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.

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.

Exposure to malachite green (MG) may pose great health risks to humans, thus it is of prime importance to develop fast and robust methods to quantitatively screen the presence malachite green in environment. Herein application of extractive electrospray ionization mass spectrometry (EESI-MS) has been extended to the trace detection of MG within lake water and aquiculture water, due to the intensive use of MG as biocide in fisheries. This method has the advantage of obviating offline liquid-liquid extraction or tedious matrix separation prior to the measurement of malachite green in native aqueous medium. The experimental results indicate that the extrapolated detection limit for MG was ~3.8 ug L-1 (S/N=3) in lake water samples and ~ 0.5 ug L-1 in ultrapure water under optimized experimental conditions. The signal intensity of MG showed good linearity over the concentration range of 10–5000 ug L-1. Measurement of practical water samples fortified with MG at 0.01 and 0.1 mg L-1 gave a good validation of the established calibration curve. The average recoveries of malachite green in lake water and Carassius carassius fish farm effluent water were 114.9% (6.6% RSD) and 85.4% (9.2% RSD), respectively. Overall, the established EESI-MS/MS method has been demonstrated suitable for sensitive and rapid (<2 min per sample) quantitative detection of malachite green in various aqueous media, indicating its potential for online real-time monitoring of real life samples.

In the field of 2-D image processing and computer vision, accurately detecting and segmenting objects in scenarios where they overlap or are obscured remains a challenge. This difficulty is worse in the analysis of shoeprints used in forensic investigations because they are embedded in noisy environments such as the ground and can be indistinct. Traditional Convolutional Neural Networks (CNNs), despite their success in various image analysis tasks, struggle with accurately delineating overlapping objects due to the complexity of segmenting intertwined textures and boundaries against a background of noise. This study introduces employs the YOLO (You Only Look Once) model enhanced by edge detection and image segmentation techniques to improve the detection of overlapping shoeprints. By focusing on the critical boundary information between shoeprint textures and the ground, our method demonstrates improvements in sensitivity and precision, achieving confidence levels above 85% for minimally overlapped images and maintaining above 70% for extensively overlapped instances. Heatmaps of convolution layers were generated to show how the network converges towards successful detection using these enhancements. This research may provide a potential methodology for addressing the broader challenge of detecting multiple overlapping objects against noisy backgrounds.

Ultrasound (US) scans of the inferior vena cava (IVC) provide useful information on the volume status of a patient. However, their investigation is user-dependent and prone to measurement errors. An important technical problem is the objective difficulty in studying a very compliant blood vessel like IVC, which makes large respirophasic movements and shows a complicated three dimensional geometry. Using bi-dimensional (2D) B-mode views either in long or short axis has improved the characterization of IVC dynamics compared to a measurement along a single direction (M-mode). However, specific movements of the IVC can challenge also the information provided by these 2D sections. Thus, these two orthogonal views, provided by an US system in X-plane, are here integrated by an innovative method. It is tested on simulated videos of the IVC performing complicated movements, that are compensated by the new method, overcoming the biased measurements provided by 2D scans. The method is then applied on example experimental data.

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 research introduces a hybrid feature extraction approach that combines Linear Discriminant Analysis (LDA) and Multilayer Perceptron (MLP) methods to address the challenges of reducing feature vector dimensionality and accurately classifying smartphone-based human activities. Moreover, to refine activity classification accuracy, Support Vector Machine (SVM) optimization with Stochastic Gradient Descent (SGD) is employed. LDA, a statistical tool, is leveraged to derive a new feature space for data projection, enhancing class separation and test feature label prediction. The proposed approach, named LMSS, was evaluated using the UCI-HAR dataset and compared with state-of-the-art models. The results demonstrate that the proposed approach outperformed the best-performing method over this dataset. It achieved an accuracy rate of 99.52%, precision of 99.55%, recall of 99.53%, and an F1-score of 99.54%, highlighting the effectiveness of the proposed method in accurately classifying the data.

Analysing the human body by direct observation can lead to misinterpretation of underlying trends, whereas in vitro organ models facilitate their understanding. Likewise, in vitro organ models serve as valuable tools for assessing the toxicity of compounds. However, none of the existing models had the features we considered critical for toxicity assessment, so we developed an in vitro liver model for toxicity assessment. We used four different types of primary liver cells: Hepatic sinusoidal endothelial cells, hepatic stellate cells, Kupffer cells and hepatocytes. We cultured them in different combinations of composition and volume of cell medium, hepatocyte proportion of total cells, and addition of extracellular matrix. We added rifampicin, ibuprofen and 5-fluorouracil to this model and observed the microanatomy and physiology changes for a week with preclinical and clinical instruments. Among the different model configurations, we selected the feature combination of the in vitro model that had similar biomarker values to those measured by the clinical instruments used in clinical diagnostics. When we exposed the selected model configuration to rifampicin, ibuprofen and 5-fluorouracil, the viability of Kupffer cells and liver sinusoidal endothelial cells was significantly lower than in the untreated samples. In contrast, we observed negligible viability of hepatocytes compared to the untreated samples. We have built an in vitro liver model that resembles the liver microenvironment and we have analysed it with clinical instrumentation to facilitate the data translation. In this sense, we have established that Kupffer and LSEC cells are suitable candidates for the search for clinical diagnostic markers of liver function.

