Stability evaluation of candidate reference genes for real-time qPCR normalization in Rhyzopertha dominica (Coleoptera: Bostrycidae)

Rhyzopertha dominica is a serious stored grain insect pest around the world. Real-time quantitative polymerase chain reaction (RT-qPCR) is a widely used experimental method in molecular biology for detecting the expression of target genes. As appropriate reference genes are essential for normalizing gene expression, the selection of suitable reference genes is the basis of RT-qPCR experiments. In this study, the expression profiles of 7 candidate reference genes of rps3, rps6, rps13, actin, gadph, tubulin, and 18S rRNA were analyzed under 4 different experimental conditions. The expression stability of candidate genes was evaluated using the ΔCt, GeNorm, BestKeeper, NormFinder, and RefFinder methods. The results revealed that different reference genes were suitable for various experiments. Specifically, rps3 and rps6 were appropriate for the developmental stages and all samples: 18S rRNA and rps13 for temperature-related experiments, actin and rps6 for sex-related experiments, and rps6 and gadph for starvation stress. Our results lay essential groundwork for the normalization of RT-qPCR analyses and contribute to genomic and gene functional research of R. dominica.

Stability Analysis of SARS-CoV-2 with Heart Attack Effected Patients and Bifurcation

The aim of this study is to analyze and investigate the SARS-CoV-2 (SC-2) transmission with effect of heart attack in United Kingdom with advanced mathematical tools. Mathematical model is converted into fractional order with the help of fractal fractional operator (FFO). The proposed fractional order system is investigated qualitatively as well as quantitatively to identify its stable position. Local stability of the SC-2 system is verified and test the proposed system with flip bifurcation. Also system is investigated for global stability using Lyponove first and second derivative functions. The existence, boundedness, and positivity of the SC-2 is checked which are the key properties for such of type of epidemic problem to identify reliable findings. Effect of global derivative is demonstrated to verify its rate of effects of heart attack in united kingdom. Solutions for fractional order system are derived with the help of advanced tool FFO for different fractional values to verify the combine effect of COVID-19 and heart patients. Simulation are carried out to see symptomatic as well as a symptomatic effects of SC-2 in the United Kingdom as well as its global effects, also show the actual behavior of SC-2 which will be helpful to understand the outbreak of SC-2 for heart attack patients and to see its real behavior globally as well as helpful for future prediction and control strategies.

Relationship of Hoarding and Depression Symptoms in Older Adults

Hoarding disorder (HD) is a debilitating neuropsychiatric condition that affects 2%-6% of the population and increases in incidence with age. Major depressive disorder (MDD) co-occurs with HD in approximately 50% of cases and leads to increased functional impairment and disability. However, only one study to date has examined the rate and trajectory of hoarding symptoms in older individuals with a lifetime history of MDD, including those with current active depression (late-life depression; LLD). We therefore sought to characterize this potentially distinct phenotype. We determined the incidence of HD in two separate cohorts of participants with LLD (n = 73) or lifetime history of MDD (n = 580) and examined the reliability and stability of hoarding symptoms using the Saving Inventory-Revised (SI-R) and Hoarding Rating Scale-Self Report (HRS), as well as the co-variance of hoarding and depression scores over time. HD was present in 12% to 33% of participants with MDD, with higher rates found in those with active depressive symptoms. Hoarding severity was stable across timepoints in both samples (all correlations >0.75), and fewer than 30% of participants in each sample experienced significant changes in severity between any two timepoints. Change in depression symptoms over time did not co-vary with change in hoarding symptoms. These findings indicate that hoarding is a more common comorbidity in LLD than previously suggested, and should be considered in screening and management of LLD. Future studies should further characterize the interaction of these conditions and their impact on outcomes, particularly functional impairment in this vulnerable population.

Numerical Analysis of Compound Biochemical Calcium Oscillations Process in Hepatocyte Cells

The hepatocyte cells regulate the wide range of liver function by moderating cellular activities such as lipid, protein metabolism, carbohydrate, and interact with other cells for proliferation and maintenance. In hepatocyte cells, the concentration of calcium uptake is quite extensive from various agonists such as activeG α ${G_\alpha}$ subunit, active phospholipase C, free calcium in the cytosol, and endoplasmic reticulum. The overproduction and degradation of calcium signals can cause homeostasis, liver inflammation, and liver diseases. The spatiotemporal behavior of calcium oscillation reveals the physiological role of these cellular entities in understanding the process of production and degradation. No computational attempt has been registered to date on the compound calcium regulation of these cellular entities including the memory of cells. Hence, the authors proposed a fractional order compartmental model that systematically simulates the exchange of calcium intake in cellular entities. The nonlinear equations of the rate of changes in the activeG α ${G_\alpha}$ subunit, active phospholipase C, free calcium in the cytosol, and endoplasmic reticulum are coupled to form a nonlinear fractional order initial value problem. The existence and uniqueness, stability analysis of the model is performed that validate the theoretical results and explore the dynamic behaviour of calcium oscillation in each compartment.

Stability Analysis and Design of n-DOF Vibration Systems Containing Both Semi-Active and Passive Mechanical Controllers

This paper is concerned with the stability analysis and design of the n-DOF (n-degree-of-freedom) mass-chain vibration systems containing both semi-active and passive mechanical controllers. Based on Lyapunov's stability theory, sufficient conditions are derived for the n-DOF vibration system containing a semi-active switched inerter and a passive mechanical network with the first-order admittance to be globally asymptotically stable. Furthermore, the optimization designs of a quarter-car vibration control system and a three-storey building vibration system are conducted together with the derived stability results, and the instability cases contradicting the stability conditions are presented for illustration. The optimization and simulation results show that the combination of semi-active and passive mechanical controllers in vibration systems can clearly enhance system performances in comparison with the conventional semi-active or passive control. The novelty of this paper is that the stability problem of a general n-DOF vibration system that simultaneously contains a semi-active controller and a first-order passive controller is investigated for the first time, where such a system combines the advantages of both semi-active and passive mechanical controllers. The investigations and results can provide an essential foundation for further exploring the stability problems of more general systems, and can be applied to the controller designs of many vibration systems in practice.

The effect of emulgel preparation on the stability of Kojic acid in the topical anti-hyperpigmentation products

BACKGROUND

The emulgel, a novel drug delivery system, merges emulsion and gel, offering advantages like enhanced stability, precise control over drug release kinetics, and increased drug absorption compared to emulsions alone. Kojic acid (KA) demonstrates potent inhibition of the tyrosinase enzyme, a crucial player in the melanin synthesis pathway.

AIMS

The main objective of this experimental study is to formulate KA within an emulgel framework and assess its stability under various environmental conditions.

METHODS

One percent of KA emulgel and 1% simple gel, serving as the control product, were supplemented with varying concentrations of sodium metabisulfite (SMBS) for its antioxidant properties. The formulations were segregated into four groups and subjected to diverse maintenance and stress conditions over a three-month period. Monthly evaluations of physicochemical alterations were conducted, initially employing digital photography, followed by the extraction of KA and subsequent quantification of its concentration through high performance liquid chromatography (HPLC).

RESULTS

The best formulations for retaining KA among the prepared ones were the 0.25% SMBS KA emulgel and the 0.1% SMBS KA simple gel, capable of retaining 86% and 76% of the initial KA content under stress conditions, respectively (p < 0.0001).

