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This study deals with the Lonngren wave equation, which is used to model the transmission of electrical signals in a type of semiconductor material called a tunnel diode. The aim of this study is to produce dark soliton, singular soliton, trigonometric, complex rational solutions to the Lonngren wave equation by using the sub-equation method. Graphs representing the Lonngren wave are drawn by giving different values to the variables in the solutions obtained. Graphs are presented using a special package program. In the light of the data obtained as a result of the study, it is thought that this new method used in the research of the solution of the Lonngren wave equation will contribute to the literature. [ABSTRACT FROM AUTHOR]

Background and Purpose: The classical theory of receptor action has been used for decades as a powerful tool to estimate molecular determinants of ligand‐induced receptor activation (i.e., affinity and efficacy) from experimentally observable biological responses. However, it is also a well‐recognized fact that the receptor‐binding and activation mechanisms, and the parameters thereof, described in the classical theory contradict with the modern view of receptor activation based on allosteric principles. Experimental Approach: We used mathematical analysis, along with some numerical simulations, to answer the key question as to what extent the classical theory is compatible—if at all—with the modern understanding of receptor activation. Key Results: Here, we showed conclusively that (1) receptor activation equations based on allosteric principles contain the logic of the classical theory in disguise, and therefore, (2) estimates of "intrinsic efficacy" (ε) obtained by means of classical techniques (i.e., null methods or fitting the operational model to concentration‐response data) are equivalent to the allosteric coupling factors that represent the molecular efficacy of ligands. Conclusion and Implications: Thus, we conclude that despite the justified criticisms it has received so far, the classical theory may continue to be useful in estimating ligand efficacy from experimental data, if used properly. Here, we also provide rigorous criteria for the proper use of the theory. These findings not only have implications for ligand classification but also resolve some long lasting discussions in the field of bias agonism in GPCR, which requires reasonable estimates of relative ligand efficacies at different signalling pathways. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the asymptotic behavior of a modified chemostat model. We first demonstrate the existence of equilibria. Then, we present a mathematical analysis for the model, the invariance, the positivity, the persistence of the solutions, and the asymptotic global stability of the interior equilibrium. Some numerical simulations are carried out to illustrate the main results. [ABSTRACT FROM AUTHOR]

Summary: Increasing the voltage gain of traditional boost converter topologies necessitates an unsustainable increase in the operating duty ratio. Because of their inherent architecture, these topologies are incapable of shielding their individual components from the detrimental effects of extreme duty cycle operation, resulting in increased power loss and inefficient performance. With the objective of attaining a higher voltage gain at a lower duty cycle, this research presents a new quadratic type boost converter derived from an improved voltage‐lift (IVL) cell and the conventional boost converter (CBC). By including an IVL cell in CBC, the voltage conversion ratio is quadratic in nature, and the steady‐state performances are improved over those of CBC. This proposed architecture includes a few new parts, such as capacitors, diodes, and an inductor but no controllable switches, thus the close loop control stays the same. During the entire range of the duty cycle, the proposed boost topology outperforms the conventional quadratic boost converter (CQBC) in terms of dc voltage gain. In addition, the voltage stresses on devices (such as switch and diodes) and intermediate capacitors are reduced compared with CQBC. In steady‐state conditions, the voltage gain and design expressions of the storage elements are determined using time‐domain analysis. The suggested extended quadratic gain boost converter (EQGBC) stands out because of its multiple benefits over existing step‐up converter topologies. The suggested EQGBC has been tested by simulation and hardware implementation to ensure its key performance features. A laboratory‐scaled prototype is developed, which has the capability of boosting the low input voltage of 12 V to a higher value of 48 V at a switching frequency of 100 kHz. The experimental outputs are in close accord with the simulation findings and mathematical analysis. [ABSTRACT FROM AUTHOR]

Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections, and mappings. Projective geometry identifies a line with a single point, like the perspective on the horizon line and, due to this fact, it requires a restructuring of the real mathematical and numerical analysis. In particular, the problem of interpolating data must be refocused. In this paper, we define a linear structure along with a metric on a projective space, and prove that the space thus constructed is complete. Then, we consider an iterated function system giving rise to a fractal interpolation function of a set of data. [ABSTRACT FROM AUTHOR]