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.

Let BT4l denotes a subclass of bounded turning functions connected with a four-leaf-type domain. The goal of the study is to probe into coefficients of |b6|, |b7|, |b8|, the bounds of the logarithmic coefficients and the third-order determinants of H3,1, H3,2, H3,3 for functions in this class.

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.

We develop an action principle for producing a single fluid, two-constituent system with dissipation in general relativity. The two constituents in the model are particles and entropy. The particle flux creation rate is taken to be zero, while the entropy creation rate is non-zero. Building on previous work, it is demonstrated that a new term (the proper time derivative of the matter space ``metric'') is required in the Lagrangian in order to produce terms typically associated with bulk and shear viscosity. Equations of motion, entropy creation rate, and energy-momentum-stress tensor are derived. Using an Onsager approach of identifying thermodynamic ``forces'' and ``fluxes'' a model is produced which delivers the same entropy creation rate as the standard, relativistic Navier-Stokes equations. This result is then contrasted with a model generated in the spirit of the action principle, which takes as its starting point a specific Lagrangian and then produces the equations of motion, entropy creation rate, and energy-momentum-stress tensor. Unlike the equations derived from Onsager reasoning, where the analogs of the bulk and shear viscosity coefficients are prescribed ``externally'', we find that the form of the coefficients in the second example are a direct result of the specified Lagrangian. Furthermore, the coefficients are shown to satisfy evolution equations along the fluid worldline; also a product of the specific Lagrangian.

This paper proposes a methodology for the development and its Verification and Validation(V&amp;V) of safety-rated software. The development methodology is based on the structured analysis and structured design methodology, which has been proven in the field of safety software development during long period. The suggested the development and the V&amp;V methodology additionally focuses on the quality attributes 3C+T (completeness, Correctness, Consistency and traceability), which are important criteria in IEC international standards. The software development life cycle is compiled from IEC international standardization, which are of the requirements analysis phase, design phase, implementation phase, testing phase, installation/commissioning phase, and operation &amp; maintenance phases. The activities of the development process method were defined from requirements analysis to implementation, and the activities of the verification and validation were defined to include the scope of the developer's activities and then to include the test phase, installation/commissioning phase, and operation phases additionally. In other words, testing phase performed by the developer was defined as informal testing, and testing performed by the verifier according to test criteria, test plans, and test procedures was defined as formal testing. According to proposed methodology, the requirements phase defines the sequence of Entity Relationship Diagram (ERD)-Context Diagram-Data Flow Diagram (DFD), functional decomposition process and defines operational scenario. In the design phase, module design such as task analysis and task allocation were defined. In the implementation phase, we listed the coding guidelines that must be followed for safety-related system. The test phase defined the test criteria, test plan, test procedure, and test result report activities. In the installation/commissioning and operation phases, recommendations for improving reliability, quality, and safety were proposed for deliverables such as user documentation and technical documentation.

The importance of XAI is undeniable in the current scenario and thus it's importance in considerable. Unfortunately, there are a couple of scenarios where the current XAI models fail. Additionally, attackers seek vulnerabilities in these models. This review paper is intended to cover some of the important scenarios where the existing XAI models may fail and some progresses made which shows their vulnerabilities and how to secure them.

In developing his cosmological model of 1917, de Sitter theoretically predicted the phenomenon of cosmological redshift (the de Sitter effect), which he did long before the discovery of this phenomenon in observations. The de Sitter effect is gravitational by its nature, as it is due to differences between the coordinate systems of the observer and the distant source. However, the relationship between the redshift and distance derived from the de Sitter metric is at odds with observations, since this relationship is nonlinear (quadratic) for small redshifts, while the observed relationship between the same quantities is strictly linear. This paper discusses the possibility that cosmological redshift is gravitational by its nature, as in de Sitter’s 1917 model. At the same time, here, as in de Sitter’s model, an elliptical space is used, the main characteristic of which is the identification of its antipodal points. But, unlike de Sitter’s model, here, in order to ensure a strict linear dependence of the redshift on distance, the origin of the reference system is transferred to the observer’s antipodal point. The Schwarzschild-de Sitter metric used in this model allows you to estimate the curvature of space from observational data. To do this, a theoretical Hubble diagram is built within the framework of the model with the Schwarzschild-de Sitter metric, which is compared with observations from the Pantheon+ catalogue of type Ia supernovae and the Amati catalogue of gamma-ray bursts in the redshift range of 0&lt;z&lt;8. As a results of the comparison, the lower estimate of the radius of curvature of space turned out to be quite large: 2.3·1015 Mpc. This means that the observational data indicate a negligible curvature of space.