CONCLUSIONS

Regarding to this study, ideal storage condition for KA emulgel and simple gel is in the refrigerator temperatures. Moreover, optimal SMBS concentrations for stability enhancement are 0.25% for emulgel and 0.1% for the simple gel. A significant statistical difference was observed between refrigerated emulgel and simple gel in the retention of KA in the presence of optimum concentration of antioxidants (p < 0.0001).

Driving Principle and Stability Analysis of Vertical Comb-Drive Actuator for Scanning Micromirrors

We have developed a manufacturing process for micromirrors based on microelectromechanical systems (MEMS) technology. The process involves designing an electrostatic vertically comb-driven actuator and utilizing a self-alignment process to produce a height difference between the movable comb structure and the fixed comb structure of the micromirror. To improve the stability of the micromirror, we propose four instability models in micromirror operation with the quasi-static driving principle and structure of the micromirror considered, which can provide a basic guarantee for the performance of vertical comb actuators. This analysis pinpoints factors leading to instability, including the left and right gap of the movable comb, the torsion beams of the micromirror, and the comb-to-beams distance. Ultimately, the voltages at which device failure occurs can be determined. We successfully fabricated a one-dimensional micromirror featuring a 0.8 mm mirror diameter and a 30 μm device layer thickness. The height difference between the movable and fixed comb structures was 10 μm. The micromirror was able to achieve a static mechanical angle of 2.25° with 60 V@DC. Stable operation was observed at voltages below 60 V, in close agreement with the theoretical calculations and simulations. At the driving voltage of 80 V, we observed the longitudinal displacement movement of the comb fingers. Furthermore, at a voltage of 129 V, comb adhesion occurred, resulting in device failure. This failure voltage corresponds to the lateral torsional failure voltage.

Stochastic Antiresonance for Systems with Multiplicative Noise and Sector-Type Nonlinearities

The paradigm of stochastic antiresonance is considered for a class of nonlinear systems with sector bounded nonlinearities. Such systems arise in a variety of situations such as in engineering applications, in physics, in biology, and in systems with more general nonlinearities, approximated by a wide neural network of a single hidden layer, such as the error equation of Hopfield networks with respect to equilibria or visuo-motor tasks. It is shown that driving such systems with a certain amount of state-multiplicative noise, one can stabilize noise-free unstable systems. Linear-Matrix-Inequality-based stabilization conditions are derived, utilizing a novel non-quadratic Lyapunov functional and a numerical example where state-multiplicative noise stabilizes a nonlinear system exhibiting chaotic behavior is demonstrated.

Analysis of the Stability of a Flat Textiles with a Two-Parameter Deflection Curve

The issue of large deflections of textiles occurs primarily when analyzing the "drape" of curtains, tablecloths and other flat textile products. The correct drape is particularly important from an aesthetic point of view. Additionally, there is a problem with the stability of the folds created during the drape process. The analysis of this problem is difficult due to the occurrence of large deflections and non-linear properties of the material. In this article, a selected fragment of the above-mentioned issue was tested, relating only to the stability of the fold formed under given loading conditions. A typical example is a fabric resting on a flat surface and loaded with compressive forces. The presented considerations lead to obtaining the deflection curve for a given self-weight and compressive force. Additionally, the obtained shape was tested for stability. Two shape parameters used in the analysis can be applied for the simulation of different shapes of the deflection curve. The analysis has been made using the energy method relating to the total potential energy of the object. The obtained results may be used in algorithms and simulation programs for fabric folding, buckling and for another applications in the area of textile mechanics.

Optimizing chemotherapy treatment outcomes using metaheuristic optimization algorithms: A case study

BACKGROUND

This study explores the dynamics of a mathematical model, utilizing ordinary differential equations (ODE), to depict the interplay between cancer cells and effector cells under chemotherapy. The stability of the equilibrium points in the model is analysed using the Jacobian matrix and eigenvalues. Additionally, bifurcation analysis is conducted to determine the optimal values for the control parameters.

OBJECTIVE

To evaluate the performance of the model and control strategies, benchmarking simulations are performed using the PlatEMO platform.

METHODS

The Pure Multi-objective Optimal Control Problem (PMOCP) and the Hybrid Multi-objective Optimal Control Problem (HMOCP) are two different forms of optimal control problems that are solved using revolutionary metaheuristic optimisation algorithms. The utilization of the Hypervolume (HV) performance indicator allows for the comparison of various metaheuristic optimization algorithms in their efficacy for solving the PMOCP and HMOCP.

RESULTS

Results indicate that the MOPSO algorithm excels in solving the HMOCP, with M-MOPSO outperforming for PMOCP in HV analysis.

CONCLUSION

Despite not directly addressing immediate clinical concerns, these findings indicates that the stability shifts at critical thresholds may impact treatment efficacy.

Stability Analysis in Milling Based on the Localized Differential Quadrature Method

Chatter stability analysis is an effective way to optimize the cutting parameters and achieve chatter-free machining. This paper proposes a milling chatter stability analysis method based on the localized differential quadrature method (LDQM), which has the advantages of simple principle, easy application, and high computational efficiency. The milling process, considering the regeneration effect, is modeled using linear periodic delay differential equations (DDE), then the state transition matrix during the adjacent cutting period is constructed based on the LDQM, and finally, the stability of the milling process is obtained based on the Floquet theory. The accuracy and computation efficiency of the proposed method are verified through two benchmark milling models. The simulation results demonstrate that the proposed method in this paper can accurately and quickly obtain the chatter stability lobe diagram (SLD) of the milling process, which will provide guidance for optimizing the process parameters.

Pattern formation and travelling waves in a multiphase moving boundary model of tumour growth

We employ the multiphase, moving boundary model of Byrne et al. (2003, Appl. Math. Lett., 16, 567-573) that describes the evolution of a motile, viscous tumour cell phase and an inviscid extracellular liquid phase. This model comprises two partial differential equations that govern the cell volume fraction and the cell velocity, together with a moving boundary condition for the tumour edge, and here we characterize and analyse its travelling-wave and pattern-forming behaviour. Numerical simulations of the model indicate that patterned solutions can be obtained, which correspond to multiple regions of high cell density separated by regions of low cell density. In other parameter regimes, solutions of the model can develop into a forward- or backward-moving travelling wave, corresponding to tumour growth or extinction, respectively. A travelling-wave analysis allows us to find the corresponding wave speed, as well as criteria for the growth or extinction of the tumour. Furthermore, a stability analysis of these travelling-wave solutions provides us with criteria for the occurrence of patterned solutions. Finally, we discuss how the initial cell distribution, as well as parameters related to cellular motion and cell-liquid drag, control the qualitative features of patterned solutions.

A dynamical analysis and numerical simulation of COVID-19 and HIV/AIDS co-infection with intervention strategies

HIV/AIDS-COVID-19 co-infection is a major public health concern especially in developing countries of the world. This paper presents HIV/AIDS-COVID-19 co-infection to investigate the impact of interventions on its transmission using ordinary differential equation. In the analysis of the model, the solutions are shown to be non-negative and bounded, using next-generation matrix approach the basic reproduction numbers are computed, sufficient conditions for stabilities of equilibrium points are established. The sensitivity analysis showed that transmission rates are the most sensitive parameters that have direct impact on the basic reproduction numbers and protection and treatment rates are more sensitive and have indirect impact to the basic reproduction numbers. Numerical simulations shown that some parameter effects on the transmission of single infections as well as co-infection, and applying the protection rates and treatment rates have effective roles to minimize and also to eradicate the HIV/AIDS-COVID-19 co-infection spreading in the community.