We investigate the structure of rank-to-rank elementary embeddings at successor rank, working in ZF set theory without the Axiom of Choice. Recall that the set-theoretic universe is naturally stratified by the cumulative hierarchy, whose levels V α are defined via iterated application of the power set operation, starting from V 0 =∅, setting V α+1 =P(V α), and taking unions at limit stages. Assuming that j:V α+1 →V α+1 is a (non-trivial) elementary embedding, we show that V α is fundamentally different from V α+1: we show that j is definable from parameters over V α+1 iff α+1 is an odd ordinal. The definability is uniform in odd α+1 and j. We also give a characterization of elementary j:Vα+2 → Vα+2 in terms of ultrapower maps via certain ultrafilters. For limit ordinals λ, we prove that if j:Vλ→Vλ is Σ1-elementary, then j is not definable over Vλ from parameters, and if β < λ and j:Vβ → Vλ is fully elementary and ∈-cofinal, then j is likewise not definable. If there is a Reinhardt cardinal, then for all sufficiently large ordinals α, there is indeed an elementary j: Vα → Vα, and therefore the cumulative hierarchy is eventually periodic (with period 2). [ABSTRACT FROM AUTHOR]

In this two-paper series, we prove the invariance of the Gibbs measure for a threedimensional wave equation with a Hartree nonlinearity. The novelty lies in the singularity of the Gibbs measure with respect to the Gaussian free field. In this paper, we focus on the dynamical aspects of our main result. The local theory is based on a paracontrolled approach, which combines ingredients from dispersive equations, harmonic analysis, and random matrix theory. The main contribution, however, lies in the global theory. We develop a new globalization argument, which addresses the singularity of the Gibbs measure and its consequences. [ABSTRACT FROM AUTHOR]

Summary: Optical millimeter‐wave generation is a predominant approach for the generation of high‐quality carrier signals for future wireless transmissions. This paper proposes an optical frequency 12‐tupling millimeter‐wave generation scheme using three cascaded‐MZMs assisted by polarization multiplexing for carrier suppression. A three‐stage MZM architecture produces the desired sixth‐order sidebands along with the undesired carrier signal. The proper adjustment of polarization direction and angle of polarization rotation lead to the effective suppression of the undesired optical carrier signal. A comprehensive mathematical analysis has been accomplished to evaluate the system's performance, and the obtained results are also validated through simulation findings. The derived results demonstrate that the proposed system is capable of operating over a broad modulation index range extending from 1.5 to 4.5, thereby relaxing the stringent requirements for a constant modulation index. The proposed system generates high‐purity mm‐wave signals with an OSSR of 62.06 dB and an RFSSR of 54.79 dB at a modulation index of 2.6. Moreover, it is also validated that even if the system parameters like modulation index, polarizer rotation angle, and phase difference among RF driving signals deviate from their ideal values to a certain degree, the system performance remains acceptable. The involvement of polarization technique, omission of wavelength‐dependent devices, and a large modulation index operating range make this methodology readily appealing for implementation in radio‐over‐fiber transmissions. [ABSTRACT FROM AUTHOR]

In cold regions, the frequent occurrence of frost damage seriously affects the safety and stability of tunnel projects during construction and service time. Analyzing the formation mechanism of ice congestion in the drainage channel is of great significance for reducing the risk of frost damage. For this purpose, a mathematical model was proposed in the present work to investigate the freezing properties of water flow in the drainage channel. In this model, the latent heat of the water–ice phase change was taken into account to describe the formation process of frazil ice. Combined with the method of energy conservation, the critical distance of water freezing was derived theoretically. The field experiment and computational fluid dynamics (CFD) simulation were carried out to verify the accuracy and effectiveness of the proposed model. It showed that the estimated critical position of water freezing agreed well with the experimental and simulation results. Subsequently, the effects of hydraulic and thermodynamic factors on the freezing process of water flow were further discussed. As a practical application, the proposed mathematical model is utilized to evaluate the safety of the drainage channel of a railway tunnel in cold regions. The results demonstrate that when the flow discharge is smaller than 2,600 m3/day, there is a risk of ice congestion in the drainage channel within a range of about 960 m from the water outlet. Therefore, freeze-proof measures such as (1) thermal insulation cover plate, (2) electric heat tracing system, and (3) ground-source heat pump system should be employed in this range. [ABSTRACT FROM AUTHOR]