With the proliferation of locating devices, more and more raw spatial trajectories are formed, and many works enrich these raw trajectories with semantics, and mine patterns from both raw and semantic trajectories, but access control of spatial trajectories is not considered yet. We present a multi-policy secure model for semantic spatial trajectories. In our model, Mandatory Access Control, Role Based Access Control and Discretionary Access control are all enforced, separately and combined, and we represent the model semi-formally in Ontology Web Language.

An imbalance between production and excretion of amyloid β peptide (Aβ) in the brain tissues of Alzheimer’s disease (AD) patients leads to Aβ accumulation and formation of noxious Aβ oligomers/plaques. A promising approach to AD prevention is reduction of free Aβ level by directed enhancement of Aβ binding to its natural depot, human serum albumin (HSA). We previously demonstrated the ability of specific low-molecular-weight ligands (LMWLs) of HSA to improve its affinity for Aβ. Here we develop this approach by bioinformatic search for the clinically approved AD-related LMWLs of HSA, followed by classification of the candidates according to the predicted location of their binding sites on HSA surface, ranking of the candidates, and selective experimental validation of their impact on HSA affinity for Aβ. The top 100 candidate LMWLs were classified into the five clusters. The specific representatives of the different clusters exhibit dramatically different behavior, with 3- to 13-fold changes in equilibrium dissociation constants for the HSA-Aβ40 interaction: prednisone favors HSA-Aβ interaction, mefenamic acid shows the opposite effect, while levothyroxine exhibits the bidirectional effects. Overall, the LMWLs of HSA chosen here provide a basis for drug repurposing for AD prevention, and for search for the medications promoting AD progression.

Keywords: Spine surgery 1; Metastatic spinal cord compression 2; Spinal metastasis 3; Cancer treatment.

The goal of the project was to understand how topography/bathymetry is imported and used in GeoFlood with an aim towards improving efficiency and computational cost of bathymetry handling in GeoFlood.GeoFlood is a software to simulate overland flooding basing on shallow water equations.Numerical methods and programming were used for this study.The GeoFlood was ran on a given data set (Malpasset data) and it was found out that indeed topography handling during simulations has to be improved to minimise the computational time and also improve the efficiency.Through this research, we also looked at the the shallow water equations, and the numerical techniques used to solve the equations

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.

The studied solar pot is a recent invention, which gained a utility model protection in 2021 from the Hungarian Intellectual Property Office under patent number 5489. The device is made for environmentally friendly cooking or heating (by utilizing solar energy) of foods and liquids. Its structure is similar to a double pipe heat exchanger, it has an outer mantle and an inner cooking tank. The goals of the paper are proposing a new physically-based mathematical model describing the solar pot and carrying out computer experiments with it, assembling an experimental system of the pot connected with a solar collector and performing measurements on it. Based on the results, the solar pot can successfully be used for cooking or sterilizing foods or liquids during the studied time period, in Hungary.

Citizen science has emerged as a potent approach for environmental monitoring, leveraging the collective efforts of volunteers to gather data at unprecedented scales. Within the framework of the I-CHANGE project, MeteoTracker, a citizen science initiative, was employed to collect and analyze meteorological measurements. This paper presents the results of our analysis, demonstrating the effectiveness of citizen science in generating valuable environmental data. Through MeteoTracker, volunteers contributed to a comprehensive dataset, enabling insights into local weather patterns and trends. Our findings underscore the potential of citizen science to augment traditional monitoring efforts and inform decision-making processes in environmental research and management. The paper discusses the methodology employed, including data collection and statistical analysis techniques. Results highlight the reliability and accuracy of citizen-generated data, as well as the strengths of the MeteoTracker platform. The implications of our findings for environmental research, policy development, and public engagement are discussed, along with recommendations for enhancing the effectiveness of citizen science initiatives in environmental monitoring.

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.

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 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.

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.

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.

Let S be a Fermat surface of degree 5 and let k be an algebraically closed field of characteristic p = 2. We give a fibration ƒ: S → P with upper limit 1 and lower limit k, and investigate the geometric properties of fiber of ƒ. Furthermore, we investigate the fibration-preserving automorphisms group Aut_{Pwith upper limit 1 and lower limit k}(S) of ƒ. We obtain that Aut_{Pwith upper limit 1 and lower limit k}(S) is a p-group of order 256.