Preparation, structure characterization, and stability analysis of peptide-calcium complex derived from porcine nasal cartilage type II collagen

BACKGROUND

Porcine nasal cartilage type II collagen-derived peptides (PNCPs) may be complexed with calcium to provide a highly bioavailable, low-cost, and effective calcium food supplement. However, the calcium-binding characteristics of PNCPs have not yet been investigated. In the present study, calcium-binding peptides were derived from porcine nasal cartilage type II collagen and the resulting PNCPs-Ca complex was characterized.

RESULTS

The study reveals that the calcium-binding capacity of PNCPs is closely related to enzymatic hydrolysis conditions. The highest calcium-binding capacity of PNCPs was observed at a hydrolysis time of 4 h, temperature of 40 °C, enzyme dosage of 1%, and solid-to-liquid ratio of 1:10. Scanning electron microscopy and energy dispersive X-ray spectroscopy revealed that the PNCPs had a pronounced capacity for calcium binding, with the PNCPs-Ca complex exhibiting a clustered structure consisting of aggregated spherical particles. Fourier-transform infrared spectroscopy, fluorescence spectroscopy, X-ray diffraction, dynamic light scattering, amino acid composition, and molecular weight distribution analyses all indicated that the PNCPs and calcium complexed via the carboxyl oxygen and amino nitrogen atoms, leading to the formation of a β-sheet structure during the chelation process. In addition, the stability of the PNCPs-Ca complex was maintained over a range of pH values consistent with those found in the human gastrointestinal tract, facilitating calcium absorption.

CONCLUSION

These research findings suggest the feasibility of converting by-products from livestock processing into calcium-binding peptides, providing a scientific basis for the development of novel calcium supplements and the potential reduction of resource waste. © 2023 Society of Chemical Industry.

On the adoption of nonpharmaceutical interventions during the pandemic: An evolutionary game model

The adoption of behavioral nonpharmaceutical interventions (NPIs) among the public is essential for tackling the COVID-19 pandemic, yet presents challenges due to the complexity of human behaviors. A large body of literature has utilized classic game theory to investigate the population's decisions regarding the adoption of interventions, where the static solution concept such as the Nash equilibrium is studied. However, individual adoption behavior is not static, instead it is a dynamic process that involves the strategic interactions with other counterparts over time. The study of quantitatively analyzing the dynamics on precautionary behavior during an outbreak is rather scarce. This article fills the research gap by developing an evolutionary game-theoretic framework to model the dynamics of population behavior on the adoption of NPI. We construct the two-group asymmetric game, where behavioral change for each group is characterized by replicator equations. Sensitivity analyses are performed to examine the long-term stability of equilibrium points with respect to perturbation of model parameters. We found that the limiting behavior of intervention adoption in the population consists of only pure strategies in a game setting, indicating that the evolutionary outcome is that everyone either takes up the preventive measure or not. We also applied the framework to examine the mask-wearing behavior, and validated with actual data. Overall, this article provides insights into population dynamics on the adoption of intervention strategy during the outbreak, which can be beneficial for policy makers to better understand the evolutionary trajectory of population behavior.

Genotypic and environmental effects on quality and nutritional attributes of Moroccan barley cultivars and elite breeding lines

Although barley is mainly used for livestock feed and beverages, its use as human feed can enrich human diets with some health benefits. The development of new hulless varieties rich in β-glucans and micronutrients can enhance the use of barley as food, but little is known about the effects of the environment on these nutritional traits. In this study, we evaluated five Moroccan varieties and two elite breeding lines of barley at four locations in Morocco during the 2016-2017 and 2017-2018 cropping seasons. The results showed highly significant differences between genotypes for β-glucan, protein, iron, and selenium contents, as well as 1000 kernel weight, but not zinc content; significant to highly significant differences between environments for all traits except β-glucan content; and significant to highly significant interactions for all traits. The highest level of β-glucan content has reached 11.57% observed at the Sidi El Aydi site during the growing season 2017-2018 for the hulless variety Chifaa. This variety has shown the highest content of β-glucan (6.2-11.57%) over all environments except at Tassaout during the 2016-2017 seasons. The breeding line M9V5 has achieved significantly higher protein content at all the locations during the two growing seasons, ranging from 12.38 to 20.14%. Most hulless lines had significantly higher β-glucan and protein contents, but lower 1000 kernel weight. For micronutrients, the content ranges were 28.94 to 38.23 ppm for Fe, 28.78 to 36.49 ppm for Zn, and 0.14 to 0.18 ppm for Se, with the highest content for Fe and Zn shown by the breeding line M9V5 and Chifaa showing average contents of 33.39 ppm, 35.34 ppm, and 0.18 ppm for Fe, Zn, and Se, respectively. The GGE biplot confirmed the high and relatively stable content of β-glucan and acceptable micronutrient contents of the Chifaa variety and identified Marchouch as the most discriminant site to breed for biofortified barley varieties.

A Mathematical Model to Study the Potential Hepatitis B Virus Infections and Effects of Vaccination Strategies in China

MOTIVATIONS

Hepatitis B is a potentially life-threatening infectious disease caused by the hepatitis B virus (HBV). Approximately 390,000 people in China die from HBV-related diseases each year. Around 86 million individuals suffer from infections of the hepatitis B virus, accounting for about 6% of the total population in the region. There are approximately 30 million chronic infections. From 2002 to 2007, China's government took part in "The Global Alliance for Vaccines and Immunization (GAVI)" initiative, which helped reduce cases of chronic HBV infections among children. However, incidences of hepatitis B remain persistently high in China. Accurately estimating the number of potential HBV infections is crucial for preventing and controlling the transmission of the hepatitis B virus. Up until now, there were no studies of potentially infectious hepatitis B virus infections.

METHODS

this study was based on data from the National Bureau of Statistics of China from 2003 to 2021; a dynamic model was built, which included a compartment for potentially infectious hepatitis B virus infections. The parameters in the model were fitted using a combination of nonlinear least-squares and genetic algorithm methods.

RESULTS

the calculated reproduction number for hepatitis B virus transmission within the population is Rc = 1.741. Considering the existing vaccine inefficiency rate of 0.1, the model estimates there are 449,535 (95%CI [415,651, 483,420]) potentially infectious hepatitis B virus infections, constituting 30.49% of total hepatitis B cases. Date fitting using MATLAB reveals that increasing the rate of hepatitis B vaccinations can effectively reduce the number of infections.

CONCLUSIONS

the results reveal that the number of potential infectious hepatitis B virus infections is so high that the number of hepatitis B patients persistently rises in China. To better control the transmission of the hepatitis B virus, an optional prevention and control strategy is needed to increase the vaccination of different age groups, and it is necessary to help the public correctly understand the transmission of hepatitis B and ensure adequate protection.

