We prove an analog of the removable singularity theorem for bounded harmonic functions on stratified sets. The harmonic functions are understood in the sense of the soft Laplacian. The result can become one of the main technical components for extending the well-known Poincaré–Perron’s method of proving the solvability of the Dirichlet problem for the soft Laplacian.

We present an open-source Star Tracker (ST) for Attitude Determination. Our implementation makes use of open source software of common usage in astronomy running on a Raspberry Pi 2 platform. The developed platform is open and available for parties interested in further development. Evaluation of the system showed that the ST is suitable for Cubesats of 2U or larger. The ST platform is capable of solving the Lost-In-Space (LIS) problem. Currently, the average accuracy reached of the algorithm is close to 5 seconds of arc with an average processing time of 75 seconds. However, a average accuracy of about 3 minutes of arc can be reached with 35 seconds in average processing time. We also describe the evaluation procedure, the found conclusions of this procedure, in particular the section of the algorithm where most of the processing time is spent and other possible source of errors not included in this study.

This paper details the comprehensive activities conducted in a laboratory setting to assess the Structural Health Monitoring (SHM) of prefabricated building envelopes. Aimed at enhancing the structural evaluation of buildings, the focus of this research lies in employing nondestructive sensors for SHM with the objective to advance in the understanding and assessment of facade conditions. The paper outlines the methodologies employed, starting with a modal analysis to define the structural vibration's modal frequency. Subsequently, tests were defined and executed to validate building envelope compliance in case of stress typical of high-rise building. Throughout these tests, continuous monitoring of the façade was conducted using both conventional (accelerometers, extensimeter washers) and non-conventional sensors (Fiber Optic Sensing) The gathered data underwent thorough processing and analysis to provide an overall perspective on the structure's behavior during the stress test. The investigation aimed to identify whether specific physical phenomena correlate with distinct signals and to evaluate if continuous façade monitoring over the building's lifespan aids in preventing potential structural damage. Moreover, two modal analyses were conducted to compare final data and frequencies with earlier data, enabling the detection of any structural alterations. The results from compliance testing and structural analysis yielded noteworthy insights contributing to the evolving field of structural health monitoring, offering valuable findings that advance our ability to proactively manage and maintain the integrity of building structures.

Every finite simple group P can be generated by two of its elements. Pairs of generators forP are available in the Atlas of finite group representations as (not necessarily minimal) permutation representations P . It is unusual but significant to recognize that a P is a Grothendieck’s dessin d’enfant D and that a wealth of standard graphs and finite geometries G - such as near polygons and their generalizations - are stabilized by a D. In our paper, tripods P − D − G of rank larger than two,corresponding to simple groups, are organized into classes, e.g. symplectic, unitary, sporadic, etc (as in the Atlas). An exhaustive search and characterization of non-trivial point-line configurationsdefined from small index representations of simple groups is performed, with the goal to recognize their quantum physical significance. All the defined geometries G's have a contextuality parameterclose to its maximal value 1.

The Steepest Descent (or Ascent) algorithm is one of the most widely used algorithms in Science, Technology, Engineering, and Mathematics (STEM). However, this powerful mathematical tool is neither taught nor even mentioned in K12 education. We study whether it is feasible for elementary school students to learn this algorithm, while also aligning with the standard school curriculum. We also look at whether it can be used to create enriching activities connected to children’s real-life experiences, thus enhancing the integration of STEM and fostering Computational Thinking. To address these questions, we conducted an empirical study in two phases. In the first phase, we tested the feasibility with teachers. In a face-to-face professional development work-shop with 457 mathematics teachers actively participating using an online platform, we found that after a 10-minute introduction they could successfully apply the algorithm and use it in a couple of models. They were also able to complete two complex and novel tasks: selecting models and adjusting the parameters of a model that uses the steepest descent algorithm. In a second phase, we tested the feasibility with 90 fourth graders from 3 low Socioeconomic Status (SES) schools. Using the same introduction and posing the same questions, we found that they were able to understand the algorithm and successfully complete the tasks on the online platform. Additionally, we found that close to 75% of the students completed the two complex modeling tasks and performed similarly to the teachers.

The Steepest Descent (or Ascent) algorithm is one of the most widely used algorithms in Science, Technology, Engineering, and Mathematics (STEM). However, this powerful mathematical tool is neither taught nor even mentioned in K12 education. We study whether it is feasible for elementary school students to learn this algorithm, while also aligning with the standard school curriculum. We also look at whether it can be used to create enriching activities connected to children’s real-life experiences, thus enhancing the integration of STEM and fostering Computational Thinking. To address these questions, we conducted an empirical study in two phases. In the first phase, we tested the feasibility with teachers. In a face-to-face professional development work-shop with 457 mathematics teachers actively participating using an online platform, we found that after a 10-minute introduction they could successfully apply the algorithm and use it in a couple of models. They were also able to complete two complex and novel tasks: selecting models and adjusting the parameters of a model that uses the steepest descent algorithm. In a second phase, we tested the feasibility with 90 fourth graders from 3 low Socioeconomic Status (SES) schools. Using the same introduction and posing the same questions, we found that they were able to understand the algorithm and successfully complete the tasks on the online platform. Additionally, we found that close to 75% of the students completed the two complex modeling tasks and performed similarly to the teachers.

As with many of the non-deterministic search algorithms, particularly those are analogous to complex biological systems, there are a number of inherent difficulties, and the Bees Algorithm (BA) is no exception. Basic versions and variations of the BA have their own drawbacks. Some of these drawbacks are a large number of parameters to be set, lack of methodology for parameter setting and computational complexity. This paper describes a Grouped version of the Bees Algorithm (GBA) addressing these issues. Unlike its conventional version, in this algorithm bees are grouped to search different sites with different neighbourhood sizes rather than just discovering two types of sites, namely elite and selected. Following a description of the GBA, the results gained for 12 benchmark functions are presented and compared with those of the basic BA, enhanced BA, standard BA and modified BA to demonstrate the efficacy of the proposed algorithm. Compared to the conventional implementations of the BA, the proposed version requires setting of fewer parameters, while producing the optimum solutions much faster.

Symbolic pole/zero analysis is an important step when designing an analog operational amplifier. Generally, a simplified symbolic analysis of analog circuits suffers from NP-hardness, i.e., an exponential growth of the number of symbolic terms of the transfer function with the circuit size. In this study, we present a mathematical model combined with a heuristic-metaheuristic solution method for the symbolic pole/zero simplification in operational transconductance amplifiers (OTA). At first, the circuit is symbolically solved and an improved root splitting method is applied to extract symbolic poles/zeroes from the exact expanded transfer function. Then, a hybrid algorithm based on heuristic information and a metaheuristic technique using simulated annealing is performed for the simplification of the derived symbolic pole/zero expressions. The developed method has been tested on three analog OTAs. The obtained results show the effectiveness of the proposed method to achieve accurate simplified symbolic pole/zero expressions with the least complexity.

Academic publishing appears to be the most important key of the academic functions (academic research, excellence in teaching and learning and community services). Selecting the right journal to publish research results is a challenge to academics. Yet, there is inadequate knowledge about a model specifically directed at the topic of the journal selection process with a mathematical certainty. The objectives of this research are: to identify the main factors that an author or researchers consider when selecting an academic journal for submitting a manuscript, and, to develop a mathematical algorithm of journal selection that provide the best journal choice with a mathematical certainty based on difficulty of each factor. Quantitative research through questionnaires has been applied as an appropriate instrument base to address the researcher’s identification of the factors that should be considered when selecting a journal. Questionnaire developed and emailed to academics in 31 public and private universities in the developing countries. Academics reported that the most important publication difficulty factors were publishing in reputable journals, and publishing in a journal that has an impact factor. However, the most least publication difficulty factors were found to be: number of issues per year and if the journal is an open access. The proposed mathematical algorithm of journal’s publication difficulty factors was developed and tested.

Eddy-driven jets are of importance in the ocean and atmosphere, and to a first approximation are governed by Rossby wave dynamics. This study addresses the time-dependent flux of fluid and potential vorticity between such a jet and an adjacent eddy, with specific regard to determining zonal and meridional wavenumber dependence. The flux amplitude in wavenumber space is obtained, which is easily computable for a given jet geometry, speed and latitude, and which provides instant information on the wavenumbers of the Rossby waves which maximize the flux. This new tool enables the quick determination of which modes are most influential in imparting fluid exchange, which in the long term will homogenize the potential vorticity between the eddy and the jet. The results are validated by computing backward- and forward-time finite-time Lyapunov exponent fields, and also stable and unstable manifolds; the intermingling of these entities defines the region of chaotic transport between the eddy and the jet. The relationship of all of these to the time-varying transport flux between the eddy and the jet is carefully elucidated. The flux quantification presented here works for general time-dependence, whether or not lobes (intersection regions between stable and unstable manifolds) are present in the mixing region, and is therefore also easily computable for wave packets consisting of infinitely many wavenumbers.

Panel data of our interest consist of a moderate number of panels, while the panels contain a small number of observations. An estimator of common breaks in panel means without a boundary issue for this kind of scenario is proposed. In particular, the novel estimator is able to detect a common break point even when the change happens immediately after the first time point or just before the last observation period. Another advantage of the elaborated change point estimator is that it results in the last observation in situations with no structural breaks. The consistency of the change point estimator in panel data is established. The results are illustrated through a simulation study. As a by-product of the developed estimation technique, a theoretical utilization for correlation structure estimation, hypothesis testing, and bootstrapping in panel data is demonstrated. A practical application to non-life insurance is presented as well.

The software industry has adopted component-based software development (CBSD) to rapidly build and deploy large and complex software systems with significant savings at minimal engineering effort, cost, and time. However, CBSD encounters issues on security trust, mainly with respect to dependability attributes. A system is considered dependable when it can produce the outputs for which it was designed with no adverse effect on its intended environment. Dependability consists of several attributes that imply availability, confidentiality, integrity, reliability, safety, and maintainability. Dependability attributes must be embedded in a CBSD model to develop dependable component software. Motivated by the importance of these attributes, this paper pursues two objectives: to design a model for developing a dependable system that mitigates the vulnerabilities of software components, and to evaluate the proposed model. The model proposed in this study is labelled as developing dependable component-based software (2DCBS). To develop this model, the CBSD architectural phases and processes must be framed and the six dependability attributes embedded according to the best practice method. The expert opinion approach was applied to evaluate 2DCBS framing. In addition, the 2DCBS model was applied to the development of an information communication technology (ICT) portal through an empirical study method. Vulnerability assessment tools (VATs) were employed to verify the dependability attributes of the developed ICT portal. Results show that the 2DCBS model can be adopted to develop web application systems and to mitigate the vulnerabilities of the developed systems. This study contributes to CBSD and facilitates the specification and evaluation of dependability attributes throughout model development. Furthermore, the reliability of the dependable model can increase confidence in the use of CBSD for industries.