In this paper, the transmutation operator method is used to construct an exact solution to the initial boundary value problem for the equation of multidimensional free transverse vibration of a thin elastic plate with a singular Bessel operator acting on geometric variables. We emphasize that multidimensional Erdélyi–Kober operators of fractional order have the property of a transmutation operator, allowing one to transform more complex multidimensional partial differential equations with singular coefficients acting over all variables into simpler ones. If formulas for solutions are known for a simple equation, then we also obtain representations for solutions to the first complex partial differential equation with singular coefficients. In particular, it is successfully applied to the singular differential equations, especially with Bessel-type operators. Using this operator, the considered problem is reduced to a similar problem without the Bessel operator. Based on the solution to the auxiliary problem, an exact solution to the original problem is constructed and analyzed.

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.

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.

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.

Under suitable continuity and uniqueness conditions, solutions of an α order Caputo fractional boundary value problem are differentiated with respect to boundary values and boundary points. This extends well-known results for nth order boundary value problems. The approach used is a standard technique and makes heavy use of recent results for differentiation of solutions of Caputo fractional intial value problems with respect to initial conditions and continuous dependence for Caputo fractional boundary value problems.

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.

This article discusses the application of thermal quality control methods for plant tissues. The purpose of the work is to determine the optimal parameters of thermal impact on a spherical-shaped plant control object, ensuring the detection of surface and subsurface defects. The authors of the work proposed mathematical models of the temperature field for a spherical body with defects and a flat sample when exposed to the thermal influence of a pulsed source. As a result of the use of mathematical models, the thermophysical characteristics of plant tissues of varying degrees of disease damage were obtained, which made it possible to simulate the temperature field of the control object and obtain an image of classified tissues. The developed recommendations made it possible to select the optimal parameters of the thermal effect on the test object.

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.

Obtaining a proper position for THA’s components is a crucial aspect for the implant perfor-mance and consequently patient outcomes. Patient specific kinematic seems to be a key factor to reach the optimal implant positioning. The aim of this study was to assess the accuracy and safety of a computed dynamic analysis system which through patient specific guides tries to improve implant positioning and functional orientation according to patient’s spinopelvic mobility and anatomy.A total of 100 consecutive patients were prospectively enrolled. All patients received an OPS dynamic hip preoperative planning. A TC scan protocol follow up analysis has done at 6 month after surgery.The mean deviation from the planned acetabular inclination and anteversion was 4.3° e 3.8° respectively. The 98% of cases was within +/- 10° of Lewinnek safe zone both for inclination and anterversion. The height of osteotomy deviated on the average of 1.6mm. The 100% cases were included within 4mm of osteotomy. Patient specific and laser guided instru-mentation is safe and accurately reproduce the dynamic planning in terms of components orien-tation, osteotomy level, leg length and offset.

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.

To curb the impacts arising from the agricultural sector the actions undertaken by policymakers, and ultimately by the farmers, are of paramount importance. However, finding the best strategy to reduce impacts, and especially assessing the effects of the interactions and mutual influence among farmers, is very difficult. To this aim, this paper shows an application of an agent-based model (ABM) coupled with life cycle assessment (LCA), which also includes multi objective optimization of farming activities (including both crop cultivation and livestock breeding) from an economic and environmental perspective. The environmental impacts are assessed using the impact assessment scores calculated with the Environmental Footprint (EF) 3.0 life cycle impact assessment (LCIA) method and the study is conducted “from cradle to farm gate”. The model is applied to all the farms in Luxembourg, whose network is constructed utilizing neighborhood interactions, through which a parameter known as farmer's green consciousness (GC) is updated at each time step. The optimization module is instantiated at the end of each time step, and decision variables (the number of livestock units and land allocation) are assigned based on profitability and specified environmental impact categories. If only profit optimization is considered (i.e. when farmers’ GC is de-activated), the results show a 9% reduction in the aggregated environmental impacts (obtained as EF “single score”) and a 5.5% increase in overall profitability. At the farm level, simulations display a clear trade-off between environmental sustainability and financial stability, with a 25% reduction in overall emissions possible if farming activities are carried using the EF single score impact in the objective function, though this results in an 8% reduction in profitability over ten years.

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.

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.

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

Under the main features required on portable devices in electrochemical instrumentation is to have a small size, low power consumption, economically affordable, and precision in the measurements. This paper describes the development of a programmable Embedded Potentiostat System (EPS) capable of performing electrochemical sensing over system-on-a-chip platforms. Furthermore, the study explains a circuit design and develops some validation of the entire system. The hardware validation is performed by electrochemical experiments such as Double Step Chronoamperometry (DSC), Linear Sweep Voltammetry (LSV) and Cyclic Voltammetry (CV); moreover, a comparison of the experimental signals between a commercial potentiostat and the EPS was done by analysis of errors on the response signal. Results illustrate that the EPS is capable of handling currents in the range of absolute values of 86.44 to 3000 nA, and having control voltages in the range of ± 2 V. The device can support from 50 to 2000 samples per second. The EPS capabilities were compared with other compact potentiostats. The programmable EPS is an original approach which hugely reduces the hardware complexity and leads the way to create new applications for Point-of-Care or industrial developments with a reusable full electronics module.