Stability Analysis of Switched Linear Singular Systems with Unstable and Stable Modes

In this paper, stability is studied for a class of switched singular systems containing both stable and unstable modes. By introducing a time-varying piecewise Lyapunov function (TVPLF) and a mode-dependent average dwell time (ADT) switching rule, the computable sufficient conditions for system stability are derived. The time-varying piecewise Lyapunov functions are piecewise continuously differentiable on every mode (but may not be differentiable at the interpolating points of the dwell time). This Lyapunov function method is particularly advantageous in overcoming the limitations of traditional multiple Lyapunov function (MLF) methods, which may not have a feasible solution when dealing with switched systems containing only unstable modes. As such, the TVPLF offers greater flexibility in application. Compared with the conventional ADT switching rule, the mode-dependent ADT switching rule not only enables each mode to have its own ADT but also allows for its own switching strategy. Specifically, the stable mode adopts a slow switching strategy while the unstable mode adopts a fast one, thereby reducing the conservatism of the ADT switching rule. Furthermore, based on the stability analysis, the time-varying controllers are proposed to stabilize the switched singular system, which can be expressed as the sequential linear combination of a series of linear state feedback on each mode. The proposed controllers are continuous for each mode, which are different from the controllers designed through the traditional MLF and MDLF methods, where the controllers designed by traditional MLF are the time-invariant linear state feedback in each mode while the controllers designed by the MDLF are piecewise continuous for each mode.

Fractional Modeling of Cancer with Mixed Therapies

BACKGROUND

Cancer is the biggest cause of mortality globally, with approximately 10 million fatalities expected by 2020, or about one in every six deaths. Breast, lung, colon, rectum, and prostate cancers are the most prevalent types of cancer.

METHODS

In this work, fractional modeling is presented which describes the dynamics of cancer treatment with mixed therapies (immunotherapy and chemotherapy). Mathematical models of cancer treatment are important to understand the dynamical behavior of the disease. Fractional models are studied considering immunotherapy and chemotherapy to control cancer growth at the level of cell populations. The models consist of the system of fractional differential equations (FDEs). Fractional term is defined by Caputo fractional derivative. The models are solved numerically by using Adams-Bashforth-Moulton method.

RESULTS

For all fractional models the reasonable range of fractional order is between β = 0.6 and β = 0.9. The equilibrium points and stability analysis are presented. Moreover, positivity and boundedness of the solution are proved. Furthermore, a graphical representation of cancerous cells, immunotherapy and chemotherapy is presented to understand the behaviour of cancer treatment.

CONCLUSIONS

At the end, a curve fitting procedure is presented which may help medical practitioners to treat cancer patients.

On the Analysis of Regularized Fuzzy Systems of Uncertain Differential Equations

This article analyzes a regularized set of fuzzy differential equations with respect to an uncertain parameter. We provide sufficient conditions for the correctness of a new regularization scheme. For the resulting family of regularized fuzzy differential equations, the following properties are analyzed, and efficient criteria are proposed: successive approximations, continuity, global existence of solutions, existence of approximate solutions, existence of solutions in the autonomous case. In addition, we develop stability criteria for the regularized family of fuzzy differential equations on the basis of the comparison technique and the method of nonlinear integral inequalities. We expect that the derived results will inspire future research work in this direction.

Theoretical Upper and Lower Limits for Normalized Bandwidth of Digital Phase-Locked Loop in GNSS Receivers

Determining the loop noise bandwidth and the coherent integration time is essential and important for the design of a reliable digital phase-locked loop (DPLL) in global navigation satellite system (GNSS) receivers. In general, designers set such parameters approximately by utilizing the well-known fact that the DPLL is stable if the normalized bandwidth, which is the product of the integration time and the noise bandwidth, is much less than one. However, actual limit points are not fixed at exactly one, and they vary with the loop filter order and implementation method. Furthermore, a lower limit on the normalized bandwidth may exist. This paper presents theoretical upper and lower limits for the normalized bandwidth of DPLL in GNSS receivers. The upper limit was obtained by examining the stability of DPLL with a special emphasis on the digital integration methods. The stability was investigated in terms of z-plane root loci with and without the consideration of the computational delay, which is a delay induced by the calculation of the discriminator and the loop filter. The lower limit was analyzed using the DPLL measurement error composed of the thermal noise, oscillator phase noise, and dynamic stress error. By utilizing the carrier-to-noise density ratio threshold which indicates the crossing point between the measurement error and the corresponding threshold, the lower limit of the normalized bandwidth is obtained.

Selection of High-Yielding and Stable Genotypes of Barley for the Cold Climate in Iran

The interaction between genotypes and environments plays an important role in selecting superior genotypes for target locations. The main objectives of the present study were to analyze the effect of the genotype-by-environment interaction (GEI) and identify superior, newly developed, and promising barley genotypes for cold regions in Iran. For these purposes, a set of genotypes obtained from breeding programs for cold climates in Iran, along with two reference genotypes, were investigated at eight research stations (Tabriz, Ardabil, Arak, Miandoab, Mashhad, Jolge Rokh, Karaj, and Hamadan) during two consecutive growing seasons (2019-2020 and 2020-2021). The results of the freezing test (LT₅₀) showed that most of the tested genotypes had significant cold tolerance at the seedling stage. Based on the additive main effect and multiplicative interaction (AMMI) analysis, environment (E) and GEI effects explained 49.44% and 16.55% of the total variation in grain yield, respectively. Using AMMI1 and AMMI2 models, G2 and G20 were found to be superior genotypes in terms of grain yield and stability. Moreover, AMMI-based stability parameters considered the G20 genotype to be the ideal genotype. A two-plot analysis of the genotype-by-environment interaction (GGE) biplot showed that the 16 experimental environments were grouped into 2 mega-environments. Of the test environments, ARK1 and KAJ2 had the highest discriminating power and representativeness ability, and these were identified as ideal environments for testing advanced genotypes for yield and stability performance during early barley breeding practices in cold areas in Iran. In conclusion, both AMMI and GGE biplot models identified several superior genotypes, among which G20, with a high average yield relative to the overall average yield and the lowest IPC1 score, was found to have high yield stability and is recommended for inclusion in breeding programs for cold climates in Iran.

Machine Learning Assisted Stability Analysis of Blue Quantum Dot Light-Emitting Diodes

The operational stability of the blue quantum dot light-emitting diode (QLED) has been one of the most important obstacles to initialize its industrialization. In this work, we demonstrate a machine learning assisted methodology to illustrate the operational stability of blue QLEDs by analyzing the measurements of over 200 samples (824 QLED devices) including current density-voltage-luminance (J-V-L), impedance spectra (IS), and operational lifetime (T95@1000 cd/m²). The methodology is able to predict the operational lifetime of the QLED with a Pearson correlation coefficient of 0.70 with a convolutional neural network (CNN) model. By applying a classification decision tree analysis of 26 extracted features of J-V-L and IS curves, we illustrate the key features in determining the operational stability. Furthermore, we simulated the device operation using an equivalent circuit model to discuss the device degradation related operational mechanisms.

Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper: part 2

In 1923, the Philosophical Transactions published G. I. Taylor's seminal paper on the stability of what we now call Taylor-Couette flow. In the century since the paper was published, Taylor's ground-breaking linear stability analysis of fluid flow between two rotating cylinders has had an enormous impact on the field of fluid mechanics. The paper's influence has extended to general rotating flows, geophysical flows and astrophysical flows, not to mention its significance in firmly establishing several foundational concepts in fluid mechanics that are now broadly accepted. This two-part issue includes review articles and research articles spanning a broad range of contemporary research areas, all rooted in Taylor's landmark paper. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (Part 2)'.

