities of the model, we also compare performance guarantees provided for URLLC, eMBB, and mMTC traffic when multiplexed over the same NR radio interface. Our results demonstrate that the performance trade-off is dictated by the offered traffic load of the highest priority sessions: (i) when it is small, mixed reservation/priority scheme outperforms the full reservation mechanism; (ii) for overloaded conditions, full reservations provides better traffic isolation. The mixed strategy is beneficial to traffic aggregates with short-lived lightweight sessions, such as URLLC and mMTC, while the reservation only scheme works better for elastic eMBB traffic. The most important feature is that the mixed strategy allows resource utilization to be improved up to 95%, which is 10–15% higher compared to the reservation-only scheme while still providing isolation between traffic types. [ABSTRACT FROM AUTHOR]

The calculation of air distribution in large mine ventilation networks is usually carried out by numerically solving a system of equations representing Kirchhoff's circuit laws. This formulation of the problem traditionally only considers the frictional air resistance of straight sections of mine airways. However, when analyzing the changing ventilation modes, it is also important to correctly consider the shock losses, which sufficiently affect the redistribution of airflows. The reason is that the shock loss factor strongly depends on the airflow rates at the junctions of mine airways. This paper presents a mathematical model of a ventilation network that considers shock losses. The model considers steady-state air distribution as well as natural draft. The significance of the shock was confirmed with a practical example; we describe the application of the proposed mathematical model for the analysis of air distribution in the ventilation network of a potash mine during planned airflow reversal. [ABSTRACT FROM AUTHOR]

Mathematical modeling is used to study the hereditary mechanism of the accumulation of radioactive radon gas in a chamber with gas-discharge counters at several observation points in Kamchatka. Continuous monitoring of variations in radon volumetric activity in order to identify anomalies in its values is one of the effective methods for studying the stress–strain state of the geo-environment with the possibility of building strong earthquake forecasts. The model equation of radon transfer, taking into account its accumulation in the chamber and the presence of the hereditary effect (heredity or memory), is a nonlinear differential Riccati equation with non-constant coefficients with a fractional derivative in the sense of Gerasimov–Caputo, for which local initial conditions are set (Cauchy problem). The proposed hereditary model of radon accumulation in the chamber is a generalization of the previously known model with an integer derivative (classical model). This fact indicates the preservation of the properties of the previously obtained solution according to the classical model, as well as the presence of new properties that are applied to the study of radon volumetric activity at observation points. The paper shows that due to the order of the fractional derivative, as well as the quadratic nonlinearity in the model equation, the results of numerical simulation give a better approximation of the experimental data of radon monitoring than by classical models. This indicates that the hereditary model of radon transport is more flexible, which allows using it to describe various anomalous effects in the values of radon volume activity. [ABSTRACT FROM AUTHOR]

Numerical methods have gained momentum among specific engineering problems that must be solved in such a manner that accuracy and speed are the two most important aspects to consider regarding the output. This paper presents a fast, semi-analytical method (SAM) and original mathematical algorithms to determine the pressure distribution and von Mises stress for spur gears' meshing teeth. The SAM begins with the Hartnett approach, based on Boussinesq's equation for the half-space theory of linear elasticity, which implicitly means an infinite width of the gear flank. To simulate more realistic quarter-space conditions, corrections based on virtual mirror pressure are introduced in the computational algorithm. Mathematical surfaces modeling is an important aspect for spur gears as an intermediate stage to determine the pressure distribution and von Mises stress. Shaft misalignment changes the contact problem from symmetric, in which the half- or quarter-space model can be used, to asymmetric. In the latter case, the model must determine the entire contact area. The obtained output is validated by comparisons between our original FEA results and results from the literature using SAMs and FEA. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the qualitative behavior of the COVID-19 pandemic under an initial vaccination program. We constructed a mathematical model based on a nonlinear system of delayed differential equations. The time delay represents the time that the vaccine takes to provide immune protection against SARS-CoV-2. We investigate the impact of transmission rates, vaccination, and time delay on the dynamics of the constructed system. The model was developed for the beginning of the implementation of vaccination programs to control the COVID-19 pandemic. We perform a stability analysis at the equilibrium points and show, using methods of stability analysis for delayed systems, that the system undergoes a Hopf bifurcation. The theoretical results reveal that under some conditions related to the values of the parameters and the basic reproduction number, the system approaches the disease-free equilibrium point, but if the basic reproduction number is larger than one, the system approaches endemic equilibrium and SARS-CoV-2 cannot be eradicated. Numerical examples corroborate the theoretical results and the methodology. Finally, conclusions and discussions about the results are presented. [ABSTRACT FROM AUTHOR]