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.

As society becomes more reliant on Lithium-ion (Li-ion) batteries, state-of-health (SOH) estimation will need to become more accurate and reliable. Therefore, SOH modelling is in the process of shifting from using simple and continuous charge/discharge profiles, to more dynamic profiles constructed to mimic real operation, when ageing the Li-ion batteries. However, in most cases, when ageing the batteries, the same exact profile is just repeated until the battery reaches its end-of-life. Using data from batteries aged in this fashion to build a model, there is a very real possibility that the model will rely on the built-in repetitiveness of the profile. Therefore, this work will examine the dependence of the performance of a multiple linear regression on the number of charges used to train the model, and their location within the profile used to age the batteries. The investigation shows that it is possible to build models using randomly selected partial charges while still reaching errors as low as 0.5%. Furthermore, it shows that only two randomly sampled partial charges are needed to achieve errors of less than 1%. Lastly, as the number of randomly sampled partial charges used to create the model increases, then the dependence on particular partial charges tends to decrease.

Nowadays, the combination of fingerprinting methodology with friendly environmental and economical analytical instrumentation are becoming increasingly relevant in the food sector. In this study, a highly versatile portable analyser based on Spatially Offset Raman Spectroscopy (SORS) to obtain the edible vegetable oils (sunflower and olive oils) fingerprints was used to evaluate the capability of such fingerprints, obtained quickly, reliable and without any sample treatment, to discriminate/classify the analysed samples. After data treatment, not only HCA and PCA as unsupervised pattern recognition techniques but also SVM, kNN and SIMCA as supervised pattern recognition techniques, showed that the main effect over the discrimination/classification was associated to those regions of RAMAN fingerprint related to the free fatty acids content, especially oleic and linoleic acid. These facts allowed the discrimination attending to the original raw material used in the oil's elaboration. In all the model established, reliable qualimetric parameters were obtained.

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

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.

Study design: Retrospective observational study. Objectives: To evaluate the change in adjacent segment disease (ASD) after hybrid dynamic stabilization with Dynesys-Transition-Optima (DTO). Methods: In 2012–2020, 115 lumbar spinal stenosis patients with spondylolisthesis re-fractory to nonsurgical management received hybrid dynamic stabilization with DTO system in a single medical center from a single neurosurgeon. After excluding those who did not receive L3–L4 dynamic stabilization and L4–L5 transforaminal lumbar interbody fusion fixation and those with incomplete postoperative data (n = 84), the 31 patients studied received follow-up vis-its at 6, 12 and 24 months postoperatively. Radiological assessment applied at the L2–L3, L3–L4 and L5–S1 segments separately included disc height, listhesis distance and angular change while in motion. Implant failure and screw loosening sign were both documented. Results: In the L3–L4 segment, the listhesis distance appeared 1 year after the operation; however, alterations in other segments showed at 6 months. At 2 years, the L3–L4 segment showed significantly less increase in listhesis distance and relatively less disc height reduction than other segments. In motion an-gular change, only the L3–L4 segment had a significant decrease at 2 years. Only the L3–L4 seg-ment maintained negative growth over 2 years in time-dependent assessment of motion angular change. Conclusions: In our study, disc height decreased, listhesis distance increased less and ASD changed later at the index level than the L2–L3 and L5–S1 levels. Angular change was re-duced at the index level while in motion. Although ASD was not significantly prevented, index level degeneration was both minor

Nitrates can cause severe ecological imbalances in aquatic ecosystems, with considerable consequences for human health. Therefore, monitoring this inorganic form of nitrogen becomes essential for any water quality management structure. This research aimed at developing a novel Nitrate Portable Measurement System (NPMS) for monitoring nitrate concentrations in water samples. NPMS is a reagent-free ultraviolet system developed using low-cost electronic components. Its operation principle is based on Beer-Lambert law for measuring Nitrate concentrations in water samples through light absorption in the spectral range 295-315 nm. The system is equipped with ready to use ultraviolet sensor, Light Emission Diode (LED), op-amp, microcontroller, liquid crystal display, quartz cuvette, temperature sensor, and battery. All the components are assembled in a 3D-printed enclosure box which allows a very compact self-contained equipment, with high portability, enabling field and near real time measurements. The proposed methodology and the developed instrument were used to analyse multiple nitrate standard solutions. The performance was evaluated in comparison with the Nicolet Evolution 300, a classical UV-Vis spectrophotometer. The results demonstrate a strong correlation between the retrieved measurements by both instruments within the investigated spectral band and for concentrations above 5 mg NO3- /l.