Mixed Convection Hybrid Nanofluid Flow Induced by an Inclined Cylinder with Lorentz Forces

Hybrid nanofluids may exhibit higher thermal conductivity, chemical stability, mechanical resistance and physical strength compared to regular nanofluids. Our aim in this study is to investigate the flow of a water-based alumina-copper hybrid nanofluid in an inclined cylinder with the impact of buoyancy force and a magnetic field. The governing partial differential equations (PDEs) are transformed into a set of similarity ordinary differential equations (ODEs) using a dimensionless set of variables, and then solved numerically using the bvp4c package from MATLAB software. Two solutions exist for both buoyancy opposing (λ < 0) and assisting (λ > 0) flows, whereas a unique solution is found when the buoyancy force is absent (λ = 0). In addition, the impacts of the dimensionless parameters, such as curvature parameter, volume fraction of nanoparticles, inclination angle, mixed convention parameter, and magnetic parameter are analyzed. The results of this study compare well with previously published results. Compared to pure base fluid and regular nanofluid, hybrid nanofluid reduces drag and transfers heat more efficiently.

Preparation, Multispectroscopic Characterization, and Stability Analysis of Monascus Red Pigments-Whey Protein Isolate Complex

Monascus red pigments (MRPs) are mainly used as natural food colorants; however, their application is limited due to their poor stability. To expand their areas of application, we investigated the binding constants and capacity of MRPs to whey protein isolate (WPI) and whey protein hydrolysate (WPH) and calculated the surface hydrophobicities of WPI and WPH. MRPs were combined with WPI and WPH at a hydrolysis degree (DH) of 0.5% to form the complexes (DH = 0.0%) and (DH = 0.5%), respectively. Subsequently, the structural characteristics of complex (DH = 0.5%) and WPI were characterized and the color retention rates of both complexes and MRPs were investigated under different pretreatment conditions. The results showed that the maximum binding constant of WPI with MRPs was 0.670 ± 0.06 U^-1 and the maximum binding capacity was 180 U/g. Furthermore, the thermal degradation of complex (DH = 0.0%), complex (DH = 0.5%), and MRPs in a water bath at 50-100 °C followed a first-order kinetic model. Thus, the interaction of WPI with MRPs could alter the protein conformation of WPI and effectively protect the stability of MRPs.

Optimization of CMT Characteristic Parameters for Swing Arc Additive Manufacturing of AZ91 Magnesium Alloy Based on Process Stability Analysis

The droplet transfer behavior and stability of the swing arc additive manufacturing process of AZ91 magnesium alloy based on the cold metal transfer (CMT) technique were studied by analyzing the electrical waveforms and high-speed droplet images as well as the forces on the droplet, and the Vilarinho regularity index for short-circuit transfer (IV_SC) based on variation coefficients was used to characterize the stability of the swing arc deposition process. The effect of the CMT characteristic parameters on the process stability was investigated; then, the optimization of the CMT characteristic parameters was realized based on the process stability analysis. The results show that the arc shape changed during the swing arc deposition process; thus, a horizontal component of the arc force was generated, which significantly affected the stability of the droplet transition. The burn phase current I_sc_wait presented a linear function relation with IV_SC, while the other three characteristic parameters, i.e., boost phase current I_boost, boost phase duration t_I_boost and short-circuiting current I_sc2, all had a quadratic correlation with IV_SC. A relation model of the CMT characteristic parameters and IV_SC was established based on the rotatable 3D central composite design; then, the optimization of the CMT characteristic parameters was realized using a multiple-response desirability function approach.

Estimating Shelf Life Through Tolerance Intervals Extended to Nonlinear Response Trends

Methods for estimating pharmaceutical shelf life based on tolerance intervals are proposed by Schwenke, et al. AAPS PharmSciTech. 2020;21:290, [1] where a critical quality attribute that follows a simple linear (straight line) response trend across storage time is presented as the traditional example. A random coefficient mixed linear regression model is used to characterize the between batch and within batch variation. These methods are further discussed for various stability study scenarios, number of stability batches, and levels of assumed risk in Schwenke, et al. AAPS PharmSciTech. 2021;22:273, [4] through a simulation study, again based on a critical quality attribute assuming a simple linear response. However, in practice, not all stability response profiles conveniently follow straight line or linear trends. The purpose of this paper is to extend the proposed tolerance interval and random coefficient mixed regression methods for estimating pharmaceutical shelf life to critical quality attributes that follow more complex stability response profiles. As an example, a nonlinear response is typically characterized by either an increasing or decreasing response, starting from an initial concentration, trending with storage time towards some limiting response or asymptote. Nonlinear responses cannot be statistically analyzed with linear model methods. Practical information supported by simulation results based on a pharmaceutical stability study are discussed to allow for appropriate statistical analyses and shelf life estimates through random coefficient mixed nonlinear regression and tolerance interval methods.

Clean Energy Based Multigeneration System for Sustainable Cities: Thermodynamic, and Stability Analyses

This paper concerns the development and analysis of multigeneration systems based on hybrid sources such as biomass and wind. Industry requires different types of sources to provide several outputs, so the goal of this research was to fulfill the industrial requirement with optimization. The multigeneration cycle supplies enough power to satiate energy demands, i.e., power, cooling, hydrogen, air conditioning, freshwater, hot water, and heating. For this, the multigeneration cycle was modeled in the Engineering Equation Solver (EES) and Simulink to obtain optimized results for the industry. Energy and exergy for the multigeneration cycle were determined to assess the performance of the cycle and to investigate the optimized results for the overall system. This study shows that for configuration selection and design, different thermodynamic, economic, and environmental aspects should be considered. Based on the results, the selection of the best location for this multigeneration system was made. Power output from the wind turbine was around 7 MW and from biogas 0.6 MW. The overall exergy efficiency of the multigeneration system was found to be 0.1401.

Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper: part 1

In 1923, the Philosophical Transactions published G. I. Taylor's seminal paper on the stability of what we now call Taylor-Couette flow. In the century since the paper was published, Taylor's ground-breaking linear stability analysis of fluid flow between two rotating cylinders has had an enormous impact on the field of fluid mechanics. The paper's influence has extended to general rotating flows, geophysical flows and astrophysical flows, not to mention its significance in firmly establishing several foundational concepts in fluid mechanics that are now broadly accepted. This two-part issue includes review articles and research articles spanning a broad range of contemporary research areas, all rooted in Taylor's landmark paper. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 1)'.

Non-Unique Solutions of Magnetohydrodynamic Stagnation Flow of a Nanofluid towards a Shrinking Sheet Using the Solar Radiation Effect

This study aims to investigate the magnetohydrodynamic flow induced by a moving surface in a nanofluid and the occurrence of suction and solar radiation effects using the Buongiorno model. The numerical findings are obtained using MATLAB software. The effects of various governing parameters on the rates of heat and mass transfer along with the nanoparticles concentration and temperature profiles are elucidated graphically. Non-unique solutions are discovered for a specific variation of the shrinking strength. The temporal stability analysis shows that only one of them is stable as time passes. Furthermore, raising the Brownian motion parameter reduces both the local Sherwood number and the local Nusselt number for both solutions. It is also observed that increasing the thermophoresis parameter reduces the rate of heat transfer, whereas the opposite trend is observed for the rate of mass transfer.

AMMI and GGE biplot analyses of Bambara groundnut [Vigna subterranea (L.) Verdc.] for agronomic performances under three environmental conditions

INTRODUCTION

The two most common styles to analyze genotype-by-environment interaction (GEI) and estimate genotypes are additive main effects and multiplicative interaction (AMMI) and genotype + genotype × environment (GGE) biplot. Therefore, the aim of this study was to find the winning genotype(s) under three locations, as well as to investigate the nature and extent of GEI effects on Bambara groundnut production.