Most plant viral infections are vector-borne. There is a latent period of disease inside the vector after obtaining the virus from the infected plant. Thus, after interacting with an infected vector, the plant demonstrates an incubation time before becoming diseased. This paper analyzes a mathematical model for persistent vector-borne viral plant disease dynamics. The backpropagated neural network based on the Levenberg—Marquardt algorithm (NN-BLMA) is used to study approximate solutions for fluctuations in natural plant mortality and vector mortality rates. A state-of-the-art numerical technique is utilized to generate reference data for obtaining surrogate solutions for multiple cases through NN-BLMA. Curve fitting, regression analysis, error histograms, and convergence analysis are used to assess accuracy of the calculated solutions. It is evident from our simulations that NN-BLMA is accurate and reliable. [ABSTRACT FROM AUTHOR]

Agent-based modeling (ABM) is a flexible and simulation-friendly modeling approach. Ambient-oriented modeling is effective for systems containing ambient and spatial representations. In this paper we propose a framework for the integrated use of agent-based modeling and ambient-oriented modeling. We analyze both agents and ambient in detail. We also compare both modeling approaches as well and analyze their similarities and differences. The integrated implementation provides a new link between mathematical modeling and simulations. The model developed using this framework has four parts. The first part constitutes the identification, definition, and relations of agents. In this part, we use agent-based modeling along with the concepts of discrete-event simulations and system dynamics. The second part of the model is the mathematical representation of the relations of agents, i.e., the parent and child relation of agents. The third part of the model is the representation of the messages along with relational symbols where we utilize the concepts and symbols of relations and messages from ambient-oriented modeling. The fourth and final part of the model is the simulation, where we describe the rules that govern the processes represented in first two parts. The framework is helpful in overcoming certain limitations of both approaches. Moreover, we provide a scenario of a bus rapid transit system (BRTS) as a proof of concept, and we examine the generic concept of BRTSs using the proposed framework. [ABSTRACT FROM AUTHOR]

Accidents on gas pipelines cause significant damage to the national economy and the economy of the state. Thus, it is necessary to always be prepared for such situations in order to restore the normal operation of the gas pipeline as soon as possible. An important role is played by the execution time of the control actions to localize the accident, pump out the gas, and change the operating modes. It is essential that such control be undertaken, especially if such a situation occurs near a gas-measuring installation for measuring the amount of vented gas. Therefore, the control actions must be error-free in order to quickly stop the non-stationary process, which can lead to undesirable consequences. The paper presents a mathematical model of the operation of the pipeline, developed for the management of the pipeline in an emergency. The analysis of the problem of the occurrence of accidents was carried out, and the effect of liquid on its walls was modeled when the operating mode of the pipeline changed. An example is presented using a numerical model carried out in ANSYS, as well as being analyzed analytically. The results of the calculations are presented, and special attention is paid to the parameters influencing the change in the operating mode of the pipeline. [ABSTRACT FROM AUTHOR]