We develop a mathematical model for adsorption based on averaging the flow around, and diffusion inside, adsorbent particles in a column. The model involves three coupled partial differential equations for the contaminant concentration both in the carrier fluid and within the particle as well as the adsorption rate. The adsorption rate is modelled using the Sips equation, which is suitable for describing both physical and chemical adsorption mechanisms. Non-dimensionalisation is used to determine the controlling parameter groups as well as to determine negligible terms and so reduce the system complexity. The inclusion of intra-particle diffusion introduces new dimensionless parameters to those found in standard works, including a form of internal Damköhler number and a new characteristic time scale. We provide a numerical method for the full model and show how in certain situations a travelling wave approach can be utilized to find analytical solutions. The model is validated against published experimental data for the removal of Mercury(II) and CO 2. The results show excellent agreement with measurements of column outlet contaminant concentration and provide insights into the underlying chemical reactions. • A model that correctly captures the multiscale nature of industrial adsorption processes is developed. • The model includes parameters to account for different partial orders in the adsorption reaction. • A travelling wave approximation is obtained and validated by comparing with the solution of the full problem. • Analytical solutions of the travelling wave approximation are provided. • Analytical solutions have been tested against experimental data showing excellent agreement. [ABSTRACT FROM AUTHOR]

In this article, we analyse the Dyson equation for the density–density response function (DDRF) that plays a central role in linear response time-dependent density functional theory (LR-TDDFT). First, we present a functional analytic setting that allows for a unified treatment of the Dyson equation with general adiabatic approximations for discrete (finite and infinite) and continuum systems. In this setting, we derive a representation formula for the solution of the Dyson equation in terms of an operator version of the Casida matrix. While the Casida matrix is well-known in the physics literature, its general formulation as an (unbounded) operator in the N -body wavefunction space appears to be new. Moreover, we derive several consequences of the solution formula obtained here; in particular, we discuss the stability of the solution and characterise the maximal meromorphic extension of its Fourier transform. We then show that for adiabatic approximations satisfying a suitable compactness condition, the maximal domains of meromorphic continuation of the initial DDRF and the solution of the Dyson equation are the same. The results derived here apply to widely used adiabatic approximations such as (but not limited to) the random phase approximation and the adiabatic local density approximation. In particular, these results show that neither of these approximations can shift the ionisation threshold of the Kohn–Sham system. [ABSTRACT FROM AUTHOR]

A combination of experimental measurement preparations using pressure and temperature sensors in conjunction with the theory of one-dimensional isentropic flow and mathematical physics analyses is presented as a tool for analysis in this paper. Furthermore, the subsequent development of a nozzle for use in environmental electron microscopy between the specimen chamber and the differentially pumped chamber is described. Based on experimental measurements, an analysis of the impact of the nozzle shaping located behind the aperture on the character of the supersonic flow and the resulting dispersion of the electron beam passing through the differential pumped chamber is carried out on the determined pressure ratio using a combination of theory and mathematical physics analyses. The results show that nozzle shapes causing under-expanded gas outflow from the aperture to the nozzle have a worse impact on the dispersion of the primary electron beam. This is due to the flow velocity control. The controlled reduction in the static pressure curve on the primary electron beam path thus causes a significantly higher course of electron dispersion values than variants with shapes causing over-expanded gas outflow. [ABSTRACT FROM AUTHOR]

The design of a mixed-mode proportional-integral-derivative (PID) controller circuit using current-feedback operational amplifiers (CFOAs) as active components is proposed. With the same circuit topology, the proposed configuration of three CFOAs, four resistors, and two capacitors is capable of performing the PID controller in each of the following four modes: voltage mode, trans-admittance mode, current mode, and trans-impedance mode. Numerous mathematical analyses are conducted to determine the controller's performance under both ideal and non-ideal conditions. Additionally, the mixed-mode second-order lowpass filter is suggested and also used to examine the workability of the proposed mixed-mode PID controller in a feedback control structure. The proposed PID controller is implemented with the commercially available IC-type CFOA AD844, and the simulation results are presented to illustrate the functionality of the controller and its closed-loop control system. According to the findings, the total power consumption of the proposed PID controller is 0.348 W, with symmetrical supply voltages of ±9 V. It also has a temperature variation of less than 0.2% over the AD844's usable range. Monte Carlo statistical analysis results revealed that the gain responses of the controller exhibited a deviation of no more than 7.72% from the theoretical value. The controlled filter in a closed-loop control system has a 43% faster rise time and peak time than the uncontrolled filter in all four modes of operation. It also has a steady-state error less than 0.2 mV for voltage responses and 0.72 µA for current responses. [ABSTRACT FROM AUTHOR]