METHODS

The experiment was carried out in the fields of three environments with 15 Bambara groundnut accessions using the randomized complete block design (RCBD) with three replications each in Ibadan, Osun, and Odeda. Yield per plant, fresh seed weight, total number of pods per plant, hundred seed weight, length of seeds, and width of seeds were estimated.

RESULTS

According to the combined analysis of variance over environments, genotypes and GEI both had a significant (p < 0.001) impact on Bambara groundnut (BGN) yield. This result revealed that BGN accessions performed differently in the three locations. A two-dimensional GGE biplot was generated using the first two principal component analyses for the pattern of the interaction components with the genotype and GEI. The first two principal component analyses (PCAs) for yield per plant accounted for 59.9% in PCA1 and 40.1% in PCA2. The genotypes that performed best in each environment based on the "which-won-where" polygon were G8, G3, G2, G11, G6, and G4. They were also the vertex genotypes for each environment. Based on the ranking of genotypes, the ideal genotypes were G2 and G6 for YPP, G1 and G5 for FPW, G15 and G13 for TNPP, G3 and GG7 for HSW, G7 and G12 for LOS, and G10 and G7 for WOS. G8 was recorded as the top most-yielding genotype. G8, G4, G7, and G13 were high yielding and the most stable across the environments; G11, G14, and G9 were unstable, but they yielded above-average performance; G14, G12, G15, and G1 were unstable and yielded poorly, as their performances were below average. Bowen was the most discriminating and representative environment and is classified as the superior environment.

DISCUSSION

Based on the performance of accessions in each region, we recommend TVSU 455 (G8) and TVSU 458 (G3) in Bowen, TVSU 455 (G8) and TVSU 939 (G6) and TVSU 454 (G1) in Ibadan, and TVSU 158 (G2) and TVSU 2096 (G10) in Odeda. The variety that performed best in the three environments was TVSU 455 (G8). They could also be used as parental lines in breeding programs.

Role of Vaccines in Controlling the Spread of COVID-19: A Fractional-Order Model

In this paper, we present a fractional-order mathematical model in the Caputo sense to investigate the significance of vaccines in controlling COVID-19. The Banach contraction mapping principle is used to prove the existence and uniqueness of the solution. Based on the magnitude of the basic reproduction number, we show that the model consists of two equilibrium solutions that are stable. The disease-free and endemic equilibrium points are locally stably when R0<1 and R0>1 respectively. We perform numerical simulations, with the significance of the vaccine clearly shown. The changes that occur due to the variation of the fractional order α are also shown. The model has been validated by fitting it to four months of real COVID-19 infection data in Thailand. Predictions for a longer period are provided by the model, which provides a good fit for the data.

Comprehensive Study of a Diabetes Mellitus Mathematical Model Using Numerical Methods with Stability and Parametric Analysis

Diabetes is sweeping the world as a silent epidemic, posing a growing threat to public health. Modeling diabetes is an effective method to monitor the increasing prevalence of diabetes and develop cost-effective strategies that control the incidence of diabetes and its complications. This paper focuses on a mathematical model known as the diabetes complication (DC) model. The DC model is analyzed using different numerical methods to monitor the diabetic population over time. This is by analyzing the model using five different numerical methods. Furthermore, the effect of the time step size and the various parameters affecting the diabetic situation is examined. The DC model is dependent on some parameters whose values play a vital role in the convergence of the model. Thus, parametric analysis was implemented and later discussed in this paper. Essentially, the Runge-Kutta (RK) method provides the highest accuracy. Moreover, Adam-Moulton's method also provides good results. Ultimately, a comprehensive understanding of the development of diabetes complications after diagnosis is provided in this paper. The results can be used to understand how to improve the overall public health of a country, as governments ought to develop effective strategic initiatives for the screening and treatment of diabetes.

COVID-19 Model with High- and Low-Risk Susceptible Population Incorporating the Effect of Vaccines

It is a known fact that there are a particular set of people who are at higher risk of getting COVID-19 infection. Typically, these high-risk individuals are recommended to take more preventive measures. The use of non-pharmaceutical interventions (NPIs) and the vaccine are playing a major role in the dynamics of the transmission of COVID-19. We propose a COVID-19 model with high-risk and low-risk susceptible individuals and their respective intervention strategies. We find two equilibrium solutions and we investigate the basic reproduction number. We also carry out the stability analysis of the equilibria. Further, this model is extended by considering the vaccination of some non-vaccinated individuals in the high-risk population. Sensitivity analyses and numerical simulations are carried out. From the results, we are able to obtain disease-free and endemic equilibrium solutions by solving the system of equations in the model and show their global stabilities using the Lyapunov function technique. The results obtained from the sensitivity analysis shows that reducing the hospitals' imperfect efficacy can have a positive impact on the control of COVID-19. Finally, simulations of the extended model demonstrate that vaccination could adequately control or eliminate COVID-19.

Effects of Concentration of Soybean Protein Isolate and Maltose and Oil Phase Volume Fraction on Freeze-Thaw Stability of Pickering Emulsion

There is growing interest in enhancing the freeze-thaw stability of a Pickering emulsion to obtain a better taste in the frozen food field. A Pickering emulsion was prepared using a two-step homogenization method with soybean protein and maltose as raw materials. The outcomes showed that the freeze-thaw stability of the Pickering emulsion increased when prepared with an increase in soybean protein isolate (SPI) and maltose concentration. After three freeze-thaw treatments at 35 mg/mL, the Turbiscan Stability Index (TSI) value of the emulsion was the lowest. At this concentration, the surface hydrophobicity (H₀) of the composite particles was 33.6 and the interfacial tension was 44.34 mN/m. Furthermore, the rheological nature of the emulsions proved that the apparent viscosity and viscoelasticity of Pickering emulsions grew with a growing oil phase volume fraction and concentration. The maximum value was reached in the case of the oil phase volume fraction of 50% at a concentration of 35 mg/mL, the apparent viscosity was 18 Pa·s, the storage modulus of the emulsion was 575 Pa, and the loss modulus was 152 Pa. This research is significant for the production of freeze-thaw resistant products, and improvement of protein-stabilized emulsion products with high freeze-thaw stability.

Mathematical model and stability analysis on the transmission dynamics of skin sores

In this study, a non-linear deterministic model for the transmission dynamics of skin sores (impetigo) disease is developed and analysed by the help of stability of differential equations. Some basic properties of the model including existence and positivity as well as boundedness of the solutions of the model are investigated. The disease-free and endemic equilibrium were investigated, as well as the basic reproduction number, R₀, also calculated using the next-generation matrix approach. When R₀ < 1, the model's stability analysis reveals that the system is asymptotically stable at disease-free critical point globally as well as locally. If R₀ > 1, the system is asymptotically stable at disease-endemic equilibrium both locally and globally. The long-term behaviour of the skin sores model's steady-state solution in a population is investigated using numerical simulations of the model.