The key links of face recognition are digital image preprocessing, facial feature extraction and pattern recognition, this article aimed at the current problem of slow speed and low recognition accuracy of face recognition , from the above three key links, on the basic of analyzing the therories of Fractional Differential Masks Operator (FDMO), Principal Component Analysis (PCA) and Support Vector Machine (SVM), design a kind of FDMO+PVA+SVM coupling algorithm that applies to face recognition to improve the speed and accuracy of it. To realize FDMO+PCA+SVM coupling algorithm, first, we should apply FDMO to face image processing binary marginalization, the purpose is getting face contour; Then, we apply PCA to get the feature of face image which is disposed by binary marainalization. At last, we can apply One-Against All of the SVM classifier and LibSVM software package to realize face recognition. Beside, the article with nine different coupling algorithm design four groups of experimental reaults on the ORL face database verified by comparative analysic FDMO+PCA+SVM coupling algorithm in the superiority of face recognition accuracy and speed.

We introduce the notion of generalized contraction on dualistic partial metric spaces. A fixed point theorem for mappings satisfying above mentioned contraction is obtained. Some consequences of our result are obtained. We construct an example to demonstrate the effectiveness of our result among the corresponding results in partial metric spaces. Our results provide substantial generalizations and improvements of several well known results existing in the comparable literature. We discuss an application of our fixed point results to show the existence of solution of functional equations.

Considering that cryptocurrencies are now present in practically every financial transaction because they are widely accepted as an alternate means of making payments and exchanging currencies, academics and economists have more opportunities to study cryptocurrency prices. Over the years, investors, traders and investment banks have found it difficult to predict the closing daily price of Ethereum due to its rapid price fluctuation. The daily closing price of cryptocurrency is essential to consider when trading or investing in Ethereum. This report focuses on carrying out a comparative study of the predictive capabilities of deep machine learning algorithms with a stacking ensemble modelling framework using daily historical observations of the price of Ethereum obtained from Coindesk, tweets extracted from Twitter ranging from the 1st of August 2022 to the 8th of August 2022 and other five covariates (closing price lag1, closing price lag2, noltrend, daytype and month) engineered from the closing price of Ethereum. Seven models are used to compute the forecasts for the daily closing price of Ethereum; these are the recurrent neural network, ensemble stacked recurrent neural network, gradient boosting machine, generalized linear model, distributed random forest, deep neural networks and stacked ensemble for gradient boosting machine, generalized linear model, distributed random forest and deep neural networks. The main evaluation metric used is the mean absolute error. According to MAE, RNN forecasts outperform the other model’s forecasts in this study, producing an MAE of 0.0309.

With the increasing concern of environment, the energy-efficiency scheduling of manufacturing industry is becoming urgent and popular. In turning processes, both spindle speed and processing time can affect the final energy consumption and thus the spindle speed and scheduling scheme need to be optimized simultaneously. Since the turning workshop can be regarded as the flexible flow shop, this paper formulates a mixed integer linear programming model for energy-efficient scheduling of flexible flow shop. Accordingly, a new decoding method is developed by considering of the optimization of spindle speed and scheduling scheme simultaneously, and an estimation of distribution algorithm adopting the new decoding method is proposed to solve large-size problems. The parameters of this algorithm are determined by statistical technique with a simplified practical case. In order to validate the proposed method, a case from practical factories is studied, in which the makespan can be shortened by 25.22%, and the consumed energy can be saved by 5.48%. These results demonstrate the effectiveness of the proposed mathematical model and algorithm.

We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals.

In order to overcome the limitation of the traditional adaptive Unscented Kalman Filtering (UKF) algorithm in noise covariance estimation for statement and measurement, we propose a hybrid adaptive UKF algorithm based on combining Maximum a posteriori (MAP) criterion and Maximum likelihood (ML) criterion, in this paper. First, to prevent the actual noise covariance deviating from the true value which can lead to the state estimation error and arouse the filtering divergence, a real-time covariance matrices estimation algorithm based on hybrid MAP and ML is proposed for obtaining the statement and measurement noises covariance, respectively; and then, a balance equation the two kinds of covariance matrix is structured in this proposed to minimize the statement estimation error. Compared with the UFK based MAP and based ML, the proposed algorithm provides better convergence and stability.

In this article, a generalization of the geometry of Grassmannian chain complex of free abelian groups generated by the projective configuration of points and Cathelineau's infinitesimal complex of polylogarithmic groups is proposed. Firstly, homomorphisms for weight n =2 up to weight n=6 will be introduced to connect sub-complexes of Grassmannian and Cathelineau. Lately, generalization of these morphisms will be shown for weight n=N. The associated diagrams will also be proven to be commutative and bi-complex.

Earth observation satellites can capture images of specific areas in Earth's orbit based on user requirements. Despite the high demand for satellite imagery, satellites remain a scarce resource. When there are many observation tasks that are large and dense, they may interfere with each other due to satellite mobility. To address this issue, a multi-satellite scheduling algorithm based on a task merging mechanism has been proposed. This paper proposes a two-stage approach to the problem: task merging phase and merging task scheduling phase. The task merging phase introduces two methods based on Mean Shift and Complete Graph to generate the merging task set. In the merging task scheduling phase, a multi-satellite scheduling algorithm based on merging tasks is employed to solve the problem. Finally, certain measurement experiments suggest the effectiveness of the algorithm.

In wireless sensor networks (WSNs), each sensor node can estimate the global parameter from the local data in distributed manner. This paper proposed a robust diffusion estimation algorithm based on minimum error entropy criterion with self-adjusting step-size, which are referred to as diffusion MEE-SAS (DMEE-SAS) algorithm. The DMEE-SAS algorithm has fast speed of convergence and is robust against non-Gaussian noise in the measurements. The detailed performance analysis of the DMEE-SAS algorithm is performed. By combining the DMEE-SAS with diffusion minimum error entropy (DMEE) algorithms, an Improving DMEE-SAS algorithm is proposed, in non-stationary environment where tracking is very important. The Improving DMEE-SAS algorithm can avoid insensitivity of the DMEE-SAS algorithm due to the small effective step-size near the optimal estimator, and obtain a fast convergence speed. Numerical simulations are given to verify the effectiveness and advantages of these proposed algorithms.

The philosophy of testing statistical hypothesis is a natural consequence and functional extension of mathematical analysis of Probability. Along with the concept of recurrence when applied to random sequences and functions, it leads to the analysis of a priori and posterior which implies testing statistical hypothesis. Testing statistical hypothesis also involves algebraic, functional and dimensional considerations, which are found in the works of Laplace. Aspects of mathematical analysis such as universality of solutions, Laws of Large Numbers, Entropy, Information, and various functional dependencies are the main factors explained in the five properties that lead to implication of testing statistical hypothesis. Various interesting examples with modern scientific significance from genetics, astrophysics, and other areas give methodological access to answers of different problems and phenomena which are involved in the logic of testing statistical hypothesis.

This paper is motivated by spatio-temporal pattern in the occurrence of Leishmaniasis in Afghanistan and the relatively high number of zero counts. We hold the view that correlations that arise from spatial and temporal sources are inherently distinct. Our method decouples these two sources of correlations, there are at least two advantages in taking this approach. First, it circumvents the need to inverting a large correlation matrix, which is a commonly encountered problem in spatio-temporal analyses. Second, it simplifies the modelling of complex relationships such as anisotropy, which would have been extremely difficult or impossible if spatio-temporal correlations were simultaneously considered. We identify three challenges in the modelling of a spatio-temporal process: (1) accommodation of covariances that arise from spatial and temporal sources; (2) choosing the correct covariance structure and (3) extending to situations where a covariance is not the natural measure of association. Moreover, because the data covers a period that overlaps with the US invasion of Afghanistan, the high number of zero counts may be the result of no disease incidence or lapse of data collection. To resolve this issue, a model truncated at zero built on a foundation of the generalized estimating equations was proposed.

Managing a portfolio whose value closely tracks an index by trading only in a subset of the index constituents involves an NP-hard optimisation problem. In the prior literature, it has been suggested to solve this problem using sequential Monte Carlo (SMC, a.k.a. particle filter) methods. However, this literature does not take transaction costs into account, although transaction costs are the primary motivation for attempting to replicate the index by trading in a subset, rather than the full set of index constituents. This paper extends the SMC approach to index tracking to allow for proportional transaction costs and implements this extended method on empirical data for a variety stock indices. In addition to providing a more practically useful tracking strategy by allowing for transaction costs, we find that including a penalty for transaction costs in the optimisation objective can actually lead to better tracking performance.

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests developed. However, most of the previously developed testing procedures for fractional cointegration were primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test development is based on bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between [0,1], and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes.

High-precision conical threads are widely used in responsible joints in the drilling of oil and gas wells. Difficult underground drilling conditions due to the occurrence of significant mechanical loads and an aggressive environment in wells require the use of workable materials that are often difficult to machine. The huge need for such connections dictates the use of high-performance cutting tools, which means that high demands are placed on their effective geometric performance. The study describes the theoretical dependence of the profile precision of the tapered drill-string tool-joint threads of all standard sizes on the complex of a cutting tool geometric parameters and cutting tool setting accuracy. The experiments include an assessment of the geometric accuracy of the profile of the obtained NC23 thread connector, depending on the values of the installation angles and the declared tangential displacement of the standard threaded carbide insert.

In this paper, we first discuss the research status and application progress of the finite element method and the smoothed particle method. By analyzing the advantages of the smoothed particle method and the finite element method, a new coupling algorithm, namely FEM-SPH algorithm, is proposed. By the method of comparison, it shows that finite element method and SPH method in the simulation of large deformation problems each have advantages and disadvantages, the finite element method smoothed particle coupling algorithm is effective to achieve the performance of high computational efficiency and can naturally simulate large deformation problems across. In the process of calculation, the large deformation unit can be freely into an algorithm to facilitate the calculation accuracy and efficiency of three methods of numerical simulation. Through the study found, FEM-SPH algorithm not only overcome the defect of smooth particle tensile instability, but also overcomes the problem of low efficiency of finite element computation. To further test the FEM-SPH algorithm has advantages in the practical engineering, we have carried out the actual test to the example of the super high speed collision, concluded that, since the target of most of the computational domain is always finite element, smoothed particle focused only in contact with the projectile and target of local area, particle number is not much, the whole calculation process just ten minutes, computational efficiency has been greatly improved, at the same time in the simulation of large deformation, the advantage is very obvious .This provides a criterion for the actual project, depending on the specific material deformation mode and choose a more appropriate conversion algorithm.