The results of an experimental and mathematical study into the MmNi4.2Mn0.8 compound's hydrogen storage properties are presented in the present research. Plotting and discussion of the experimental isotherms (P-C-T) for different starting temperatures (288 K, 298 K, 308 K, and 318 K) were carried out first. Then, the enthalpy and entropy of formation (ΔH0, ΔS0) were deduced from the plot of van't Hoff. Following that, the P-C-T were contrasted with a mathematical model developed via statistical physics modeling. The steric and energetic parameters, such as the number of the receiving sites (n1, n2), their densities (Nm1, Nm2), and the energy parameters (P1, P2) of the system, were calculated thanks to the excellent agreement between the numerical and experimental results. Therefore, plotting and discussing these parameters in relation to temperature preceded their application in determining the amount of hydrogen in each type of site per unit of metal ([H/M]1, [H/M]2) as well as for the entire system [H/M] versus temperature and pressure besides the absorption energies associated with each kind of site (ΔE1, ΔE2) and the thermodynamic functions (free energy, Gibbs energy, and entropy) that control the absorption reaction. [ABSTRACT FROM AUTHOR]

We study the long-time behaviour of a run and tumble model which is a kinetic-transport equation describing bacterial movement under the effect of a chemical stimulus. The experiments suggest that the non-uniform tumbling kernels are physically relevant ones as opposed to the uniform tumbling kernel which is widely considered in the literature to reduce the complexity of the mathematical analysis. We consider two cases: (i) the tumbling kernel depends on the angle between pre- and post-tumbling velocities, (ii) the velocity space is unbounded and the post-tumbling velocities follow the Maxwellian velocity distribution. We prove that the probability density distribution of bacteria converges to an equilibrium distribution with explicit (exponential for (i) and algebraic for (ii)) convergence rates, for any probability measure initial data. To the best of our knowledge, our results are the first results concerning the long-time behaviour of run and tumble equations with non-uniform tumbling kernels. [ABSTRACT FROM AUTHOR]

In this paper, a new microstrip triplexer is designed to work at 2.5 GHz, 4.4 GHz and 6 GHz for mid-band 5G applications. All channels are flat with three low group delays (GDs) of 0.84 ns, 0.75 ns and 0.49 ns, respectively. Compared to the previously reported works, the proposed triplexer has the minimum group delay. The designed triplexer has 18.2%, 13.7%, 23.6% fractional bandwidths (FBW%) at 2.5 GHz, 4.4 GHz and 6 GHz, respectively. The obtained insertion losses (ILs) are low at all channels. These features are obtained without a noticeable increase in the overall size. A novel and simple resonator is used to design the proposed triplexer, which includes two pairs of coupled lines combined with a shunt stub. A perfect mathematical analysis is performed to find the resonator behavior and the layout optimization. The type of shunt stub is determined mathematically. Also, the smallness or largeness of some important physical dimensions is determined using the proposed mathematical analysis. Finally, the designed triplexer is fabricated and measured, where the measurement results verify the simulations. [ABSTRACT FROM AUTHOR]

Micropolar fluids provide a more accurate description of fluid behavior at small scales, where classical continuum models may fail to capture complicated microscale interactions. These interactions become significant in situations involving non-Newtonian fluids, complex geometries, and materials with internal structures. Unlike traditional fluids, micropolar fluids consider the effects of micro-rotations and micro-deformations. The objective of this exploration is to investigate the characteristics of flow in a micropolar-Casson fluid that is doubly stratified, and is induced by a stretching sheet. Additionally, the study investigates the transfer of both thermal energy and mass species over a two-dimensional porous medium. By utilizing suitable similarity transformations, a system of nonlinear ordinary differential equations (ODEs) is derived by transforming the governing partial differential equations (PDEs) that describe the physics of the problem. The combination of a fourth-order Runge–Kutta integration scheme and the Shooting method is utilized to solve these equations. Various graphs and tables are utilized to illustrate the impact of physical parameters on the dimensionless quantities. Our findings exhibit strong conformity with the existing results in literature for specific scenarios. Furthermore, the outcomes highlight that the velocity and micro-rotation are enhanced by the material parameter. [ABSTRACT FROM AUTHOR]