MODELLING OF PATHOGENS IMPACT ON THE HUMAN DISEASE TRANSMISSION WITH OPTIMAL CONTROL STRATEGIES

This study concentrates on a nonlinear deterministic mathematical model for the impact of pathogens on human disease transmission with optimal control strategies. Both pathogen-free and coexistence equilibria are computed. The basic reproduction number R₀, which plays a vital role in mathematical epidemiology, was derived. The qualitative analysis of the model revealed the scenario for both pathogen-free and coexistence equilibria together with R₀. The local stability of the equilibria is established via the Jacobian matrix and Routh-Hurwitz criteria, while the global stability of the equilibria is proven by using an appropriate Lyapunov function. Also, the normalized sensitivity analysis has been performed to observe the impact of different parameters on R₀. The proposed model is extended into optimal control problem by incorporating three control variables, namely, preventive measure variable based on separation of susceptible from contacting the pathogens, integrated vector management based on chemical, biological control, ... etc. to kill pathogens and their carriers, and supporting infective medication variable based on the care of the infected individual in quarantine center. Optimal disease control analysis is examined using Pontryagin minimum principle. Numerical simulations are performed depending on analytical results and discussed quantitatively.

Some novel mathematical analysis on the fractional-order 2019-nCoV dynamical model

Since December 2019, the whole world has been facing the big challenge of Covid-19 or 2019-nCoV. Some nations have controlled or are controlling the spread of this virus strongly, but some countries are in big trouble because of their poor control strategies. Nowadays, mathematical models are very effective tools to simulate outbreaks of this virus. In this research, we analyze a fractional-order model of Covid-19 in terms of the Caputo fractional derivative. First, we generalize an integer-order model to a fractional sense, and then, we check the stability of equilibrium points. To check the dynamics of Covid-19, we plot several graphs on the time scale of daily and monthly cases. The main goal of this content is to show the effectiveness of fractional-order models as compared to integer-order dynamics.

Stability Analysis of Two Power Converters Control Algorithms Connected to Micro-Grids with Wide Frequency Variation

Distributed power generation, micro-grids, and networks working in islanding mode have strong deviations in voltage quantities. These deviations can be divided into amplitude and frequency. Amplitude deviations are well-known and studied, as they are common in small and big grids. However, deviations on the ac mains frequency have not been widely studied. The literature shows control schemes capable of bearing these variations, but no systematic analysis has been performed to ensure stability. As the majority of power converters are designed for big grids, their analysis and design neglect frequency disturbances, therefore those devices allow a very small frequency operating window. For instance, in power converters that need to be synchronized to the grid, the standard deviation does not go beyond 0.5 Hz, and for grid-tied inverters it does not go beyond 1 Hz, whereas variations of around 8 Hz can be expected in micro-grids. This work presents a comprehensive analysis of the control system's stability, where two different control schemes for a back-to-back static converter topology are implemented and studied under a wide variable grid frequency. Because the behavior of power converters is nonlinear and coupled, dynamic and static decouplers are usually introduced in the controller, being a key element on the scheme according to the findings. The results show that using just a static decoupler does not guarantee stability under frequency variations; meanwhile, when a dynamic decoupler is used, the operating window can be greatly extended. The procedure shown in this paper can also be extended to other control algorithms, making it possible to carefully choose the control system for a variable frequency condition. Simulated and experimental results confirm the theoretical approach.

Modeling the transmission of second-wave COVID-19 caused by imported cases: A case study

As the first-wave COVID-19 has passed in 2020, people's awareness of self-protection began to decline gradually. How to prevent and control the second-wave COVID-19 has become an important issue in many countries and regions. By analyzing the transmission of the second-wave COVID-19 caused by an imported case in Tonghua City, Jilin Province, China, in January 2021, we establish a new mathematical COVID-19 model to simulate the transmission characteristics of the second-wave COVID-19. First, we analyze the basic properties of the model, prove the existence of the equilibrium point, and obtain the expression of the basic reproduction number with important biological significance. Secondly, we use the weighted nonlinear least square estimation method to fit the cases in Tonghua City of Jilin Province in January 2021, and get the estimated value of the parameters. The basic reproduction number of the second-wave COVID-19 in Tonghua City is R 0 = 1 . 0695 , which is much smaller than that of the first-wave COVID-19 in Wuhan in 2020. Finally, in the optimal control part, we consider two control methods (keeping social distance and nucleic acid detection of all people in the city) to simulate the control of the disease. The results show that the control intensity of the two control methods needs to be dynamically changed and adjusted, so that the cost can be minimized with the least infection. The results of this paper can not only provide suggestions for health management departments, but also provide a reference for the analysis of the second-wave COVID-19 in other countries or regions.

Mathematical model for the novel coronavirus (2019-nCOV) with clinical data using fractional operator

Coronavirus infection (COVID-19) is a considerably dangerous disease with a high demise rate around the world. There is no known vaccination or medicine until our time because the unknown aspects of the virus are more significant than our theoretical and experimental knowledge. One of the most effective strategies for comprehending and controlling the spread of this epidemic is to model it using a powerful mathematical model. However, mathematical modeling with a fractional operator can provide explanations for the disease's possibility and severity. Accordingly, basic information will be provided to identify the kind of measure and intrusion that will be required to control the disease's progress. In this study, we propose using a fractional-order SEIARPQ model with the Caputo sense to model the coronavirus (COVID-19) pandemic, which has never been done before in the literature. The stability analysis, existence, uniqueness theorems, and numerical solutions of such a model are displayed. All results were numerically simulated using MATLAB programming. The current study supports the applicability and influence of fractional operators on real-world problems.

Field phenotyping and quality traits of grass pea genotypes in South Italy

BACKGROUND

Grass pea (Laithyrus sativus L.) is a rustic plant whose seeds are rich in polyphenols and antioxidants, and it has been consumed as food by human beings since ancient times. This study was conducted in Italy between 2017and 2019 to evaluate, under field conditions, the stability of seed yield, biomass and 1000-seed weight (THS) and to assess the antioxidant composition and activity of 11 grass pea accessions.

RESULTS

Analysis of variance revealed significant effects of the environment, accession and accession × environment (A × E) on the yield, above-ground biomass and THS. We found that the environment (year) and A × E explained 52.61% and 23.76% of the total seed yield variation, respectively. No relationship was observed between the yield and the total protein of seeds. Most grass pea accessions showed sensitivity to frost conditions that occurred in the third growing season. The total phenolic content ranged from 50.51 to 112.78 mg 100 g-1 seeds and antioxidant activity ranged from 0.576 to 0.898 mmol Trolox equivalents 100 g-1 seeds and from 0.91 to 1.6 mmol Fe2+  100 g-1 seeds in 2,20-azinobis-3-ethylbenzothiazoline-6-sulfonic acid and ferric-reducing antioxidant power, respectively. Among the accessions, the 'Campi Flegrei' and 'di Castelcività' showed the best performance with the highest yield and stability, phenolic content and superior antioxidant activity.

CONCLUSION

The results showed that the yield of grass pea was mainly influenced by different climate conditions. This variability in yield, phenolic content and antioxidant activity among different accessions could help breeders and farmers select high-performance accessions for cultivation. © 2020 Society of Chemical Industry.

Research on Soft Rock Damage Softening Model and Roadway Deformation and Failure Characteristics

To determine a reasonable control strategy for deep buried soft rock roadways, a study on deformation and failure characteristics was carried out. The Weibull distribution damage variable was introduced to construct a damage-softening model considering the lateral deformation of the rock mass, and the functional relationship between the model parameters F₀ and m and the confining pressure were discussed. The nonlinear fitting method was used to correct the model parameters. Using the model, the failure characteristics of deep buried soft rock roadways were analyzed. A comprehensive and step-by-step joint support control strategy was proposed based on the numerical simulation results. The research results showed that the damage-softening model curve established could genuinely reflect the whole process of mudstone failure. The apparent stress concentration phenomenon occurred in the surrounding rock. The surrounding rock deformation showed that roadway floors had larger plastic failure areas than sides and vaults. The plastic failure depth could reach 2.45 m. After a comprehensive and step-by-step joint support control strategy was adopted, the deformation rate of the roadway at the section was less than 0.1 mm/d. The optimized support scheme can effectively improve the stability of the roadway.