The mevalonate pathway is an attractive target for many areas of research, such as autoimmune disorders, atherosclerosis, Alzheimer's disease and cancer. Indeed, manipulating this pathway results in the alteration of malignant cell growth with promising therapeutic potential. There are several pharmacological options to block the mevalonate pathway in cancer cells, one of which is zoledronic acid (ZA) (an N-bisphosphonate (N-BP)), which inhibits the farnesyl pyrophosphate (FPP) synthase enzyme, inducing cell cycle arrest, apoptosis, inhibition of protein prenylation, and cholesterol reduction, as well as leading to the accumulation of isopentenyl pyrophosphate (IPP). We extrapolated the data based on two independently published papers that provide numerical data on the uptake of zoledronic acid (ZA) and the accumulation of IPP (Ag) and its isomer over time by using in vitro human cell line models. Two different mathematical models for IPP kinetics are proposed. The first model (Model 1) is a simpler ordinary differential equation (ODE) compartmental system composed of 3 equations with 10 parameters; the second model (Model 2) is a differential algebraic equation (DAE) system with 4 differential equations, 1 algebraic equation and 13 parameters incorporating the formation of the ZA+enzyme+Ag complex. Each of the two models aims to describe two different experimental situations (continuous and pulse experiments) with the same ZA kinetics. Both models fit the collected data very well. With Model 1, we obtained a prevision accumulation of IPP after 24 h of 169.6 pmol/mgprot/h with an IPP decreasing rate per (pmol/mgprot) of ZA ( k X G Z ) equal to 13.24/h. With Model 2, we have comprehensive kinetics of IPP upon ZA treatment. We calculate that the IPP concentration was equal to 141.6 pmol/mgprot/h with a decreasing rate/percentage of 0.051 ( k X G U ). The present study is the first to quantify the influence of ZA on the pharmacodynamics of IPP. While still incorporating a small number of parameters, Model 2 better represents the complexity of the biological behaviour for calculating the IPP produced in different situations, such as studies on γ δ T cell-based immunotherapy. In the future, additional clinical studies are warranted to further evaluate and fine-tune dosing approaches. [ABSTRACT FROM AUTHOR]

Within the scope of the presented work, a mathematical model of a prototype of a complex motion transmission on a ship was developed. The abovementioned motion transmission includes long elastic elements with distributed mechanical parameters. The system, containing the motion transmission under consideration, is driven by an engine via epicyclic gearing. The torque is transmitted via a long drive shaft to a propeller working with a variable blade geometry. The rotor of a synchronous generator is mounted on the ship's long drive shaft. This shaft generator produces electricity that is fed to the ship's electrical network. With the use of the developed mathematical model, electromechanical transients occurring during the transmission of mechanical power are analyzed. This paper analyzes the motion transmission with the use of computer simulation and presents the results of research. [ABSTRACT FROM AUTHOR]

The development of mathematical models and efficient technologies for the processing of protein-containing dairy and vegetable raw materials and the production of food and feed concentrates with controlled functional properties is one of the most promising areas within the agricultural industry. In this work, the suitability of the electroflotation coagulation method for the combined extraction of vegetable and milk proteins was established by changing the electrolysis parameters and directed regulation of the isoelectric state of proteins. The research methodology is based on modern achievements of leading domestic and foreign researchers in the field of electrolysis of solutions and the creation of reagentless technologies for extracting proteins, as well as on the use of guest methods of physicochemical analysis, pH-metry, potentiometric and organoleptic analysis, methods of cyclic chronovoltammetry and currentless chronopotentiometry. The paper presents technological schemes for the extraction of vegetable and milk proteins, based on the combination of electroflotation and electrocoagulation processes. We carried out technological tests, which made it possible to determine the optimal conditions that ensure the highest yield of the product and its quality indicators. Ready-made isolates and concentrates of chickpea proteins and curd whey were obtained. [ABSTRACT FROM AUTHOR]

Our paper aims at testing the impact of separate elements of the intellectual capital (IC) represented for instance by the human, structural, and customer capital, on the functioning and performance of the small and medium-sized enterprises (SMEs) using mathematical modeling. We assess the intellectual capital with respect to the resource-based view theory. Our study is based on the data obtained from the 206 surveys with the representatives of small and medium-sized enterprises from Commonwealth of Independent States (CIS) countries. We employed a mathematical modeling approach as well as the SPSS application package in order to test our hypotheses about the influence of intellectual capital on the enterprise's efficiency. Our results helped us to determine that the concept of intellectual capital is practically not used in the management of small and medium-sized enterprises in CIS countries. It becomes apparent that individual techniques for managing intellectual resources can only be identified intuitively, based on an in-depth analysis of the current tasks facing managers. These findings confirmed the positive impact of intellectual capital on the performance of small and medium-sized enterprises in the conditions of the economies in transition represented hereinafter in our paper by CIS countries, but only with the availability of financial resources and with some important reservations. [ABSTRACT FROM AUTHOR]