This paper proposes a new approach for multi-focus images fusion based on Region Mosaicing on Contrast Pyramids (REMCP). A density-based region growing method is developed to construct a focused region mask for multi-focus images. The segmented focused region mask is decomposed into a mask pyramid, which is then used for supervised region mosaicking on a contrast pyramid. In this way, the focus measurement and the continuity of focused regions are incorporated and the pixel level pyramid fusion is improved at the region level. Objective and subjective experiments show that the proposed REMCP is more robust to noise than compared algorithms and can fully preserves the focus information of the multi-focus images meanwhile reducing distortions of the fused images.

In a recent paper, Sarikaya et al. introduced a new analogue of the classical Gamma function which they called, the conformable Gamma function. Motivated by their results, this paper seeks to establish some inequalities for the conformable Gamma and Polygamma functions. Among other analytical tools, the procedure relies on the generalized forms of some classical inequalities.

Pavement crack detection is one of the key links in highway pavement maintenance management. In the current road crack detection, the network model easily ignores the shallow geometric features of cracks and cannot extract the key feature information of cracks. Aiming at the above problems, an EC-YOLOX network model is proposed. The CFPN is constructed to cross-fuse different scale features to solve the feature scale invariance. In the strengthen feature extraction layer, ECANet is fused to enhance the ability to pay attention to key information. The WEIoU loss function is proposed, which assigns different penalty terms to the target box in the vertical and horizontal directions. In terms of data, geometric distortion constraint correction is performed on the single-point perspective pavement image. The experimental data show that the accuracy of EC-YOLOX on the self-built data set reaches 76.34% [email protected], which is 4.45% higher than that of YOLOX. The loss curve of EC-YOLOX is smoother than that of YOLOX, and the minimum training loss value is 2.136, which is 0.648 lower than the minimum loss value 2.784 of YOLOX. Many experiments have verified the effectiveness of EC-YOLOX in improving the detection effect in pavement crack detection.

Splines and quasi-interpolation operators are important both in approximation theory and applications. In this paper, we construct a family of quasi-interpolation operators for the bivariate quintic spline spaces S₅³ (∆_mn⁽²⁾). Moreover, the properties of the proposed quasi-interpolation operators are studied, as well as its applications for solving two-dimensional Burgers’ equation and image reconstruction. Some numerical examples show that these methods, which are easy to implement, provide accurate results.

Classifying network flow subsequences in an Industrial IoT gateway is an effective method for identifying Industrial IoT faults. This paper proposes a subsequence classification algorithm SSGBUL-IKNN based on unsupervised learning encoding to address the problem of low classification accuracy. Firstly, we built a network module based on unsupervised learning to encode the flow sequence of the Industrial IoT gateway. In the encoding module, a subsequence calibration algorithm controls the increasing error during the coding process. Then, the specific fault type is obtained through an improved KNN classification algorithm based on the indication distance source from the integrated coding sequences converted by multi-dimensional network flow sequences. The test result on three Industrial IoT datasets of a sewage treatment plant shows that the accuracy of SSGBUL-IKNN in this paper exceeds 92%, significantly higher than the algorithm DTW and TSF. It reaches the classification requirements of Industrial IoT fault diagnosis.

Computer simulation of normal and diseased human heart activity requires a 3D anatomical model of the myocardium, including myofibres. For clinical applications, such a model has to be constructed based on routine methods of cardiac visualisation such as sonography. Symmetrical models are shown to be too rigid, so an analytical non-symmetrical model with enough flexibility is necessary. Based on previously made anatomical models of the left ventricle, we propose a new, much more flexible spline-based analytical model. The model is fully described and verified against DT-MRI data. We show a way to construct it on the basis of sonography data. To use this model in further physiological simulations, we propose a numerical method to utilise finite differences in solving the reaction-diffusion problem together with an example of scroll wave dynamics simulation.

With the integrated development of the Internet, wireless sensor technology, cloud computing, and mobile Internet, there has been a lot of attention given to research about and applications of the Internet of Things. A Wireless Sensor Network (WSN) is one of the important information technologies in the Internet of Things; it integrates multi-technology to detect and gather information in a network environment by mutual cooperation, using a variety of methods to process and analyze data, implement awareness, and perform tests. This paper mainly researches the localization algorithm of sensor nodes in a wireless sensor network. Firstly, a multi-granularity region partition is proposed to divide the location region. In the range-based method, the RSSI (Received Signal Strength indicator, RSSI) is used to estimate distance. The optimal RSSI value is computed by the Gaussian fitting method. Furthermore, a Voronoi diagram is characterized by the use of dividing region. Rach anchor node is regarded as the center of each region; the whole position region is divided into several regions and the sub-region of neighboring nodes is combined into triangles while the unknown node is locked in the ultimate area. Secondly, the multi-granularity regional division and Lagrange multiplier method are used to calculate the final coordinates. Because nodes are influenced by many factors in the practical application, two kinds of positioning methods are designed: the unknown node is in the positioning unit or not. When the unknown node is on the side of the positioning unit, we use the method of vector similarity. Moreover, we use the centroid algorithm to calculate the ultimate coordinates of unknown node. When the unknown node is not on the side of the positioning unit, we establish a Lagrange equation containing the constraint condition to calculate the first coordinates. Furthermore, we use the Taylor expansion formula to correct the coordinates of the unknown node. In addition, this localization method has been validated by establishing the real environment.

The paper presents an error model of a measurement chain containing link performing discrete wavelet transform algorithm which is most often the last stage of measurement signal processing. The goal is to determine the uncertainty budget of the input quantities of the wavelet transform algorithm. The error model takes into account parts of analog, analog-to-digital and digital processing, describing the properties of subsequent fragments of the chain using their transmittance and processing functions. The proposed model enables the description of both deterministic and non-deterministic properties of signal errors. The proposed model was validated using an example measurement chain created for this purpose.

The conventional well placement was done manually by using a numerical reservoir simulator, and it required a lengthy trial-and-error process. It required great experience and expertise to manipulate the variables and uncertainties that lie on the reservoir to determine the best placement of the well. In addition, the traditional gradient-based methods such as Line-search and Trust-region were not viable in terms of maximum results obtained. Gradient-based methods were too dependent on the surface gradient of the solution and may only converge to local optima instead of global optima. Complex reservoirs have rough surfaces with high uncertainties, which hinders the traditional gradient-based method from converging to global optima. Thus, genetic algorithms were utilized to automate the manual trial-and-error process and to overcome the limitations of the traditional gradient-based method. The objectives of this study were to analyse the effect of different initial well placement distributions, the number of random solution sizes, and the crossover rate on cumulative oil production. A synthetic reservoir model built using CMG Builder was used as the testing platform for the optimization problems. Well-placement parameterization and optimization set-up were carried out using the CMG CMOST optimization tool. The integration of CMG IMEX and CMOST optimized cumulative oil production based on the objectives of the study. The results obtained showed that the higher number of random solutions used resulted in higher cumulative oil production, with more generations needed to reach the optimum solution. It can be concluded that the larger number of random solutions used increased the probability of reaching the optimum solution, but will take more generations.

Depth-sensing technology has led to broad applications of inexpensive depth cameras that can capture human motion and scenes in 3D space. Background subtraction algorithms can be improved by fusing color and depth cues, thereby allowing many issues encountered in classical color segmentation to be solved. In this paper, we propose a new fusion method that combines depth and color information for foreground segmentation based on an advanced color-based algorithm. First, a background model and a depth model are developed. Then, based on these models, we propose a new updating strategy that can eliminate ghosting and black shadows almost completely. Extensive experiments have been performed to compare the proposed algorithm with other, conventional RGB-D algorithms. The experimental results suggest that our method extracts foregrounds with higher effectiveness and efficiency.

Underwater Sensor Networks (UWSNs) can enable a broad range of applications such as resource monitoring, disaster prevention, and navigation-assisted. It is especially relevant for sensor nodes location in UWSNs. Global Positioning System (GPS) is not suitable for using in UWSNs because of the underwater propagation problems. Hence some localization algorithms based on the precise time synchronization between sensor nodes have been proposed which are not feasible for UWSNs. In this paper, we propose a localization algorithm called Two-Phase Time Synchronization-Free Localization Algorithm (TP-TSFLA). TP-TSFLA contains two phases, namely, range-based estimation phase and range-free evaluation phase. In the first phase, we address a time synchronization-free localization scheme base on the Particle Swarm Optimization (PSO) algorithm to decrease the localization error. In the second phase, we propose a Circle-based Range-Free Localization Algorithm (CRFLA) to locate the unlocalized sensor nodes which cannot obtain the location information through the first phase. In the second phase, sensor nodes which are localized in the first phase act as the new anchor nodes to help realize localization. Hence in this algorithm, we use a small number of mobile beacons to help achieve location without any other anchor nodes. Besides, to improve the precision of the range-free method, an extension of CRFLA by designing a coordinate adjustment scheme is updated. The simulation results show that TP-TSFLA can achieve a relative high localization ratio without time synchronization.

Keywords: Marine Coasts; Protected Areas; Defense and Conservation; Asbestos Cement Materials; Wastes; Contamination; Human Health Risk; Medical Geology.

Insulated Gate Bipolar Transistor (IGBT) may convey high current and sustain high breakdown voltages; it may provide high power control. In a sense, how IGBT demonstrates the capability of power control was not specifically described, and the equivalent bipolar junction transistors (BJT) activated by an applied bias to the insulated gate is intriguing. As seen in Figure 1, IGBT shows an equivalent circuit structure containing two types of BJT, (NPN-type Bipolar transistor and PNP-type Bipolar transistor), which can be modeled as diode-associated transistor. Apparently, as a bias applies to the controlling gate, the channel beneath the gate oxide gets strongly inversed and turns out to be conductive just like what happens on metal-oxide-silicon field effect transistor (MOSFET), which provides necessary igniting currents to both BJTs and thus causes high current gain flowing through them-selves from the bottom. A proposed and renewed formula provides addressing the above scenario and successfully fitting the measured data that forms the characteristic curves. Some parameters in the proposed formula, which includes size and mobility associated constant, threshold voltage, and Early-Voltage-related lambda for MOSFET, explain and explore the underlying physics. IGBT thus enjoy high input impedance and high current gain due to MOSFET (Insulated Gate) and BJT, respectively. This formula combines both merits of MOSFET and BJT in order to fit the measured data. Indeed, the formula intimately fits IGBT electrical characteristic curves, and thus may be qualified and served as a model. The new model is then advisable for designing power integrated circuit to exactly achieve power saving, power control, and power efficiency.