Vibration Analysis of a 1-DOF System Coupled with a Nonlinear Energy Sink with a Fractional Order Inerter

The fluid inerter described by the fractional derivative model is introduced into the traditional nonlinear energy sink (NES), which is called fractional-order NES in this paper. The slowly varying dynamic equation (SVDE) of the system coupled with fractional-order NES is obtained by the complex averaging method, in which the fractional derivative term is treated using the fractional Leibniz theorem. Then, the discriminants (Δ, Δ₁, and Δ₂) of the number of equilibrium points are derived. By using the variable substitution method, the characteristic equation for judging the stability is established. The results show: (1) the approximate SVDE is sufficient to reflect the slowly varying characteristics of the system, which shows that the mathematical treatment of the fractional derivative term is reliable; (2) the discriminant conditions (Δ₁, Δ₂) can accurately reflect the number of equilibrium points, and the corresponding range of nonlinear parameter κ can be calculated when the system has three equilibrium points. The expressions of Δ₁, Δ₂ are simpler than Δ, which is suitable for analysis and design parameters; (3) the stability discrimination methods of schemes 1 and 2 are accurate. Compared with scheme 2, scheme 1 is more prone to various responses, especially various strongly and weakly modulated responses. In scheme 2, the inertia effect of mass can be completely replaced by integer order inerter. Compared with integer order inerter, the introduction of fractional order inerter, whether in series or in parallel, means that the amplitude of the equilibrium point on the NES vibrator is smaller, but it is also for this reason that it is not easy to produce a modulated response with scheme 2, and the vibration suppression effect of the main structure is not good.

Positive input observer-based controller design for blood glucose regulation for type 1 diabetic patients: A backstepping approach

In practice, there are many physical systems that can have only positive inputs, such as physiological systems. Most conventional control methods cannot ensure that the main system input is positive. A positive input observer-based controller is designed for an intravenous glucose tolerance test model of type 1 diabetes mellitus (T1DM). The backstepping (BS) approach is employed to design the feedback controller for artificial pancreas (AP) systems, based on the Extended Bergman's Minimal Model (EBMM). The EBMM represents the T1DM in terms of the blood glucose concentration (BGC), insulin concentration, and plasma level and the disturbance of insulin during medication due to either meal intake or burning sugar by doing some physical exercise. The insulin concentration and plasma level are estimated using observers, and these estimations are applied as feedback to the controller. The asymptotic stability of the observer-based controller is proved using the Lyapunov theorem. Moreover, it is proved that the system is bounded input-bounded output (BIBO) stable in the presence of uncertainties generated by uncertain parameters and external disturbance. For realistic situations, we consider only the BGC to be available for measurement and additionally inter-and intra-patient variability of system parameters is considered.

A robust study of a piecewise fractional order COVID-19 mathematical model

In the current manuscript, we deal with the dynamics of a piecewise covid-19 mathematical model with quarantine class and vaccination using SEIQR epidemic model. For this, we discussed the deterministic, stochastic, and fractional forms of the proposed model for different steps. It has a great impact on the infectious disease models and especially for covid-19 because in start the deterministic model played its role but with time due to uncertainty the stochastic model takes place and with long term expansion the use of fractional derivatives are required. The stability of the model is discussed regarding the reproductive number. Using the non-standard finite difference scheme for the numerical solution of the deterministic model and illustrate the obtained results graphically. Further, environmental noises are added to the model for the description of the stochastic model. Then take out the existence and uniqueness of positive solution with extinction for infection. Finally, we utilize a new technique of piecewise differential and integral operators for approximating Caputo-Fabrizio fractional derivative operator for the purpose of constructing of the fractional-order model. Then study the dynamics of the models such as positivity and boundedness of the solutions and local stability analysis. Solved numerically fractional-order model used Newton Polynomial scheme and present the results graphically.

Modeling and analysis on the transmission of covid-19 Pandemic in Ethiopia

The newest infection is a novel coronavirus named COVID-19, that initially appeared in December 2019, in Wuhan, China, and is still challenging to control. The main focus of this paper is to investigate a novel fractional-order mathematical model that explains the behavior of COVID-19 in Ethiopia. Within the proposed model, the entire population is divided into nine groups, each with its own set of parameters and initial values. A nonlinear system of fractional differential equations for the model is represented using Caputo fractional derivative. Legendre spectral collocation method is used to convert this system into an algebraic system of equations. An inexact Newton iterative method is used to solve the model system. The effective reproduction number (R0) is computed by the next-generation matrix approach. Positivity and boundedness, as well as the existence and uniqueness of solution, are all investigated. Both endemic and disease-free equilibrium points, as well as their stability, are carefully studied. We calculated the parameters and starting conditions (ICs) provided for our model using data from the Ethiopian Public Health Institute (EPHI) and the Ethiopian Ministry of Health from 22 June 2020 to 28 February 2021. The model parameters are determined using least squares curve fitting and MATLAB R2020a is used to run numerical results. The basic reproduction number is R0=1.4575. For this value, disease free equilibrium point is asymptotically unstable and endemic equilibrium point is asymptotically stable, both locally and globally.

A new comparative study on the general fractional model of COVID-19 with isolation and quarantine effects

A generalized version of fractional models is introduced for the COVID-19 pandemic, including the effects of isolation and quarantine. First, the general structure of fractional derivatives and integrals is discussed; then the generalized fractional model is defined from which the stability results are derived. Meanwhile, a set of real clinical observations from China is considered to determine the parameters and compute the basic reproduction number, i.e., R0≈6.6361. Additionally, an efficient numerical technique is applied to simulate the new model and provide the associated numerical results. Based on these simulations, some figures and tables are presented, and the data of reported cases from China are compared with the numerical findings in both classical and fractional frameworks. Our comparative study indicates that a particular case of general fractional formula provides a better fit to the real data compared to the other classical and fractional models. There are also some other key parameters to be examined that show the health of society when they come to eliminate the disease.

Delay differential equations for the spatially resolved simulation of epidemics with specific application to COVID-19

In the wake of the 2020 COVID-19 epidemic, much work has been performed on the development of mathematical models for the simulation of the epidemic and of disease models generally. Most works follow the susceptible-infected-removed (SIR) compartmental framework, modeling the epidemic with a system of ordinary differential equations. Alternative formulations using a partial differential equation (PDE) to incorporate both spatial and temporal resolution have also been introduced, with their numerical results showing potentially powerful descriptive and predictive capacity. In the present work, we introduce a new variation to such models by using delay differential equations (DDEs). The dynamics of many infectious diseases, including COVID-19, exhibit delays due to incubation periods and related phenomena. Accordingly, DDE models allow for a natural representation of the problem dynamics, in addition to offering advantages in terms of computational time and modeling, as they eliminate the need for additional, difficult-to-estimate, compartments (such as exposed individuals) to incorporate time delays. In the present work, we introduce a DDE epidemic model in both an ordinary and partial differential equation framework. We present a series of mathematical results assessing the stability of the formulation. We then perform several numerical experiments, validating both the mathematical results and establishing model's ability to reproduce measured data on realistic problems.