Mathematical computer models of the permittivity of silicon-based nanostructures upon interaction with electromagnetic radiation in a wide frequency range have been developed. To implement computer models for studying the electrophysical properties of the structures under study, algorithms and a set of programs have been developed. The results of the study of materials will not only provide fundamental information about the physical effects occurring in composite nanostructures but will also be useful for solving problems related to calculations for given electrophysical problems. For a nanocomposite based on ceramics and semiconductor oxides of zinc grains, resonant bursts of permittivity are observed within a wavelength of 300–400 nm; it has been found that this is due to the presence of electronic polarization of the nanocomposite core. The paper presents the results of modeling the current-voltage characteristics of a nanocomposite based on ceramics and semiconductor grains of zinc oxide. The obtained results show that the geometrical parameters, such as the number of layers and sample width, affect the CVC of the nanocomposite, and the operating point of the CVC shifts. This may be of interest in the development of materials with desired electrical characteristics for the creation of varistors. [ABSTRACT FROM AUTHOR]

In this paper, we considered a mathematical model concerned with the treatment of Chronic Lymphocytic Leukemia (CLL) taking into account the effect of superficially infused T cells in this particular type of tumor. The model is described thoroughly by the system of non-linear differential equations explaining the interaction of naïve, infected, cancer and immune cell population. The detailed sensitivity analysis with the application is the major part of this paper. The basic objective is to provide insight to how parameters' behavior varies model results by elaborating the results obtained from the application of sensitivity analysis. The sensitivity of the model was evaluated not only theoretically, but also with the help of a numerical approach, producing graphs providing better imminent of results. We argue that the application of the sensitivity analysis method endows an insight into how and which parameters are of primary significance in controlling the spread of leukemia. [ABSTRACT FROM AUTHOR]

Biomedical data (structured and unstructured) has grown dramatically in strength and volume over the last few years. Innovative, intelligent, and autonomous scientific approaches are needed to examine the large data sets that are gradually becoming widely available. In order to predict unique symmetric and asymmetric patterns, there is also an increasing demand for designing, analyzing, and understanding such complicated data sets. In this paper, we focused on a different way of processing biological and medical data. We provide an overview of known methods as well as a look at optimized mathematical approaches in the field of biological data analysis. We deal with the RGB threshold algorithm, new filtering based on the histogram and on the RGB model, the Image J program, and the structural similarity index method (SSIM) approaches. Finally, we compared the results with the open-source software. We can confirm that our own software based on new mathematical models is an extremely suitable tool for processing biological images and is important in research areas such as the detection of iron in biological samples. We study even symmetric and asymmetric properties of the iron existence as a design analysis of the biological real data. Unique approaches for clinical information gathering, organizing, analysis, information retrieval, and inventive implementation of contemporary computing approaches are all part of this research project, which has much potential in biomedical research. These cutting-edge multidisciplinary techniques will enable the detection and retrieval of important symmetric and asymmetric patterns, as well as the faster finding of pertinent data and the opening of novel learning pathways. [ABSTRACT FROM AUTHOR]

In general, the state of a system in which a physical quantity such as mass is distributed over space can be modeled by a function that represents the density distribution. The purpose of this paper is to introduce special functions that can be applied when in the system to be modeled, where the quantity is distributed over isolated points. For that matter, the expanded real numbers are introduced as an ordered subring of the hyperreal number field that does not contain any infinitesimals, and hyperreal delta functions are defined as special functions from the real numbers to the expanded real numbers satisfying the condition that (i) the support is a singleton, and (ii) the integral over the reals is a nonzero real number. These newly defined hyperreal delta functions, and tensor products thereof, then provide a general tool, applicable for the mathematical modeling of physical systems in which infinitely high densities occur. [ABSTRACT FROM AUTHOR]