Problem solving is one of the most important components of the human cognition that affects for ages the progress of the human society. Mathematical modelling is a special type of problem solving concerning problems related to science or everyday life situations. The present study is a review of the author’s earlier works on problem solving and mathematical modelling from the scope of Education. Its real goal is that it presents in a systematic way and in a few pages only the results of many years research on the subject. This helps the reader to get a comprehensive idea about a very important topic belonging to the core of Mathematics Education, which is very useful to those wanting to study deeper the subject and get directions for further research in the area.

Anomalous waves and rogue events are closely associated with irregularities and unexpected events occurring at various levels of physics, such as in optics, in oceans and in the atmosphere. Mathematical modeling of rogue waves is a highly actual field of research, which has evolved over the last decades into a specialized part of mathematical physics. The applications of the mathematical models for rogue events is directly relevant to technology development for prediction of rogue ocean waves, and for signal processing in quantum units. In this survey, a comprehensive perspective of the most recent developments in methods for representing rogue waves is given, along with discussion of the devised and forms and solutions. The standard nonlinear Schrödinger equation, the Hirota equation, the MMT equation and further to other models are discussed, and their properties highlighted. This survey shows that the most recent advancement in modeling rogue waves give models which can be used to establish methods for prediction of rogue waves at open seas, which is important for the safety and activity of marine vessels and installations. The study further puts emphasis on the difference between the methods, and how the resulting models form a basis for representing rogue waves in various forms, solitary or with a wave-background. This review has also a pedagogic component directed towards students and interested non-experts, and forms a complete survey of the most conventional and emerging methods published until recently

Deadlock is a real problem that can cause expensive, time-dependent hang-ups or failures in distributed computing systems. Some studies have been conducted with deadlock detection and resolution in generalized request computing models, most of these studies are based on the diffusing computation scheme, where forward and backward propagated probe and reply messages respectively are diffused between dependent processes. The replies carry the dependency information between processes for the initiator. Using this dependency information initiator can detect and resolve the deadlock cycle. It has been proven in the literature that a deadlock cycle length distribution is skewed with a large majority of cycles (90%) having length two. Based on this fact an improved algorithm is proposed for handling deadlock detection in distributed computing systems under the distributed request model where each process has several requests at a time. The improved algorithm depends mainly on message propagation and timeout policy. Probe and reply messages are propagated between the initiator and its successors only to detect deadlock cycles between them. Global timeout policy is used to detect potential deadlock cycles with large length distribution. The proposed algorithm can handle concurrent executions. Simulation experiments are performed to see the effectiveness of the improved algorithm. It is found that the improved algorithm compares favorably with other existing algorithms and it shows better results for several performance metrics especially in reducing deadlock latency and execution time.

Preventive Maintenance (PM) is a periodic maintenance strategy, which has great results for devices in extending their life, increasing productivity, and most importantly, help avoid unexpected breakdowns and their costly consequence. A preventive maintenance scheduling (PMS) is determining the time for carrying out PM, and it represents a sensitive issue in terms of impact on production if the time for the PM process is not optimally distributed. In this study, hybrid heuristic methods were used to solve the PMS problem, as genetic algorithm and Tabu research were adopted. The optimal solution was reached in a short time compared to previous studies in which optimal methods were used, integer programming and nonlinear integer programming. Also, sensitivity analysis was applied to measure the robustness and strength of the method used, where an optimal solution was obtained for all experiments and in record time. This method can be used for power plants in privet or public sectors, to generate an optimal PMS, to save money, and to avoid water or electricity cuts.

Detection of subsurface archaeological remains using a range of remote sensing methods, poses several challenges until today. Recent studies regarding the detection of archaeological proxies like those of cropmarks highlight the complexity of the phenomenon. In this work we present three different methods, and associated indices, for identifying stressed reflectance signatures indicating buried archaeological remains, based on a dataset of measured ground spectroradiometric reflectance. Several spectral profiles between the visible and near infrared part of the spectrum, were taken over a controlled environment in Cyprus during the 2011-2012 and are re-used in this study. The first two (spectral) methods are based on a suitable analysis of the spectral signatures in (1) the visible part of the spectrum, and in particular in the neighborhood of 570 nm, and (2) the red edge-near infrared part of the spectrum, in the neighborhood of 730 nm. Machine learning (decision trees) allows for the deduction of suitable wavelengths to focus on, in order to formulate the proposed indices and the associated classification criteria (decision boundaries) that can enhance the detection probability of stressed vegetation. Noise in the signal is taken into account by simulating reflectance signatures perturbed by white noise. Applying decision tree classification on the ensemble of simulations and basic statistical analysis we refine the formulation of the indices and criteria for the noisy signatures. The success rate of the proposed methods is over 90%. The third method rests on the estimation of vegetation/canopy reflectance parameters through inversion of the physical-based PROSAIL reflectance model and the associated classification through machine learning methods. The obtained results provide further insights into the formation of stress vegetation that occurred due to the presence of shallow buried archaeological remains, which are well aligned with physical-based models and existing empirical knowledge. To the best of the authors' knowledge, this is the first study demonstrating the usefulness of radiative transfer models such as PROSAIL for understanding the formation of cropmarks. Similar studies can support future research directions towards the development of regional remote sensing methods and algorithms if systematic observations are adequately dispersed in space and time.

Amid the swift progression of the global automobile industry, the aspiration for lightweight vehicle design has surfaced as a crucial approach to boost fuel efficiency and curtail environmental impact. The objective of this study revolves around achieving holistic optimization of vehicle structure via detailed scrutiny of vehicle process characteristics, amalgamated with a Back Propagation neural network (BPNN) optimized by a genetic algorithm (GA) and a topology optimization (TO) method.The process initiates with an examination of the vehicle's technical characteristics, succeeded by an optimization protocol that couples GA with BPNN. This exhaustive optimization procedure derives the best-fit values of design parameters and identifies the globally optimal lightweight design approach. Subsequently, a comprehensive structural optimization is actualized by modifying the topological distribution of the structure.A simulation experiment of the conceptual car body beam skeleton is conducted as a conclusive step, and the anti-collision capacity of the car body beam skeleton is assessed by measuring deformation intrusion. The findings reveal that in the vehicle topology optimization, a comparative analysis of pre and post-optimization results indicates an improved topological density across diverse sections. The topological density of the vehicle's frontal structure escalates from 0.75 to 0.8. Following optimization, the stiffness assessment records a marginal increase (within the range of 0.02–0.05), implying that the lightweight design does not compromise the general rigidity of the structure.The optimized body structure manifests superior crashworthiness in the crash test: the deformation intrusion diminishes by 27% in front-end collisions. In side impacts, the deformation and intrusion at critical points are reduced by 13.15% to 10% respectively. The comprehensive method proposed herein proves to be an efficient strategy to actualize the lightweight design of vehicles.

The impacts of inflation on international finance are generally reflected in the decline of buying power, risks of investment and deposit loss from currency devaluation. For the purpose of optimized allocation and management of asset values, i.e., annual income or research grants, a framework of a three-level model for static financial management is presented to maximize banking interests, bonuses, and the remaining balance after spending necessary expenditures. Meanwhile, in retrospect to higher-level financial inflation, strategies of dynamic investment, i.e., posing regular tests of flipping coins, exploiting variations of the currency exchange rate, as well as applying the theory of broad money, are presented to increase the appreciation rate of net assets in and post the era of COVID-19. Quantitative evaluations in case studies verify the feasibility of improving the financial situation, indicating broader applications for budgeting and investing when US inflation rate is below 3.0%. Besides, combining approaches of static and dynamic strategies, the expected annual growth rate of individual zero-risk asset investment is predicted as within the range of 8.30~9.62% according to budgeted appreciation on net assets in 12 months, which is capable of overcoming negative impacts from higher level annual inflation, i.e., those as highest as 8.01% in the Year 2022.

Gaze tracking of high-speed moving targets is a novel application mode for low Earth orbit microsatellites. In this mode, small satellites are equipped with high-resolution narrow-field-of-view video cameras for stable gaze-tracking imaging of high-speed moving targets. This paper proposes a high-precision attitude adaptive integral sliding mode control method with a feedforward compensation disturbance observer to enhance the capability of a microsatellite attitude control system for gaze tracking of high-speed moving targets. Specifically, first, we present the attitude control system model for microsatellites and the calculation method for the desired attitude of target tracking based on image feedback. Then, an adaptive integral sliding mode attitude control algorithm with a feedforward compensation disturbance observer, which meets the requirements of high-precision tracking control, is designed. The developed algorithm utilizes the disturbance observer to observe the friction torque of the flywheel and compensates for it through feedforward control. It also employs the adaptive integral sliding mode control algorithm to reduce the impact of uncertain disturbances, decrease the steady-state error of the system, and enhance the attitude control precision. Simulation experiments demonstrated that the designed disturbance observer can successfully observe the frictional disturbance torque of the flywheel. The attitude Euler angle control precision for high-speed moving target tracking reached 0.009°, and the angular velocity control precision reached 0.005°/s, validating the effectiveness of the proposed approach.

YOLOv8, as an efficient object detection method, can swiftly and precisely identify objects within images. However, traditional algorithms encounter difficulties when detecting small targets in remote sensing images, such as missing information, background noise, and interactions among multiple objects in complex scenes, which may affect performance. To tackle these challenges, we propose an enhanced algorithm optimized for detecting small objects in remote sensing images, named HP-YOLOv8. Firstly, we design the C2f-D-Mixer (C2f-DM) module as a replacement for the original C2f module. This module integrates both local and global information, significantly improving the ability to detect features of small objects. Secondly, we introduce a feature fusion technique based on attention mechanisms, named Bi-Level Routing Attention in Gated Feature Pyramid Network (BGFPN). This technique utilizes an efficient feature aggregation network and reparameterization technology to optimize information interaction between different scale feature maps, and through the Bi-level Routing Attention (BRA) mechanism, it effectively captures critical feature information of small target objects. Finally, we propose the Smooth Mean Perpendicular Distance Intersection over Union (SMPDIoU) loss function. The method comprehensively considers the shape and size of detection boxes, enhances the model's focus on the attributes of detection boxes and provides a more accurate bounding box regression loss calculation method. To demonstrate our approach's efficacy, we conduct comprehensive experiments across the RSOD, NWPU VHR-10, and VisDrone2019 datasets. The experimental results show that the HP-YOLOv8 achieves 95.11%, 93.05%, and 53.49% in the [email protected] metric, and 72.03%, 65.37%, and 38.91% in the more stringent [email protected]:0.95 metric, respectively.