Genetic similarity determines the extent to which two genotypes share common genetic material. It can be measured in various ways, such as comparing DNA sequences, proteins, or other genetic markers. The significance of genetic similarity is multifaceted and encompasses various fields, including evolutionary biology, medicine, forensic science, animal and plant breeding, and anthropology. Genetic similarity is an important concept with wide application across different scientific disciplines. In the presented study, six measures for calculating genetic similarity were compared: Euclidean, Jaccard, Kulczyński, Sokal and Michener, Nei, and Rogers. The research material included 21 rapeseed genotypes (ten interspecific Brassicaceae hybrids of F2 generation, and 11 of their parental forms) and 146 alleles, obtained using 21 ISSR molecular markers. The results indicate that the research material was divided into two identical groups using any of the proposed methods, despite differences in the values of genetic similarity coefficients. Two of the presented measures of genetic similarity (Sokal and Michener, and Euclidean) were the same.

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.

In this article, we consider a class of nonsmooth interval-valued multiobjective semi-infinite programming problems with vanishing constraints (in short, NIMSIPVC). We introduce the VC-Abadie constraint qualification (in short, VC-ACQ) for NIMSIPVC and employ it to establish Karush-Kuhn-Tucker (in short, KKT)-type necessary optimality conditions. Related to NIMSIPVC, we formulate interval-valued vector Lagrange type dual and scalarized Lagrange type dual problems. Subsequently, we establish weak, strong, and converse duality results relating NIMSIPVC and corresponding dual problems. In addition, we introduce the notions of saddle points for interval-valued vector Lagrangian and scalarized Lagrangian of NIMSIPVC. Moreover, we establish the saddle point optimality criteria for NIMSIPVC. Various non-trivial examples are provided to demonstrate the validity of established results. To the best of our knowledge, optimality conditions, Lagrange type duality, and saddle point optimality criteria for NIMSIPVC have not been investigated yet via Clarke subdifferentials.

Investigation of functional magnetic resonance imaging (fMRI) data with machine learning (ML) techniques, including also deep learning (DL) methods, have been widely used to study Autism Spectrum Disorder (ASD). This disorder is characterized by symptoms that affect the individual’s behavioral aspects and social relationships. Early diagnosis is crucial for intervention, but the complexity of ASD poses challenges for treatment development. This study compares traditional ML techniques with deep learning (DL) methods in the analysis of functional connectivity measures obtained from the time series of multicentric ABIDE dataset. Specifically, Support Vector Machines (SVM) classifiers, with both linear and Radial Basis Function (RBF) kernels, as well as eXtreme Gradient Boosting (XGBoost) classifiers, are compared against the TabNet classifier, which is a DL architecture customized for tabular data analysis and a Multi Layer Perceptron (MLP). The findings suggest that DL classifiers may not be optimal for the type of data analyzed, as their performance trails behind that of standard classifiers. SVMs achieve performances, in terms of AUC, around 75%, compared to the best TabNet and MLP results, which are 65% and 71%, respectively. Additionally, this work investigates the brain regions that contribute most to the classification task, which are found to be those primarily responsible for sensory and spatial perception, as well as attention modulation, known to be altered in ASD.

Sharing confidential information is a critical concern in today’s world. Secret sharing schemes facilitate the sharing of secrets in a way that ensures only authorized participants (shareholders) can access the secret using their allocated shares. Hierarchical secret sharing schemes (HSSSs) build upon Shamir’s scheme by organizing participants into different levels based on priority. Within HSSS, participants at each level can reconstruct the secret if a specified number, denoted as the threshold value (t), or more of them are present. Each level has a predetermined threshold value. If the number of participants falls below the threshold at any level, higher-level participants must be involved in reconstructing the secret at lower levels. Our paper proposes schemes that implement hierarchical access structures and enable the sharing of multiple secrets. Additionally, our proposed scheme includes share verification. We have analyzed potential attacks and demonstrated the scheme’s resistance against them. Through security analysis and comparison with existing schemes, we highlight the novelty and superiority of our proposed approach, contributing to advancements in secure information sharing practices.

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.

Worldwide, different strategies are elaborated in order to ensure optimum conditions for the development and growth of the economic competitiveness, but also for increasing the quality of life and environment protection. All these strategies are closely linked with the development and modernization of the systems for producing energy from clean and renewable sources. In this context, the present paper presents the results of the researches regarding the evaluation of the sustainability of the briquettes production, using the biomass resulted from vine winter pruning as raw material. An analysis of the scientific references indicates that nearly 8 Mt of biomass result from over 7.4 million hectares of vine plantations existent worldwide, biomass that could be valorized through densification in order to produce solid biofuels with a lower calorific value of more than 17 MJ·kg-1. When designing the scientific endeavor, the following aspects were considered: defining the aim and objectives of the research; design of the research algorithm; collection, preparation and conditioning of the biomass; chemical analysis of the briquettes; evaluation of the technological characteristics of the briquettes; evaluation of the energy consumption and energy efficiency for producing the briquettes, taking into account two drying methods (natural and artificial drying). In the meantime, some specific laboratory equipment was design and built for the artificial drying of biomass, evaluation of the mechanical durability, measurement of the energy consumption etc. The analysis of the experimental data has led to the conclusion that the agricultural waste from vine pruning can constitute an important and sustainable source of energy in the form of bri-quettes, which fulfill most of the requirements imposed by the international standards.