Composite materials consisting of a dielectric matrix with conductive inclusions are promising in the field of micro- and optoelectronics. The properties of a nanocomposite material are strongly influenced by the characteristics of the substances included in its composition, as well as the shape and size of inclusions and the orientation of particles in the matrix. The use of nanocomposite material has significantly expanded and covers various systems. The anisotropic form of inclusions is the main reason for the appearance of optical anisotropy. In this article, models and methods describing the electrical conductivity of a layered nanocomposite of a self-similar structure are proposed. The method of modeling the electrical conductivity of individual blocks, layers, and composite as a whole is carried out similarly to the method of determining the dielectric constant. The advantage of the method proposed in this paper is the removal of restrictions imposed on the theory of generalized conductivity associated with the need to set the dielectric constant. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model was developed to simulate SARS-CoV-2 dynamics in infected patients. The model considers both the innate and adaptive immune responses and consists of healthy cells, infected cells, viral load, cytokines, natural killer cells, cytotoxic T-lymphocytes, B-lymphocytes, plasma cells, and antibody levels. First, a mathematical analysis was performed to discuss the model's equilibrium points and compute the basic reproduction number. The accuracy of such mathematical models may be affected by many sources of uncertainties due to the incomplete representation of the biological process and poorly known parameters. This may strongly limit their performance and prediction skills. A state-of-the-art data assimilation technique, the ensemble Kalman filter (EnKF), was then used to enhance the model's behavior by incorporating available data to determine the best possible estimate of the model's state and parameters. The proposed assimilation system was applied on the real viral load datasets of six COVID-19 patients. The results demonstrate the efficiency of the proposed assimilation system in improving the model predictions by up to 40 % . [ABSTRACT FROM AUTHOR]

The paper presents the results of an experimental study of heating and the structural resultant changes of source rocks under the influence of the electromagnetic field in the microwave and radio-frequency ranges. The samples from the Bazhenov Formation (West Siberia, Russia) and the Domanic Formation (Ural, Russia) have been tested. It is shown that samples from these formations demonstrate very different heating rates at the same electromagnetic field parameters and the their heating rate depends on the type of the electromagnetic field (radio-frequency or microwave) applied. The temperature of the Bazhenov Formation samples reaches 300 °C within one hundred seconds of the microwave treatment but it slowly rises to 200 °C after twelve minutes of the radio-frequency influence. The samples of the carbonate Domanic Formation heat up more slowly in the microwave field (within two hundred seconds) and to lower temperatures in the radio-frequency (150 °C) than the Bazhenov Formation samples. The study of the structure of the samples before and after experiments on the electromagnetic treatment shows fracture formation during the heating process. Numerical simulations of heating dynamics of source rock samples have been based on a simple mathematical model of the electromagnetic influence and main features of heating for different types of source rock have been revealed. The opportunities for application of electromagnetic heating for oil source rock recovery are discussed. [ABSTRACT FROM AUTHOR]

International research has pointed out the importance of integrating mathematical modeling and inquiry processes into the teaching and learning of mathematics. This paper aims to present an integrative model that enables analyzing the characteristics inquiry and modeling processes share in the same model with a view to using them when designing and implementing interdisciplinary teaching sequences. After presenting a synthesis of the literature review, our theoretical approach to inquiry and modeling for the analysis of an interdisciplinary teaching sequence will be introduced. We focus here on the case of an inquiry situation in an archaeological context where mathematics and history are interrelated. It was implemented at secondary school level with students aged 13–14. We use this particular case study to analyze the appearance of both processes, in order to look for coincidences, concatenations and synergies. The main result is an integrative model for the joint analysis of both processes. [ABSTRACT FROM AUTHOR]

This paper shows a tool for the analysis of written productions that allows for the characterization of the mathematical models that students develop when solving modeling tasks. For this purpose, different conceptualizations of mathematical models in education are discussed, paying special attention to the evidence that characterizes a school model. The discussion leads to the consideration of three components, which constitute the main categories of the proposed tool: the real system to be modeled, its mathematization and the representations used to express both. These categories and the corresponding analysis procedure are explained and illustrated through two working examples, which expose the value of the tool in establishing the foci of analysis when investigating school models, and thus, suggest modeling skills. The connection of this tool with other approaches to educational research on mathematical modeling is also discussed. [ABSTRACT FROM AUTHOR]