Count data analysis presents unique challenges due to its discrete nature, often exhibiting excessive zeros and overdispersion. To address these complexities, count models, such as Poisson regression and Negative Binomial regression, have been developed, enabling modeling and prediction of count-based phenomena. Additionally, it’s important to notice that zero inflation, a phenomenon commonly observed in count data, requires specialized techniques for robust analysis. This article provides an overview of count data and count models, explores zero inflation, introduces Likelihood Ratio Tests, and explains how the Vuong Test can be used as a model selection criteria. Furthermore, we created a Vuong Test implementation from scratch using the Python programming language. This implementation enhances the accessibility and applicability of the Vuong Test in real-world scenarios, providing a valuable contribution to the academic community, since Python didn’t have an implementation of this statistical test.

This work promotes new methods in Mathematical Modeling, consisting in the use of the methods of Non-standard Analysis in Topoi, having as its main purpose, the mathematical definitions of the pseudoparticles from the title, with arguments from Biology/Physiology (Mathematical Neuroscience), Physics (String Theory and Emergent Quantum Mechanics), and Cybernetics (Global Brain, including Natural and Artificial Intelligence). The connections between brain and mind will be scketched via the genetic/epigenetic interplay. The topoi model the intuitionistic logic (multi-valued) and have been used in Quantum Physics while Non-Standard Analysis in SET (= the Category of sets) has been applied in Mathematical Economics; topics from Theory of Categories were also used in the study of Consciousness; however, the combination topoi - non-standard analysis was never used until now in Applied Mathematics. Another important objective is to produce progress in this aria of Pure Mathematics also - the build of non-standard analysis in classes of topoi, already used in Physics. We propose the logic of non-standard extensions in topoi as a model of the human thinking (based on infons/receptons), these theories representing new top and very difficult results in Abstract Mathematics either.

The main sources of intrinsic noise in excitable cells at the microcircuit and network levels are the stochastic characteristics of ion channel gating and activation of the synaptic conductance. Studies using in vivo, in vitro, and in silico methods to examine the effects of synaptic background activity were not adequately investigated in non-neuronal excitatory cells, where neurotransmitter-based innervation also occurs. We created a mathematical model to replicate the background synaptic noise dynamics in a non-neuronal cell. We utilized the stochastic Ornstein-Uhlenbeck process to represent excitatory synaptic conductance, which was incorporated into a whole-cell model to produce spontaneous and evoked cellular electrical activities. The single-cell model includes many biophysically detailed ion channels represented by a set of ordinary differential equations in Hodgkin-Huxley and Markov formalisms. This paradigm effectively induced irregular spontaneous depolarizations (SDs) and spontaneous action potential (sAP) resembling in vitro-like electrical activity in the cells. The input resistance decreased by multiple factors, and the spontaneous action potential firing rate elevated. The potential to reach the action potential threshold is altered. Background synaptic activity can alter the input/output characteristics of non-neuronal excitatory cells. Suppressing these baseline activities would facilitate the discovery of new pharmaceutical targets for different clinical diseases.

In this paper, we consider a class of bilevel programming problems (abbreviated as, BLPP). Exploiting the generalized approximate convexity assumptions, we investigate the relations among the solutions of approximate Minty (respectively, Stampacchia) type variational inequalities (abbreviated as, AMTVI (respectively, ASTVI)), and the local ϵ-quasi solutions of the BLPP. Moreover, by employing the generalized Knaster–Kuratowski–Mazurkiewicz (abbreviated as, KKM)-Fan’s lemma, we derive some existence results for the solutions of approximate variational inequalities (abbreviated as, AVI), namely, AMTVI and ASTVI. A non-trivial example is given to highlight the importance of the established results. To the best of our knowledge, there is no research paper available in the literature that establishes relationships between the AVI and the BLPP under the assumptions of generalized approximate convexity in terms of limiting subdifferentials.

In this note we introduce the notion of polynions and discuss their mathematical relevance. We note that the well-known mathematical structures like quaternions, octonions and sedenions etc. are special cases of polynions.

This paper presents a study about the integration of Piezoelectric Energy Harvesting Systems (PE-EHS) in building envelopes for powering Fiber Bragg Grating (FBG) sensors, enabling efficient and low-consumption monitoring with the objective to leverage Structural Health Monitoring (SHM). The research includes preliminary tests conducted in a real environment to validate the PE-EHS when fully integrated into the façade, capturing mechanical vibrations generated mainly by wind loads. Based on these activities, the final configuration of PE-EHS is defined to provide a complete system for façade monitoring. This integrated system includes the Piezoelectric Generator (PEG), Supercapacitor (SC), Power Conditioner Circuit (PCC), Fibre Optic Sensing (FOS) Interrogator, and the IoT Gateway trans-mitting measurement data within an Internet of Things (IoT) monitoring platform. This configuration is tailored to address the challenges related to the structural integrity of building envelopes. Results demonstrate a potential for a stand-alone solution in the façade sector, but, raising issues for certain limitations, requiring further investigation. In particular, the study emphasizes constraints related to the energy production of PE-EHS for façade integration. It highlights the necessity to carefully consider these limitations within the broader context of their applicability, providing insights for the informed deployment of Piezoelectric Energy Harvesting technology in building envelope monitoring.

Accurate forecasting of icing thickness has a great significance for ensuring the security and stability of power grid. In order to improve the forecasting accuracy, this paper proposes an icing forecasting system based on fireworks algorithm and weighted least square support vector machine (W-LSSVM). The method of fireworks algorithm is employed to select the proper input features with the purpose of eliminating the redundant influence. In addition, the aim of W-LSSVM model is to train and test the historical data-set with the selected features. The capability of this proposed icing forecasting model and framework is tested through the simulation experiments using real-world icing data from monitoring center of key laboratory of anti-ice disaster, Hunan, South China. The results show that the proposed W-LSSVM-FA method has a higher prediction accuracy and it may be a promising alternative for icing thickness forecasting.

The weight coefficients of the diaphragm spring depend on experiences in the traditional optimization. However, this method not only cannot guarantee the optimal solution but it is also not universal. Therefore, a new optimization target function is proposed. The new function takes the minimum of average compress force changing of the spring and the minimum force of the separation as total objectives. Based on the optimization function, the result of the clutch diaphragm spring in a car is analyzed by the non-dominated sorting genetic algorithm (NSGA-II) and the solution set of Pareto is obtained. The results show that the pressing force of the diaphragm spring is improved by 4.09%by the new algorithmand the steering separation force is improved by 6.55%, which has better stability and steering portability. The problem of the weight coefficient in the traditional empirical design is solved. The pressing force of the optimized diaphragm spring varied slightly during the abrasion range of the friction film, and the manipulation became remarkably light.

The main purpose of this paper is to present a comprehensive view of the application mathematical models in the designing and implementing SSCM beside to solving problems and making decision. The research questions are: what mathematical models are used for designing and implementing sustainable supply chain management, how to use them, which industries implemented in, what modules of SSCM depth in and finally finding the gaps of researches. The methodology of research is Systematic Literature review through peer review papers which are published in high ranking journals. In this paper, First, we search all papers through scientific data bases like Scopus, science direct, MDPI, Springer, Google Scholar, then, screening papers based on the criteria such as subject of paper, journals impact factor which is published in-should be peer review journal- and relative content of the papers. Finally, we selected 245 papers with three steps screening through 2806 papers that they have enough quality and relative to our research goals for context analysis. Through context analysis, first we categorized the information of the papers and drew the current situation of researches in the framework of our topic. Then, we evaluate and compare the goals of sustainability and current situation and found the gapes, then, offered new suggestions like implementing SSCMs models in pollutant industries like casting industry, Heavy industry, coal Industry and so on. On the other hand, there are gaps in researches in some modules of SSCM such as packaging, designing products, etc.

P-band radar remote sensing applied during the Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) mission has shown great potential for estimation of root zone soil moisture. When retrieving the soil moisture profile (SMP) from P-band radar, a mathematical function describing the vertical moisture distribution is required. Because only a limited number of observations are available, the number of free parameters of the mathematical model must not exceed the number of observed data. For example, a second order polynomial that contains 3 free parameters was presumed based on in-situ SMP data. The polynomial is currently parameterized based on 3 backscatter observations provided by AirMOSS (i.e. one frequency at three polarizations of HH, VV and HV). In this paper, a more realistic, physically-based SMP model containing 3 free parameters is derived based on a solution to Richards’ equation for unsaturated flow in soils. Evaluation of the new SMP model based on both numerical simulations and measured data revealed that it exhibits greater flexibility for fitting measured and simulated SMPs than the currently applied polynomial. It is also demonstrated that the new SMP model can be reduced to a second order polynomial at the expense of fitting accuracy.

The identification of fetal cells in the blood and tissues of healthy mothers raised questions about the potential alloreactive origins of various diseases, such as autoimmunity, diabetes, arteriosclerosis, and cancer. However, the extent to which alloreactivity contributes to these diseases remains unverified. This study presents a basic mathematical disease model based on the genes’ origin and immunological interactions. This model, grounded in set theory, classifies these immunological interactions based on their intrinsic, extrinsic, and allogeneic nature. Therefore, this model offers an unexpected common theoretical foundation for understanding alloreactivity, genetic diseases, and infections. Furthermore, this model provides a valuable framework for scrutinizing the role of alloreactivity in health and disease.

The generation and maintenance of membrane potential is considered a fundamental element of the cellular machinery. They are based on elements of physics and chemistry. Mathematics is used to validate the equations and evaluate the results. However, this computation process can lead to a misunderstanding of the phenomena involved or to the masking of crucial events. It is even possible that the calculation no longer corresponds to the hypothesis considered. Membrane theory is no exception to these trivial considerations, which are essential for normal theory validation.

This article introduces a novel nature-inspired metaheuristic algorithm called Frilled Lizard Optimization (FLO), which emulates the hunting behavior of frilled lizards in their natural habitat. FLO draws in-spiration from the sit-and-wait strategy observed in frilled lizards during hunting. The underlying theory of FLO is presented and mathematically formulated in two phases: (i) an exploration phase, simulating the frilled lizard's attack towards prey, and (ii) an exploitation phase, simulating the lizard's retreat to the top of the tree after feeding. To assess FLO's efficacy in solving optimization problems, the algorithm's performance is evaluated across fifty-two standard benchmark functions, encompassing unimodal, high-dimensional multimodal, fixed-dimensional multimodal, and the CEC 2017 test suite. Comparative analyses with twelve existing metaheuristic algorithms are conducted. The simulation results reveal that FLO, distinguished by its adeptness in exploration, exploitation, and balancing them during search process, outperforms competing algorithms. Additionally, FLO is implemented on twenty-two constrained optimization problems from the CEC 2011 test suite and four engineering design problems, demonstrating its effectiveness in addressing real-world optimization applications.