Background: Emerging evidence suggests that shortened, simplified treatment regimens for rifampicin-resistant tuberculosis (RR-TB) can achieve comparable end-of-treatment (EOT) outcomes to longer regimens. We compared a 6-month regimen containing bedaquiline, pretomanid, linezolid, and moxifloxacin (BPaLM) to a standard of care strategy using a 9- or 18-month regimen depending on whether fluoroquinolone resistance (FQ-R) was detected on drug susceptibility testing (DST). Methods and findings: The primary objective was to determine whether 6 months of BPaLM is a cost-effective treatment strategy for RR-TB. We used genomic and demographic data to parameterize a mathematical model estimating long-term health outcomes measured in quality-adjusted life years (QALYs) and lifetime costs in 2022 USD ($) for each treatment strategy for patients 15 years and older diagnosed with pulmonary RR-TB in Moldova, a country with a high burden of TB drug resistance. For each individual, we simulated the natural history of TB and associated treatment outcomes, as well as the process of acquiring resistance to each of 12 anti-TB drugs. Compared to the standard of care, 6 months of BPaLM was cost-effective. This strategy was estimated to reduce lifetime costs by $3,366 (95% UI: [1,465, 5,742] p < 0.001) per individual, with a nonsignificant change in QALYs (−0.06; 95% UI: [−0.49, 0.032] p = 0.790). For those stopping moxifloxacin under the BPaLM regimen, continuing with BPaL plus clofazimine (BPaLC) provided more QALYs at lower cost than continuing with BPaL alone. Strategies based on 6 months of BPaLM had at least a 93% chance of being cost-effective, so long as BPaLC was continued in the event of stopping moxifloxacin. BPaLM for 6 months also reduced the average time spent with TB resistant to amikacin, bedaquiline, clofazimine, cycloserine, moxifloxacin, and pyrazinamide, while it increased the average time spent with TB resistant to delamanid and pretomanid. Sensitivity analyses showed 6 months of BPaLM to be cost-effective across a broad range of values for the relative effectiveness of BPaLM, and the proportion of the cohort with FQ-R. Compared to the standard of care, 6 months of BPaLM would be expected to save Moldova's national TB program budget $7.1 million (95% UI: [1.3 million, 15.4 million] p = 0.002) over the 5-year period from implementation. Our analysis did not account for all possible interactions between specific drugs with regard to treatment outcomes, resistance acquisition, or the consequences of specific types of severe adverse events, nor did we model how the intervention may affect TB transmission dynamics. Conclusions: Compared to standard of care, longer regimens, the implementation of the 6-month BPaLM regimen could improve the cost-effectiveness of care for individuals diagnosed with RR-TB, particularly in settings with a high burden of drug-resistant TB. Further research may be warranted to explore the impact and cost-effectiveness of shorter RR-TB regimens across settings with varied drug-resistant TB burdens and national income levels. Author summary: Why was this study done?: Drug resistance poses a major barrier to the effective treatment of tuberculosis, especially in Moldova and other post-Soviet states which have the highest levels of resistance in the world. Individuals with tuberculosis resistant to the key drug rifampicin face a worse prognosis, a longer and more expensive course of treatment, and more side effects than individuals with rifampicin-susceptible tuberculosis. Until recently, the standard of care for rifampicin-resistant tuberculosis (RR-TB) involved many drugs in combination, often given for 18 months or longer. The newer, 6-month "BPaLM" regimen is comprised of 4 drugs (bedaquiline, pretomanid, linezolid, and moxifloxacin) to which resistance levels are currently low, and while it was shown to be just as effective as the standard of care when health outcomes were measured at 72 weeks from treatment initiation, its effect on lifetime health outcomes, costs, and the acquisition of drug resistance was less clear. What did the researchers do and find?: Using a mathematical model, we projected the lifetime health benefits and costs of the 6-month BPaLM regimen as compared to 9–18 month, standard of care treatments for RR-TB, and found that 6 months of BPaLM would be likely to provide similar health benefits, at lower cost. Compared to the standard of care, we also found that the 6-month BPaLM regimen could shorten the average duration of tuberculosis resistant to the drugs amikacin, bedaquiline, clofazimine, cycloserine, moxifloxacin, and pyrazinamide, while it may increase the average duration of tuberculosis resistant to delamanid and pretomanid. For individuals receiving BPaLM who had to stop taking the drug moxifloxacin, we found that it would likely be beneficial on both health and cost grounds to replace it with clofazimine, thereby topping the regimen back up to 4 drugs. What do these findings mean?: Using conventional benchmarks for value-for-money, we estimated that 6 months of BPaLM would be a cost-effective approach for the treatment of RR-TB in Moldova, and potentially other post-Soviet countries. Though the impact of the 6-month BPaLM regimen on the spread of drug resistance is uncertain and not addressed directly by this study, this combination of newer drugs appears to achieve cure more quickly, thereby reducing the amount of time an individual is potentially infectious. This may be beneficial in fighting resistance to several drugs, even while it may increase the spread of resistance to others. Further studies may be warranted to explore how well these findings would translate to different global regions where health system capabilities, costs, and existing resistance patterns may differ. [ABSTRACT FROM AUTHOR]