Trajectory optimization is the series of actions that are taken into consideration in order to produce the best path such that it improves the overall performances of physical properties or reduces the consumption of the resources where the restriction system remains maintained. In this paper, first, a compact mathematical model for a symmetrical annular-shaped omnidirectional wheeled mobile robot (SAOWMR) is derived and verified. This general mathematical model provides an opportunity to conduct research, experiments, and comparisons on these omnidirectional mobile robots that have two, three, four, six, or even more omnidirectional wheels without the need to switch models or derive a new model. Then, a new computationally efficient method is proposed to achieve improvements in the trajectory planning optimization (TPO) for a SAOWMR. Moreover, the proposed method has been tested in collision-free navigation by incorporation of the path constraints. Numerical tests and simulations are presented aiming to ensure the efficiency and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Passive solar distillation is cheap and energy-efficient technology but its main disadvantage is low productivity. Thus, there are many attempts to improve solar stills' productivity, and one of them is changing the mass of the water. This paper presents the results of validation of the thermal processes modeling in a solar still (SS). In order to validate the model, the experimental studies were conducted in a laboratory to ensure uniform climatic conditions. The studies were carried out for 10 kg, 15 kg, and 20 kg of water under three different solar irradiance conditions. The results show that 10 kg and 20 kg of water ensure the highest and the lowest daily productivity, respectively, independently of solar irradiance. When the water mass is 10 kg, the solar still's productivity is 800 mL/m2/day, 3732 mL/m2/day, and 9392 mL/m2/day for low, medium, and high solar irradiance, respectively. Additionally, it is found that reducing the water mass from 20 kg to 10 kg can improve solar still's productivity by a maximum value of 21.6%, which is obtained for low solar irradiance. The proposed mathematical model allows predicting the performance of the SS. The results of the theoretical calculations are in good agreement with the results of the experiments. The minimum and maximum deviation between the actual and theoretical productivity of the SS is 1.1% and 8.3%, respectively. [ABSTRACT FROM AUTHOR]

Having a method for analyzing and designing regulators of controls that contain many current loops such as active filters is not a trivial task. There can be many parameters of regulators and filters that must be carefully selected in order to fulfill certain desired requirements. For instance, these can be stability, dynamic response, robustness under uncertainty of parameters, and rejection capability to switching harmonics. Hence, this paper provides general analysis guidelines for designing current control loops by using mathematical models in an αβ reference frame. Then, by using the proposed modeling tool, a multi-objective tuning algorithm is proposed that helps obtain all the control loops' regulator and filter parameters, meeting all the desired requirements. Thus, the proposed analysis and design methodology is illustrated by applying it to three different controls conceived in a dq rotating reference frame with PI (Proportional Integral) regulators. The first control presents two current loops (simple dq current control), the second control uses four current loops (dual vector control, for unbalanced loads), while the third control presents eight current loops (active filter controlling current harmonics). Several experimental and simulation results show the effectiveness and usefulness of the proposed method. Since the mathematical model employed is in the αβ reference frame, it can also be easily applied to controls conceived in a αβ reference frame using resonant regulators, providing also a common comparative framework. [ABSTRACT FROM AUTHOR]

This paper presents a case study carried out at an elementary school that led to a characterization of mathematical modeling projects aimed at generating social impact. It shows their potential as generators of mathematical learning opportunities. In the school project, upper-grade students (sixth grade, 11-year-olds) studied the way in which the rest of the students at the institution traveled from their homes to school. Its purpose was to identify risk points from the standpoint of road safety and to develop a set of recommendations so that all the children could walk safely to school. In our study, we identified, on the one hand, the mathematical learning opportunities that emerged during the development of the project and, on the other, the mathematical models created by the students. We discuss the impact of the project on the different groups in the school community (other students, parents, and teachers). We conclude with a characterization of the mathematical modeling projects oriented towards social impact and affirm that they can be generators of mathematical learning opportunities. [ABSTRACT FROM AUTHOR]

Concurrent enrollment refers to partnerships between postsecondary institutions and schools through which secondary school students can complete a university class taught by a qualifying secondary school teacher at their secondary school. We propose that concurrent enrollment programs are an under-recognized tool for extending the impact of Universal Design for Learning (UDL). The context of our study is an equity-focused university course in algebraic mathematical modeling that is also offered through concurrent enrollment in over 30 secondary schools to over 800 secondary students annually in our state of Minnesota, U.S.A. This paper presents a qualitative analysis of secondary school teachers' experiences implementing the inquiry pedagogy and the equity goals of the course. Several results are important for UDL. Teachers (1) describe equity in social terms of race, ethnicity, income, immigration, and language status in addition to measures of academic success; (2) perceive improvements in students' attitudes towards mathematics, school, and university education; (3) perceive student academic growth through mathematical writing; and (4) report close relationships with students. If higher education faculty design their on-campus classes to incorporate UDL principles, concurrent enrollment offers the potential to improve inclusive pathways from secondary schools to universities. [ABSTRACT FROM AUTHOR]