Globally, zoonotic diseases have been on the rise in recent years. Predictive modelling approaches have been successfully used in the literature to identify the underlying causes of these zoonotic diseases. We examine the latest research in the field of predictive modeling that verifies the growth of zoonotic pathogens and assesses the factors associated with their spread. The results of our survey indicate that popular mathematical models can successfully be used in modeling the growth rate of these pathogens under varying storage temperatures. Additionally, some of them are used for the assessment of the inactivation of these pathogens based on various conditions. Based on the results of our study, machine learning models and deep learning are commonly used to detect pathogens within food items and to predict the factors associated with the presence of the pathogens.

Differential equation models to understand interaction between plant and nutrient solution are presented. The root cells selectively emit H+ ions with active transport consuming ATPs to establish electrical gradient along the cell membrane. It establishes electrical field with Nernst potential to make positively charged ions outside the cell membrane flow into the root cell. Anion influx is also modulated by H+ ion concentration because plant root cell absorbs negatively charged particles with symport. If an anion collides with H+ cell to make net charge as neutral, at symport channel, it can flow through. In this paper, mathematical models for cation and anion absorption are introduced. Cation absorption model was induced from Ohm's law combined with Goldman's equation. Anion absorption model is similar to chemical reaction rate model. Both models have physiological terms influenced by gene expression pattern, species or phenotypes. Cation model also includes terms for ion's kinetic and electrical properties, growth of plant and interaction between the root and the surroundings. Simulation for 20 different sets of coefficients showed that the physiology-related coefficient has important role on nutrition absorption tendencies of plants.

This article investigates a proposed new mathematical model that considers the infected individuals using various rate coefficients such as transmission, progression, recovery and vaccination. The fact that the dynamic analysis is completely determined by the basic reproduction number is established. More specifically, local and global stabilities of the disease-free equilibrium and the endemic equilibrium are proved under certain parameter conditions when the basic reproduction number is below or above unity. A realistic computer simulation is performed for better understanding of the variations in trends of different compartments after the outbreak of the disease.

In this paper mathematical analysis of the HIV/AIDS deterministic model exposed in [Espitia, C. et. al. Mathematical Model of HIV/AIDS Considering Sexual Preferences Under Antiretroviral Therapy, a Case Study in San Juan de Pasto, Colombia, Journal of Computational Biology 29 (2022) 483–493] is made. The objective is to gain insight into the qualitative dynamics of the model determining the conditions for the persistence or effective control of the disease in the community through the study of basic properties such as positiveness and boundedness, calculus of basic reproduction number, stationary points such as disease free equilibrium (DFE), boundary equilibrium (BE) and endemic equilibrium (EE) are calculated, local stability (LAS) of disease free equilibrium. It research allow to conclude that the best way to reduce contagion and consequently to reach a DFE is thought to be the reduction of homosexual partners rate as they are the most affected population by the virus, and are therefore the most likely to become infected and to spread the infection. Increasing the departure rate of infected individuals, leads to a decrease in untreated infected heterosexual men and untreated infected women.

Creative thinking is increasingly recognised as an essential ability that should be part of school curricula. Given the move towards online learning and assessment, we investigate whether mathematical creativity can be assessed at-scale in the Numbers game, an arithmetic game in Math Garden, a popular online math practice platform. In the Numbers game, a generalisation of the 24 Game, children are asked to figure out how to compute a target number using basic arithmetic operations and a given set of numbers. We argue that creative thinking is required when the search space is complex, and propose that the base-pattern, i.e., the sequence of the operations needed to solve a Numbers game item, indicates search space complexity. We then demonstrate that items with disordered base-patterns are more likely to require mathematical creativity to figure out. Specifically, our analysis shows that for items with only one solution sequence, those with disordered base-patterns are more difficult and take longer to solve compared to items with ordered base-patterns. For items where multiple solution sequences are possible, nine times out of ten children choose ordered over disordered base-patterns. We conclude that the Numbers game has potential for assessing mathematical creativity at-scale.

This paper emphasises on the analogous modelling of hardwood (Acacia) pyrolysis. The effect of physical characteristics of hardwood chips on the pyrolysis is examined through the conservation of solid mass fraction of biomass. The chip size of G30 and G50 are used in the pyrolysis reactor. In the analogous situation, the fixed bed is assumed to be a wooden slab with a porosity equivalent to the voidage of bed. The bulk density, the length of the bed and the porosity are some of the physical attributes of a fixed bed used to determine the variation of solid mass of the hardwood across the fixed bed. The four-temperature sensors separated from each other by 80 mm are used to determine the temperature along the length of the pyrolysis unit. The heating element of 2 kWe is used to initiate the pyrolysis of biomass. The experiments are conducted in three different stages. The ONORM standard chips, G30 and G50, and the combination of them are separately pyrolysis to determine the validity of a model for different sizes of chips. The proposed model is also used to establish the relationship between the kinetics of pyrolysis and decomposition of the hardwood.

Nuclear Magnetic Resonance (NMR) and its various forms are extensively utilized in both research and clinical settings to analyse molecules. NMR data pre-processing, while essential to NMR data analysis, can be uniquely complex. Despite the availability of software tools, understanding these processes can be challenging, complicating the selection of appropriate pre-processing steps. In this review, we elucidate pre-processing steps in the time domain from a mathematical and statistical perspective, explaining direct current offset removal, eddy current correction, shift and linear prediction, weighting, zero filling, and domain transformation using plain language and fundamental mathematical formulas. Our objective is to clarify these processes in simple terms and provide general guidance.

Magnetic Resonance Imaging (MRI) is widely used in clinics and research due to its accurate disease identification and non-invasive nature. MRI is based on Nuclear Magnetic Resonance (NMR), which is also extensively employed in various fields. NMR and its modern versions involve intricate pre-processing steps before data analysis. These steps are initially processed in the time domain and subsequently in the frequency domain. While our previous review focused on time domain pre-processing (https://www.preprints.org/manuscript/202310.2032/v1), this review delves into the mathematical and statistical aspects of frequency domain pre-processing. We discuss essential pre-processing steps like phase error correction, baseline correction, solvent filtering, calibration and alignment, reference deconvolution, binning/bucketing and peak picking, peak fitting/deconvolution and compound identification, integration and quantification, normalization and transformation. Furthermore, we offer practical recommendations for each step.

Numerical simulations of standard situations in the transition region from gas kinetics to fluid dynamics at small Mach numbers indicate a clear dependence of the simulation results on the underlying kinetic model (here: nonlinear and linearized Boltzmann collision operator vs. BGK relaxation model). We develop an improved mathematical framework (trace theory) to explain these differences. In particular we reveal certain deficiencies for the classical BKG system as well as for the standard Navier Stokes approach.

Malaria is a critical fevered illness caused by Plasmodium parasites transmitted among people through the bites of infected female Anopheles mosquitoes. Public awareness about the disease is important for the control of disease. This article proposes a mathematical model to study the dynamics of malaria disease transmission with the influence of awareness-based control interventions. We found two equilibria of the model, namely the disease-free and endemic equilibrium. Disease-free equilibrium is stable globally if basic reproduction number (R0) is less than unity (R0<1). Some basic mathematical properties of the proposed model, such as nonnegativity and boundedness of solutions, the feasibility of the equilibrium points and their stability properties, have been studied. Finally, we adopted optimal control to minimize the cost of disease control and solve the problem by formulating Hamiltonian functional. The optimal use of insecticides for controlling the mosquito population is determined. Numerical simulations have been provided for the confirmation of the analytical results. We conclude that media awareness with optimal control approach is best for cost-effective malaria disease management.

A mathematical model is proposed for quantitative description of the outbreak of novel coronavirus COVID-19 Although the model is relatively simple, the comparison with the public data shows that an exact solution solution of the model (with the correctly-specified parameters) leads to the results, which are in good agreement with the measured data in China and Austria. Prediction of the total number of the COVID-19 cases is discussed and examples are presented using the measured data in Austria, France and Poland.

The managers’ strategic behavior of commercial real estate in a competitive environment is discussed. The means of this research are methods of mathematical and experimental game theory. Illustrates an example of a decision-theoretic game problem with two players engaged in the management of competing shopping centers. The strategies of these players are determined by the costs of the development. Since the number of visitors is constantly and changing the quality of shopping centers, managers actually pull visitors from each other, the game-theoretical formulation of the problem of management of shopping centers corresponds to the zero-sum game. The model example shows that with the help of mathematical modeling it is possible to determine the theoretical expected behavior of agents. The model of the software module created specifically for experimental research is described. The experiments are designed to compare the theoretically predicted behavior with the real actions of people. The novelty is that at significant costs of the Manager for the development and promotion of shopping and entertainment centers, the strategies of managers are resistant to each other's actions, in contrast to changes in the external environment is shown.

Nowadays genetic algorithm (GA) is greatly used in engineering pedagogy as an adaptive technique to learn and solve complex problems and issues. It is a meta-heuristic approach that is used to solve hybrid computation challenges. GA utilizes selection, crossover, and mutation operators to effectively manage the searching system strategy. This algorithm is derived from natural selection and genetics concepts. GA is an intelligent use of random search supported with historical data to contribute the search in an area of the improved outcome within a coverage framework. Such algorithms are widely used for maintaining high-quality reactions to optimize issues and problems investigation. These techniques are recognized to be somewhat of a statistical investigation process to search for a suitable solution or prevent an accurate strategy for challenges in optimization or searches. These techniques have been produced from natural selection or genetics principles. For random testing, historical information is provided with intelligent enslavement to continue moving the search out from the area of improved features for processing of the outcomes. It is a category of heuristics of evolutionary history using behavioral science-influenced methods like an annuity, gene, preference, or combination (sometimes refers to as hybridization). This method seemed to be a valuable tool to find solutions for problems optimization. In this paper, the author has explored the GAs, its role in engineering pedagogies, and the emerging areas where it is using, and its implementation.

Knowledge is a property that measures the degree of awareness of an agent about a target in an environment. The goal in conventional intelligent and cognitive agent development is to build agents that can be trained to gain knowledge about a target. The definition and operations of this knowledge associated to the agent is not clear, whereas these are required for developing a reliable, scalable and flexible agent. In this paper, we provide a concise theoretical framework for the description and quantification of the knowledge property needed for an efficient design of cognitive and rational intelligent agents. We relate the quantification scheme to the epistemological description of knowledge and present many illustrative examples on the usefulness of the quantification scheme.

A mathematical model is proposed to analyze the spreading dynamics of COVID-19. By using the parameters of the model, namely the basic reproduction number (R0) and the attenuation constant (k), the daily number of infections (DNI) and the cumulative number of infections (CNI) are deduced and shown to be in good agreement with experimental data. This model effectively addresses three key issues: explaining the waveform pattern of DNI, predicting the occurrence of the second wave of infection, and understanding the competitive spread of two viruses in a region. The findings demonstrate that these significant challenges can be comprehensively tackled using a simple mathematical framework. The theoretical insights derived from this model hold potential in guiding the estimation of the severity of an infection wave and formulating effective strategies for the control and mitigation of epidemic outbreaks.