Minimizers and convolutional neural networks (CNNs) are two quite distinct popular techniques that have both been employed to analyze categorical biological sequences. At face value, the methods seem entirely dissimilar. Minimizers use min-wise hashing on a rolling window to extract a single important k-mer feature per window. CNNs start with a wide array of randomly initialized convolutional filters, paired with a pooling operation, and then multiple additional neural layers to learn both the filters themselves and how they can be used to classify the sequence. In this study, our main result is a careful mathematical analysis of hash function properties showing that for sequences over a categorical alphabet, random Gaussian initialization of convolutional filters with max-pooling is equivalent to choosing a minimizer ordering such that selected k-mers are (in Hamming distance) far from the k-mers within the sequence but close to other minimizers. In empirical experiments, we find that this property manifests as decreased density in repetitive regions, both in simulation and on real human telomeres. We additionally train from scratch a CNN embedding of synthetic short-reads from the SARS-CoV-2 genome into 3D Euclidean space that locally recapitulates the linear sequence distance of the read origins, a modest step toward building a deep learning assembler, although it is at present too slow to be practical. In total, this article provides a partial explanation for the effectiveness of CNNs in categorical sequence analysis. [ABSTRACT FROM AUTHOR]

A mathematical model is presented for the optimisation of an Electromagnetic Halbach Array (EHA) for wireless power transfer. The mathematical model is based on Biot‐Savart's law of magnetic field in a current‐carrying square loop. The model is validated through static electromagnetic simulations in ANSYS Maxwell and found to be accurate and effective when predicting the magnetic field within the EHA box. To verify the analytical and simulation results, an EHA was fabricated, and experimental verification was carried out. The results show that the mathematical model can be widely used in the analysis and design optimisation of EHAs of any size and with diverse parameters in the case of single‐layer square spiral planar coils. [ABSTRACT FROM AUTHOR]

The voltage‐source virtual synchronous generator is a grid‐forming type power electronic control technology and is able to support converters that have the ability of inertial, primary frequency and voltage regulation. Firstly, the authors build the small‐signal model of the voltage‐source virtual synchronous generator and conventional converters, compare and analyse the characteristics of the high‐frequency resonance modes, the results show that the voltage‐source virtual synchronous generator has almost the same high‐frequency resonance characteristics as the conventional converter. Secondly, the different control parameters and power grid strength that affect the high‐frequency resonance characteristic are analysed with eigenvalue, and the mechanism of voltage‐source VSG that caused high‐frequency resonance is derived. The leading factor that causes high‐frequency resonance is power grid strengths, and the authors proposed introducing virtual impedance into the front‐end channel of the current inner loop control strategy to suppress resonance for the voltage‐source virtual synchronous generator based on the theoretical analysis with the small‐signal model and eigenvalue analysis. In addition, the electromagnetic transient simulation model and RT‐LAB controller‐in‐loop platform are built, and the simulation and experiment results indicate the effectiveness of the virtual impedance control strategy. [ABSTRACT FROM AUTHOR]

In this article, we are working on an SEIR-SI type model for dengue disease in order to better observe the dynamics of infection in human beings. We calculate the basic reproduction number R 0 and determine the equilibrium points. We then show the existence of global stability in each of the different states depending on the value of R 0 . Moreover, to support the theoretical work, we present numerical simulations obtained using Python. We also study the sensitivity of the parameters included in the expression of R 0 with the aim of identifying the most influential parameters in the dynamics of dengue disease spread. Finally, we introduce two functions u and v, respectively indicating the treatment of the infected people and any prevention system minimizing contact between humans and the disease causing vectors. We present the curves of the controlled system after calculating the optimal pair of controls capable of reducing the dynamics of the disease spread, still using Python. [ABSTRACT FROM AUTHOR]

Reliable detection of substances present at potentially low concentrations is a problem common to many biomedical applications. Complementary to well-established enzyme-, antibody-antigen-, and sequencing-based approaches, so-called microbial whole-cell sensors, i.e., synthetically engineered microbial cells that sense and report substances, have been proposed as alternatives. Typically these cells operate independently: a cell reports an analyte upon local detection. In this work, we analyze a distributed algorithm for microbial whole-cell sensors, where cells communicate to coordinate if an analyte has been detected. The algorithm, inspired by the Allee effect in biological populations, causes cells to alternate between a logical 0 and 1 state in response to reacting with the particle of interest. When the cells in the logical 1 state exceed a threshold, the algorithm converts the remaining cells to the logical 1 state, representing an easily-detectable output signal. We validate the algorithm through mathematical analysis and simulations, demonstrating that it works correctly even in noisy cellular environments. [ABSTRACT FROM AUTHOR]