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.

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.

Driven by mounting environmental apprehensions stemming from the over dependence on fossil fuels in energy and transportation sectors, extensive exploration into alternative energy sources, particularly biomass, has stimulated profound research on harnessing the potential of computational and mathematical techniques. This comprehensive survey delves into optimal models and strategies, unveiling their pivotal role in the design of biomass gasification processes.of hydrogen through biomass gasification. In this study, we aim to provide a comprehensive overview of the computational and mathematical techniques employed in optimizing biomass gasification processes, with a specific focus on enhancing hydrogen yield. Through an extensive literature review, various models and strategies will be examined, including thermodynamic analysis, kinetic modeling, reactor design, and process optimization. By uncovering the power of these techniques, we aim to contribute to the advancement of sustainable and efficient biomass utilization for the hydrogen-based future economy.This paper aims to provide an updated and comprehensive coverage of the investigations conducted on the potential of producing hydrogen from biomass through gasification. To achieve this, we incorporate the latest works that have utilized numerical modeling, simulation, optimization techniques, process heat integration, and co-generation in their studies. By encompassing these aspects, we aim to offer a broader and more in-depth re-appraisal of the subject matter. This will ensure that readers gain a holistic understanding of the advances made in the field and the potential for sustainable hydrogen production of biomass gasification.Through a meticulous re-appraisal and analysis of each subject, we can identify their respective strengths and areas that require further research effort. By thoroughly examining numerical modeling, simulation, optimization techniques, process heat integration, and co-generation, we can assess their effectiveness and applicability in the context of biomass gasification for hydrogen production. This analysis shed light on the areas where these techniques excel, as well as pinpoint limitations or gaps in current understanding. By identifying these areas, we can highlight the need for further research and development, enabling us to make significant advancements in biomass gasification processes and pave the way for a sustainable and efficient hydrogen-based future economy..

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.

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.

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 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.

Wall Shear Stress (WSS) abnormalities in carotid artery blood flow are key hemodynamic factors leading to arterial endothelial damage, atherosclerotic plaque formation, and carotid artery stenosis. Precise simulation of carotid artery blood flow WSS in vitro play an important role in understanding the underlying hemodynamic mechanism of carotid artery stenosis. This study presents a design for a microfluidic cell culture chamber with a variable cross-section and a step structure, leveraging microfluidic technology and principles of fluid dynamics. We propose an optimization strategy for microchannel dimensions based on Computational Fluid Dynamics (CFD) simulations. This strategy aims to replicate the distinct WSS waveform features found at various locations within the carotid bifurcation as observed in vivo. Our simulations indicate that with a step height of 0.09 mm, a width of 4 mm for the initial segment, and 5 mm for the subsequent wider channel, the device can effectively model the characteristics of low oscillatory WSS seen at sites of carotid sinus stenosis. Furthermore, it accurately represents the high-magnitude pulsatile WSS waveforms in the more uniform arterial sections downstream of the carotid sinus. The study also reveals that vortex formation and variations in low oscillatory WSS within the stepped section of the microchannel correlate with the step's height and width, as well as with the dimensions of the wider channel section. An increase in step width leads to a decrease in both the vortex area and the magnitude of negative WSS oscillations. When the step height is less than 0.03 mm, vortex formation is inhibited, challenging the simulation of low oscillatory WSS patterns. The variable cross-section microfluidic channel developed in this study provides a platform for simulating carotid artery WSS waveforms and facilitates research into the interplay between low oscillatory WSS at sites of carotid sinus stenosis and arterial endothelial dysfunction.

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.

Fractional cointegration in time series data has been explored by several authors, but panel data applications have been largely neglected. A previous study of ours discovered that the Chen and Hurvich fractional cointegration test for time series was fairly robust to a moderate degree of heterogeneity across sections, out of the six tests considered. Therefore, this paper advances a customized version of the Chen and Hurvich methodology to detect cointegrating connections in panels with unobserved fixed effects. Specifically, we develop a test statistic that accommodates variation in the long-term cointegrating vectors and fractional cointegration parameters across observational units. The behaviour of our proposed test is examined through extensive Monte Carlo experiments under various data generating processes and circumstances. The findings reveal that our modified test performs quite well comparatively and can successfully identify fractional cointegrating relationships in panels even in the presence of idiosyncratic disturbances unique to each cross-sectional unit. Furthermore, the proposed modified test procedure established the presence of long-run equilibrium between the exchange rate and labour wage of 36 countries agricultural markets.