The focus of this paper is on analyzing the role and the choice of parameters in sociophysics diffusion models, by leveraging the potentialities of sociophysics from a mathematical programming perspective. We first present a generalised version of Galam’s opinion diffusion model (see, e.g. , ). For a given selection of the coefficients in our model, this proposal yields the original Galam’s model. The generalised model suggests guidelines for possible alternative selection of its parameters that allow to foster diffusion. Examples of the parameters selection process as steered by numerical optimisation, taking into account various objectives, are provided.

The method propose in this study for stock market multi-objective mathematical model was linear programming using simplex algorithms to optimize the portfolio in the Nigerian Stock Market. The study selected five banks from the list of operators in the market and data were gathered from the banks to have individual market performances over a period of 5years. The data collected contains: Geometric Mean of Monthly Capital Gain Yields and Annual Capital Gain Yields from which Dividend Yields (%) were deducted to arrive Actual rate of return for the banks and the expected rate of return. Furthermore, the risk of semi-absolute deviation below the expected return is reduced. The data was analysed using Python programming because of some clauses in the data gathered. At first, the data assumes integer (-or +) and random in nature. As such, Python programming is one of the software suitable for such solution since the barrier for additivity is broken. Based on the analysis, the study therefore conclude that the potential investor(s) should invest in 13 units of investment x(GTbank Plc), 3 units of First Bank Plc`s Investment (y), 450 units of Zenith bank`s investment (z), and 8 units of Wema bank`s investment (m), and no units of investment of (n) Access bank. These investment quantities will result in the Optimal profit of p= 12797.902 billion naira.

Cell migration is essential for physiological, pathological and biomedical processes such as, in embryogenesis, wound healing, immune response, cancer metastasis, tumour invasion and inflammation. In light of this, quantifying mechanical properties during the process of cell migration is of great interest in experimental sciences, yet few theoretical approaches in this direction have been studied. In this work, we propose a theoretical and computational approach based on the optimal control of geometric partial differential equations to estimate cell membrane forces associated with cell polarisation during migration. Specifically, cell membrane forces are inferred or estimated by fitting a mathematical model to a sequence of images, allowing us to capture dynamics of the cell migration. Our approach offers a robust and potentially accurate framework to compute geometric mechanical membrane forces associated with cell polarisation during migration and also yields geometric information of independent interest, we illustrate one such example that involves quantifying cell proliferation levels which are associated with cell division, cell fusion or cell death.

So called Higuchi’s method of fractal dimension estimation is widely used and the term Higuchi’s fractal dimension even occurs in many publications. This paper deals with this method from mathematical point of view. Terms distance and dimension and its basic properties are explained and Higuchi’s dimension according the original source is defined. Definition of Higuchi’s dimension was comparated with mathematical definition of the distance and dimension. It is showed, that the definition of the Higuchi’s dimension does not satisfy axioms of distance and dimension. So called Higuchi’s method and Higuchi’s dimension are mathematically incorrect. Therefore, all results achieved by this method are scientifically unreliable.

Background: There is little clarity in the application of content related to improper integrals in university students, due to the absence of meaning, which prevents them from making a connection with everyday problem situations. Methods: we designed a mathematical modelling proposal where a specific situation involving the instrumentation, use and application of this type of integrals is experimented and solved with a population of engineering students, who learn to use them. Results: The importance of using mathematical modelling as a didactic-dynamic resource is highlighted because it helps students to reach an understanding of real situations involving improper integrals in different contexts. Conclusions: Despite the numerous errors detected in the students, this strategy made it possible to demonstrate the development of advanced mathematical thinking skills in young people.

Identifying the correct dosage and time are key factors to successful implementation of anthelmintic. Comparing differential evolution of infection between anthelmintic treated animals against untreated ones, we present a mathematical model that first calibrates data collected and analyzed over an extended period of 10 years (2011-2019), and then predicts the dynamical evolution of gastrointestinal parasites in livestock, focusing specifically on Stronglye \& Coccidia oocysts, the two prime negative contributors to cattle health, measured using the standard Eggs-Per-Gram (EPG) index. The model incorporates information about all three critical regimes of infection - low infection regime ($< 50$ EPG), medium infection regime ($50-100$ EPG) and high infection regime ($>100$ EPG), including fatally large doses of infection ($> 500$), and probabilistically estimates the variation in animal weight due to infection propagation. A key success of our model is its ability to accurately predict the appropriate anthelmintic treatment times for cattle from a numerical solution of the model presented. The generic model can be applied to other agroclimatic conditions and can serve as a major diagnostic tool for anthelmintic strategizing.

The corrected mechanism model of battery voltammetric function is helpful to guide the development and application of battery. There are two scientific issues that need to be answered: First, how many mechanisms do batteries have; Second, how to establish the mechanism model separately under the overlapping of these mechanisms. Volt-ampere characteristics of both linear state and nonlinear state exist; the monotonic decreasing of volt-ampere characteristics indicates that the battery have only three kinds of mechanisms. Without changing the basic form of the function and under the principle of the mechanism function’s working region considered, we propose a mechanism function which satisfies the monotonic decreasing characteristic of the voltammetric curve of battery, via the derivative law of each mechanism function in the voltammetric function of battery. By using the voltammetric data, the obtained cell mechanism function can accurately predict the potential (current or voltage) when the independent variable of the cell is zero, and provide the theoretical basis for the internal working mechanism of the cell, which can guide the practice.

We have studied the very large amount of literary works written by the Italian mystic Maria Valtorta to assess similarities and differences in her writings because she claims that most of them are due to mystical visions. We have used mathematical and statistical tools developed for specifically studying deep linguistic aspects of texts. The general trend indicates that the literary works explicitly attributable to Maria Valtorta differ significantly from her other literary works, that she claims are attributable to the alleged characters Jesus and Mary. Mathematically, they seem to have been written by different authors. The comparison with the Italian literature is very striking. A single author, namely Maria Valtorta, seems to be able to write texts so diverse to cover the entire mathematical range (suitable defined) of the Italian literature of seven centuries.

Liquid propellants are fast becoming attractive for pulsed plasma thrusters due to their high efficiency and low contamination issues. However, the complete plasma interaction and acceleration processes are still not very clear. Present paper develops a multi-layer numerical model for liquid propellant PPTs. The model proposes a possible acceleration mechanism for liquid fed pulsed plasma thrusters and accurately predicts the propellant utilization capabilities and estimations for the fraction of propellant gas that is completely ionized and accelerated to high exit velocities. Validation of the numerical model and the assumptions on which the model is based on is achieved by comparing the experimental results from two different liquid-fed thrusters developed at the University of Tokyo. Results show 50% of liquid propellant injected is completely ionized and accelerated to high exit velocities (> 50Km/s), whereas, neutral gas contribute to only 7% of the total specific impulse and accelerated to low exit velocity (< 4Km/s). The model shows an accuracy up-to 92%. Optimization methods are briefly discussed to ensure efficient propellant utilization and performance. The model acts as a tool to understand the background physics and to optimize the performance for liquid-fed PPTs.

A Friedmann-Lemaitre-Robertson-Walker space-time model with all curvatures k=0,±1 is explored in f(R,T) gravity. The solutions are obtained via the parametrization of the scale factor that leads to a model transiting from a decelerated universe to an accelerating one. The physical features of the model are discussed and analysed.

The mathematical structure underlying a sentence is made of two independent processing units in series. The conditional probability density function of sentence length (measured in words) recordable in the extended short–term memory (E–STM) buffer made of CF cells is Gaussian. The number of sentences that authors of Italian and English Literatures have written is compared to that theoretically available to them. The multiplicity factor α describes this comparison. α&gt;1 is more likely than α&lt;1 and often α≫1, therefore the same sentence pattern is reused many times. These texts are easier to read. Very few novels show α&lt;1. In these cases, there are enough diverse sentence patters to convey meaning, but most of them are not used. Texts are more difficult to read, as measured by a universal readability index GU. A mismatch index IM synthetically describes the process. α, GU. and IM increase with year of publication. Future work will concern other literatures – including ancient ones as Greek and Latin – to confirm what, in our opinion, is general feature of human mind.

Diversity as well as temporal and spatial changes of the proportional abundances of different antibiotics (cycling, mixing or combinations thereof) have been hypothesised to be an effective administrative control strategy in hospitals to reduce the prevalence of antibiotic-resistant pathogens in nosocomial or community-acquired infections. However, a rigorous assessment of the efficacy of these control strategies is lacking. The main purpose here is to present a mathematical framework for the assessment of control stategies from a processual stance. To this end, we adopt diverse measures of heterogeneity and diversity of proportional abundances based on the concept of entropy from other fields and adapt them to the needs in assessing the impact of variations in antibiotic consumption on antibiotic resistance. Thereby, we derive a family of diversity measures whose members exhibit different degrees of complexity. Most important, we extent these measures such that they account for the assessment of temporal changes in heterogeneity including otherwise undetected diversity-invariant permutations of antibiotics consumption and prevalence of resistant pathogens. We apply a correlation analysis for the assessment of associations between changes of heterogeneities on the antibiotics and on the pathogen side. As a showcase, which serves as a proof-of-principle, we apply the derived methods to records of antibiotic consumption and prevalence of antibiotic-resistant germs from University Hospital Dresden. Besides the quantification of heterogeneities of antibiotics consumption and antibiotic resistance, we show that a reduction of prevalence of antibiotic-resistant germs correlates with a temporal change of similarity with respect to the first observation of antibiotics consumption, although heterogeneity remains approximately constant. Although an interventional study is pending, our mathematical framework turns out to be a viable concept for the assessment and optimisation of control strategies intended to reduce antibiotic resistance.

The last 20 years have seen a surge in scientific activity and promising results in the study of aging and longevity. Many researchers have focused on telomeres, which are composed of a series of TTAGGG repeat nucleotide sequences at the ends of each chromosome. Measurements of the length of these telomere strands show that they decrease in length with increasing age, leading many authors to propose that when the length of these telomere strands decreases sufficiently, the cells enter into a state of replicative senescence, eventually leading to disease and death. These ideas are supported by evidence that short telomere length is correlated with increased mortality. In this paper, we extend this idea to make an actual calculation of the predicted mortality rate caused by short telomere length induced senescence (STLIS). We derive a simple equation for the mathematical relationship between telomere length and mortality rate. Using only 3 parameters based on telomere length measurement data of Canadians, we have calculated both the magnitude and the age dependence of the mortality rate, for both men and women. We show that these calculated data are in good quantitative agreement with the actual number of Canadians that die. This agreement provides strong evidence (but not proof) that the mechanism of STLIS plays an important role in the major diseases of aging (e.g., cardiovascular disease, many cancers, and diabetes mellitus) which dominate human mortality. This result represents significant progress in our understanding the factors behind the cause of aging.