This research deals with heat and mass transport in 2D, steady laminar unidirectional flow of second-grade fluid inside converging/diverging stretchable channel with no slip effects. The similarity equations were engaged for the model development and acquired a model in the form of a joint system of ODEs comprising the innovative effects of thermal radiations, magnetic field and dissipation function. Then, mathematical treatment of the model was done via HAM Package and the results were furnished under the inspiration of physical constraints. It is pointed out that the fluid moves quite slowly in diverging cases than that of converging ones under multiple Re values, whereas magnetic field effects are almost negligible for the velocity profile. The temperature of the fluid can be enlarged by increasing Ec and Pr and Rd is not proven good in this study. Further, as far as the mass transport is concerned, the dominant contribution of Sc is observed for both stretching/shrinking walls. [ABSTRACT FROM AUTHOR]

Since the left ventricle (LV) has pressure (Plv) and volume (Vlv), we can define LV elastance from the ratio between Plv and Vlv, termed as "instantaneous elastance." On the other hand, end-systolic elastance (Emax) is known to be a good index of LV contractility, which is measured by the slope of several end-systolic Plv—Vlv points obtained by using different loads. The word Emax originates from the assumption that LV elastance increases during the ejection phase and attains its maximum at the end-systole. From this concept, we can define another elastance determined by the slope of isochronous Plv—Vlv points, that is Plv—Vlv points at a certain time after the ejection onset time by using different loads. We refer to this elastance as "load-dependent elastance." To reveal the relation between these two elastances, we used a hemodynamic model that included a detailed ventricular myocyte contraction model. From the simulation results, we found that the isochronous Plv—Vlv points lay in one line and that the line slope corresponding to the load-dependent elastance slightly decreased during the ejection phase, which is quite different from the instantaneous elastance. Subsequently, we analyzed the mechanism determining these elastances from the model equations. We found that instantaneous elastance is directly related to contraction force generated by the ventricular myocyte, but the load-dependent elastance is determined by two factors: one is the transient characteristics of the cardiac cell, i.e., the velocity–dependent force drops characteristics in instantaneous shortening. The other is the force–velocity relation of the cardiac cell. We also found that the linear isochronous pressure–volume relation is based on the approximately linear relation between the time derivative of the cellular contraction force and the cellular shortening velocity that results from the combined characteristics of LV and aortic compliances. Author summary: Characteristic that the end-systolic pressure volume relation (ESPVR) of left ventricle becomes linear is one of the well known property of the heart, and its slope is considered as a good index of the heart contractility. However, the reason of the linearity is still not clarified. Recent biophysical model can reproduce the linear ESPVR, and since the model is written in the mathematical equation, the basis of the ESPVR linearity can be analytically analyzed. [ABSTRACT FROM AUTHOR]

Background: Observational studies of intermittent hemodialysis therapy have reported that the excess decrease in K+ concentration in plasma (KP) during treatment is associated with the destabilization of cardiac function. Elucidating the mechanism by which the decrease in KP impairs myocardial excitation is indispensable for a deeper understanding of prescription design. Methods: In this study, by using an electrophysiological mathematical model, we investigated the relationship between KP dynamics and cardiomyocyte excitability for the first time. Results: The excess decrease in KP during treatment destabilized cardiomyocyte excitability through the following events: (1) a decrease in KP led to the prolongation of the depolarization phase of ventricular cells due to the reduced potassium efflux rate of the Kr channel, temporarily enhancing contraction force; (2) an excess decrease in KP activated the transport of K+ and Na+ through the funny channel in sinoatrial nodal cells, disrupting automaticity; (3) the excess decrease in KP also resulted in a significant decrease in the resting membrane potential of ventricular cells, causing contractile dysfunction. Avoiding an excess decrease in KP during treatment contributed to the maintenance of cardiomyocyte excitability. Conclusions: The results of these mathematical analyses showed that it is necessary to implement personal prescription or optimal control of K+ concentration in dialysis fluid based on predialysis KP from the perspective of regulatory science in dialysis treatment. [ABSTRACT FROM AUTHOR]

In this paper, we consider a diffusive predator-prey system with fear response delay, where a benefit from the ani-predation response in addition to the cost is taken into account. As a step toward understanding the underlying mechanism of the spatiotemporal pattern formations by rigorous mathematical analysis, we are interested in how the joint effects of time delay, the fear effect strength, the carrying capacity, as well as the diffusion rates could affect the complex spatiotemporal pattern formations of the system. In particular, Turing instability of the Hopf bifurcating periodic solutions is investigated in details. To that end, a general formula is derived to determine Turing instability of the Hopf bifurcating periodic solutions for general 2-component delayed-diffusive system. This extends our earlier general results for non-delayed diffusive system to its delayed-diffusive counterparts. Our general formula tends to be new and can be applied to a variety of 2-component delayed-diffusive systems. [ABSTRACT FROM AUTHOR]