Inflammation is the body’s response to infection, injury, or other stimuli. Acute inflammation is a crucial component of the immune system’s defense, aimed at eliminating infected or damaged cells and halting disease progression. A subtle interaction between pro- and anti-inflammatory processes determines its progression to inflammation resolution or to chronic inflammation. In this study, we propose a generic model of inflammation through a system of reaction-diffusion equations involving various inflammatory and anti-inflammatory cells and cytokines. We investigate the formation of patterns, determined by the emergence of Turing structures, through linear stability analysis and numerical simulations. These theoretical findings are further supported by observations of similar patterns in skin diseases.

Droughts have negative impacts on agricultural productivity and economic growth. Effective monitoring and accurate forecasting of drought occurrences and trends are crucial for minimizing drought losses and mitigating their spatial and temporal effects. In this study, trend dynamics in monthly total rainfall time series measured at Cape Town International Airport were analyzed using Mann-Kendall (MK) test, Modified Mann-Kendall (MMK) and innovative trend analysis (ITA) were examined. Additionally, we utilized hybrid prediction method that combined the model with the complementary ensemble empirical mode decomposition with adaptive noise (CEEMDAN) technique, the autoregressive integrated moving average (ARIMA) model, the long short-term memory (LSTM) network (i.e. CEEMDAN-ARIMA-LSTM) to forecast SPI values of 6-, 9-, and 12-months using rainfall data between 1995 and 2020 from Cape Town International Airport meteorological rainfall stations. The results demonstrate the following essential points: (1) The trend analysis results of the total monthly rainfall values indicate a significant decreasing trend with the negative z-score (MK= -3.7541 and MMK= - 4.0773). ITA also indicated a significant downwards trend of rainfall in the study area. (2) As the forecasting horizon increases, the prediction accuracy of the models and CEEMDAN-combined models gradually improves, reaching their optimum performance at the 12-month horizon. (3) CEEMDAN efficiently stabilizes time-series data, resulting in greater prediction accuracy in the hybrid model compared to individual models at all timescales. (4) The RMSE and R2 values for the hybrid CEEMDAN-ARIMA-LSTM model at a 12-month forecasting horizon are 0.042 and 0.995, demonstrating the applicability of this hybrid approach for drought forecasting.

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.

Alkaloid-based urea derivatives were produced with high yield through the reaction of anabasine and cytisine with isoxazolylphenylcarbamates in boiling benzene. Their antitumor ac-tivity in combination with the commonly used six anticancer drugs namely cyclophosphane, fluorouracil, etoposide, cysplatine, ribomustine with different mechanisms of action was investi-gated. Based on the quantum chemical calculations data and molecular docking, hypotheses have been put forward to explain their mutual influence when affecting on the С6 rat glioma model cells.

Over the last fifty years, management plans have become more descriptive with regard to potential sustainability of forest systems, raising questions about the feasibility of implementing management activities and ensuring sustainability of a wide variety of ecosystem services. To assess this issue, we conducted a survey among forest planning and operation research communities to understand their perceptions regarding the potential of a sample of sustainability statements currently used in forest plans to be incorporated into optimization models or other mathematical operations. The results revealed that only a few statements from the sample were deemed to have relatively mature or firm methodologies and data to enable inclusion in modern mathematical models for land use optimization. These statements were mostly related to economic sustainability, offering quantifiable information such as a non-declining flow of wood products over time and limits on the amount of timber harvested per decade. In contrast, sociocultural and, to some extent, ecological statements regarding sustainability were generally perceived to be more difficult to translate into mathematical modeling efforts. Particularly challenging were statements corresponding to sustaining natural or scenic characteristics of a forest. These findings may be attributed to various factors, including a lack of measurable indicators for sustainability and a potential lack of understanding about the modeling components and their interactions with planned management activities.

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&lt;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.

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.

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.

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.

Bi1-xSbx crystal is one of the best n-type thermoelectric materials below 200 K, but its weak mechanical strength hinders practical applications for deep refrigeration. Herein, we adopted the mechanical enhancement method of hot extrusion to investigate the comprehensive mechanical and thermoelectric properties of Bi0.905Sb0.095. It revealed that reducing the grain size of the matrix and increasing the extrusion ratio can improve the gain size uniformity and mechanical properties. While the thermoelectric performance depends on the texture, grain size, and local composition. The extruded sample prepared by ingot with the high extrusion ratio of 9:1 generated a high texture degree of (001) plane and small grain sizes between ~4-40 mm, which resulted in the high bending strength of Bi1-xSbx ~130 Mpa and a high-power factor of ~ 68 μW·cm-1·K-2@173 K, as well as the relative high figure of merit of 0.25@173K. This work highlights the importance of the uniform distribution of the grain size and the compositions for Bi1-xSbx, as well as the required universal key parameter for the hot-extrusion method.