In the last few decades, the dynamics of tumor cells and their growths are presented via clinical, experimental, and theoretical approaches, which leads to the development of the new idea of multiple cancer therapies to control and reduce the death rate for earlier detection. In this paper, we discussed the dynamics of tumor cell growth and its treatment process. We analyzed some simple mathematical models and generalized the study to understand the growth of tumor cells. The main proposed model is a system of ordinary differential equations which combines interactions among natural killer cells, dendritic cells and cytotoxic CD8+ T cells. The model is solved numerically to explain how the tumor cells spread and become more dangerous as well as the treatment process of cancer. It is also studied that how the cell behaves in the presence of different therapy and drugs. The optimal control of chemotherapy has been discussed. It has also been explained how much the model is effective in reducing tumor cells over time. Finally, a couple of spatially distributed models are discussed for tumor cell growth.

Mathematical modelling of bioprocesses has a long and notable history, with eminent contributions from fields including microbiology, ecology, biophysics, chemistry, statistics, control theory and mathematical theory. This richness of ideas and breadth of concepts provide great motivation for inquisitive engineers and intrepid scientists to try their hand at modelling, and this collaboration of disciplines has also delivered significant milestones in the quality and application of models for both theoretical and practical interrogation of engineered biological systems. The focus of this review is the anaerobic digestion process, which, as a technology that has come in and out of fashion, still remains a fundamental process for addressing the global climate emergency. Whether with conventional anaerobic digestion systems, biorefineries, or other anaerobic technologies, mathematical models are important tools that are used to design, monitor, control and optimise the process. Both highly structured, mechanistic models and data-driven approaches have been used extensively over half a decade, but recent advances in computational capacity, scientific understanding and diversity and quality of process data, presents an opportunity for the development of new modelling paradigms, augmentation of existing methods, or even incorporation of tools from other disciplines, to ensure that anaerobic digestion research can remain resilient and relevant in the face of emerging and future challenges.

This paper develops mathematical models examining possible roles of oxytocin and oxytocin receptors in the development of autism. This is done by demonstrating that mathematical operations on normalized data from the Stanford study (K.J. Parker, 2016), which establishes a correspondence between severity of autism in children and their oxytocin blood levels, generates a graph that is the same as the graph of mathematical operations on a normalized theoretical model for the severity of autism. This procedure establishes the validity of the theoretical model and the significance of oxytocin receptors in autism. A steady-state model follows, explaining the constant baseline concentrations of oxytocin observed in the cerebral spinal fluid and blood in terms of the neuromodulation by oxytocin of oxytocin receptors on the magnocellular neurons that produce oxytocin in nuclei in the hypothalamus. The implications of these models for possible roles of oxytocin and oxytocin receptors in autism is considered for several unrelated conditions that may be associated with autism. These are: oxytocin receptor desensitization and down-regulation as factors during labor in offspring autism development; reductions in the oxytocin receptor numbers in the fixed oxytocin receptor expression that occurs before birth; MAST Immune System disease; and the excess number of dendritic spines from lack of pruning observed in brains of autistic people. Research into the feasibility of generating magnocellular neurons and other neurons from adult stem cells is suggested as a way of doing invitro studies of oxytocin and oxytocin receptors to assess the validity of theories presented in this paper.

Ensuring fire safety is an important condition for the successful operation of industrial enterprises. It is necessary to detect the threat of fire before ignition. An indicator of danger is the appearance of gas, which occurs as a result of unauthorized heating of equipment. Gas sensors make it possible to detect the appearance of gases characteristic of the decomposition of materials at the stage of smouldering and pyrolysis, which cause a change in the composition of the atmosphere. This paper presents a mathematical method for the rational placement of gas analyzers for premises of potentially hazardous industries. It is the rational placement of gas sensors, which ensures safety, taking into account economic feasibility that determines the effectiveness of their use. For the first time, the analysis of gas accumulation during the movement of the flow from the source to the ceil-ing, then propagation to the location of the sensors, is used for the first time to select the placement of gas sensors. Depending on the permissible values of the gas volume, the placement and number of gas sensors are selected. The calculation of the conditions for the rational placement of gas sen-sors for the most common indicators, such as carbon monoxide and hydrogen at different sizes and heights of rooms, is carried out. The method of calculating the location of gas analyzers makes it possible to diagnose and predict fire hazard at technological facilities on the basis of gas control, and compare the obtained values with the maximum permissible values. This method provides cal-culation of the coordinates of the gas source from the coordinates of the triggered sensors. Knowing the coordinates of all sensors, the coordinates of the sensors that gave the alarm, and the formula for determining the volume of the gas cloud under these sensors, it is possible to assess the localization of the source of dangerous gas in the protected room. This increases the efficiency of the fire safety system. The method makes it possible to control the layout of sensors depending on the volume of protected premises, types of production, the creation of new sensors, changes in the composition of hazardous gas in different technological conditions.

In this paper, we demonstrate the Collatz conjecture using the mathematical complete induction method. We show that this conjecture is satisfied for the first values of natural numbers, and in analyzing the sequence generated by odd numbers, we can deduce a formula for the general term of the Collatz sequence for any odd natural number n after several iterations. This formula is used in one case that we analyze using the mathematical complete induction method in the process of demonstrating the conjecture.

Compartmental analysis is the mathematical framework for the modelling of tracer kinetics in dynamical Positron Emission Tomography. This paper provides a review of how compartmental models are constructed and numerically optimized. Specific focus is given on the identifiability and sensitivity issues and on the impact of complex physiological conditions on the mathematical properties of the models.

Trachsummaroma is an eye infectious disease caused by Chlamydia Trachomatis bacterium, which may lead to irreversible blindness. The disease is spread directly or indirectly by contacting a contaminated material. It can also be transmitted through the disease vector known as “Musca sorbens” or “Bazaar fly”. To curtail the spread of the disease in a population, a meaningful information on the spread and possible control of the disease is required. Mathematical modeling provides efficient tools that can be used to understand and analyze the dynamics of the disease and its control. Several compartmental epidemic models have been proposed in the literature to study the dynamics of trachoma; including SI, SIR and SEIR. However, majority of the existing trachoma models consider only person to person transmission. Thus, the information provided by such models is insufficient since they did not capture the disease vector transmission. The current study proposed a novel SEIR-SEI model that consider both person-person and vector transmission dynamics. The threshold quantity, basic reproduction number R0 is obtained using the next generation matrix, and it was proved that the disease-free equilibrium is asymptotically stable when R0 < 1, and the endemic equilibrium is globally asymptotically stable when R0 > 1. Some simulation results with the aid of mesh plots for the reproductive number as a function of two different biological parameters were obtained. Furthermore, a comprehensive sensitivity analysis is conducted to identify the influence of the individual parameters on the R0. Numerical results show that the vector contact rate has the highest sensitivity with respect to R0, and the value of R0 increases with increase in, hence, the disease can be controlled by decreasing the vector contact rate. Similarly, improving the rate of environmental hygiene and facial cleanliness will decrease the size of R0 and result in the declination of the disease transmission. Moreover, a detailed parameter estimation of the model parameters and model fitting was presented with the use of field data cases from Northern Nigeria using least-square fitting method. The study provides alternative tools that can be used for planning trachoma control program to achieve global eradication of trachoma as a public heath challenge as targeted by WHO in 2030.

The "best of all possible worlds" theory (hereinafter the "possible world theory") was presented by Leibniz many centuries ago, and provided an opportunity for metaphysics to understand the ontological meaning of the world in an in-depth way. Furthermore, the theory has multiple impacts on the multiverse theory of modern physics. However, considering the ontological questions of the world solely on linguistics logic leads to basing the possible world theory or the multiverse theory on relatively uncertain inferential reasons. In this study, symbolic logic was used to consider the possible world theory on a more solid foundation. The entire world was made into oneness, and tracking the existential process at the beginning of the world, realized the existential necessity of the world, even though the initial causal point of the world was assumed to be completely void (null set). The existential system in this study, was generalized without specific elements, apart from existence and non-existence. It was discovered that existential possibility and existential necessity are logically equivalent.

The outburst of the CoVid-19 pandemic has raised several questions leading to a complex system in terms of modeling. Indeed, the modeling of the epidemic, at the level of a country, needs considering each of the different sources of contamination as well as the public health authorities' strategy, in a specific way. With this in mind, in the present paper, we develop a mathematical model of the CoVid-19 epidemic in Senegal. In the model, the population is subdivided into five compartments: susceptible, infected but asymptomatic, symptomatic, quarantined, and recovered immune people. In addition, due to its important impact on the propagation of the disease, we add one more variable: the number of infected objects. %\vspace{1mm} Therefore, the model corresponds to a system of six non-linear ordinary differential equations we submit to an analytical study to prove the relevancy of the model, simulate the evolution of the epidemic, and retrieve epidemiological parameters, namely the infection rate and the basic reproduction number, ${\cal R}_0$. Based on the senegalese territory CoVid-19 data, we simulate various scenarios as for the evolution of the epidemic in the country, in order to predict the peak and its magnitude with regard to the application of barrier measures. We also explore the option of collective immunity with special protection for vulnerable people. In doing so, non-available parameters are identified using some mathematical identification technics.

The present novel corona virus (2019-nCoV) infection has created a global emergency situation by spreading all over the world in a large scale within very short time period. The infection induced death rate is also very high. There is no vaccine or anti-viral medicine for such infection. So at this moment a major worldwide problem is that how we can control this pandemic. On the other hand, India is a high population density country, where the corona virus disease (COVID-19) has started to spread from $1^{st}$ week of March, 2020 in a significant number of COVID-19 positive cases. Due to this high population density human to human social contact rate is very high in India. So control of the pandemic COVID-19 in early stage is very urgent and challenging problem. Mathematical models are employed in this paper to study the COVID-19 dynamics, to identify the influential parameters and to find the proper prevention strategies to reduce the outbreak size. In this work, we have formulated a deterministic compartmental model to study the spreading of COVID-19 and estimated the model parameters by fitting the model with reported data of ongoing pandemic in India. Sensitivity analysis has been done to identify the key model parameters. The basic reproduction number has been estimated from actual data and the effective basic reproduction number has been studied on the basis of reported cases. Some effective preventive measures and their impacts on the disease dynamics have also been studied. Future trends of the disease transmission has been Predicted from our model with some control measures. Finally, the positive measures to control the disease have been summarized.