Background: The gut microbiota, vital for host health, influences metabolism, immune function, and development. Understanding the dynamic processes of bacterial accumulation within the gut is crucial, as it is closely related to immune responses, antibiotic resistance, and colorectal cancer. We investigated Escherichia coli behavior and distribution in zebrafish larval intestines, focusing on the gut microenvironment. Results: We discovered that E. coli spread was considerably suppressed within the intestinal folds, leading to a strong physical accumulation in the folds. Moreover, a higher concentration of E. coli on the dorsal side than on the ventral side was observed. Our in vitro microfluidic experiments and theoretical analysis revealed that the overall distribution of E. coli in the intestines was established by a combination of physical factor and bacterial taxis. Conclusions: Our findings provide valuable insight into how the intestinal microenvironment affects bacterial motility and accumulation, enhancing our understanding of the behavioral and ecological dynamics of the intestinal microbiota. [ABSTRACT FROM AUTHOR]

Air conditioning plays a vital role in modern life, but its high energy consumption, particularly in vapor compression cycles, is a major concern. This study explores absorption cycles as an alternative, where the compressor is replaced with components powered by heat instead of electricity, potentially leading to reduce energy consuming. The study has three main approaches: theoretical analysis, experimental and validation. The theoretical analysis uses Engineering Equation Solver (EES) to model the system's performance, focusing on Coefficient of Performance (COP) and cooling capacity, for two working pairs NH3-H2O and LiBr-H2O. The experimental setup was designed to validate the theoretical model. The results from the theoretical analysis show good agreement with a maximum deviation of around 0.6%. Furthermore, the analysis indicates that the LiBr-H2O pair has better COP and cooling capacity than NH3-H2O by approximately 33%. This suggests that LiBr-H2O absorption cycles have the potential to be a more efficient and sustainable alternative for air conditioning systems. [ABSTRACT FROM AUTHOR]

Achieving household food security is the tumbling issue of the century. This article explores the factors affecting household food security and solutions by utilizing a synergy of statistical and mathematical models. The methodology section is divided into two portions namely sociological and mathematical methods. Sociologically, 379 household heads were interviewed through structured questions and further analyzed in terms of descriptive and binary logistic regression. The study found that 4 independent variables (poverty, poor governance, militancy, and social stratification) showed a significant association (P = 0.000) to explain variations in the dependent variable (household FS). The Omnibus test value (χ2= 102.386; P = 0.000) demonstrated that the test for the entire model against constant was statistically significant. Therefore, the set of predictor variables could better distinguish the variation in household FS. The Nagelkerke's R Square (R2 =.333) helps to interpret that the prediction variable and the group variables had a strong relationship. Moreover, 23% to 33% variation in FS was explained by the grouping variables (Cox and Snell R2 = 0.237 and Nagelkerke's R2 = 0.333). The significant value of Wald test results for each variable confirmed that the grouping variables (poor governance P = 0.004, militancy P = 0.000, social stratification P = 0.021 and poverty P = 0.000) significantly predicted FS at the household level. Mathematically, all the statistics were validated further through the application of spherical fuzzy mathematics (TOPIS and MADM) to explore what factors are affecting household FS. Thus, the study found that F3 (poverty) > F2 (militancy) > F4 (social stratification) > F1 (poor governance) respectively. Thus, it could be concluded from these findings that the prevalence of poverty dysfunctional all the channels of household FS at the macro and micro levels. Therefore, a sound and workable model to eradicate poverty in the study area by ensuring social safety nets for the locals was put forward some of the policy implications for the government are the order of the day. [ABSTRACT FROM AUTHOR]

In addition to providing learners with a large amount of teaching resources, online teaching platforms can also provide learning resources and channels such as video courseware, Q&A tutoring groups, and forums. However, currently, there are still shortcomings in depth and dimensionality in mining student learning behavior data on the platform. In view of this situation, based on the learning interaction behavior, this study established the difficulty similarity model of knowledge points, and used spectral clustering to classify their difficulty. In addition, the study intended to use the maximum frequent subgraph under the Gspan framework to characterize learners' implicit learning patterns. The outcomes expressed that the algorithm put forward in the study achieved the highest accuracy index of 98.8%, which was 1.4%, 4.0%, and 8.6% higher than Apriori-based graph mining algorithms, K-means, and frequent subgraph discovery algorithms. In terms of F1 index, the convergence value of the algorithm proposed in the study was 95.5%, which was about 2.5% higher than the last three algorithms. In addition, learners of all three cognitive levels had the highest maximum number of frequent subgraphs with sizes above 100 when the minSup value was 60%. And when the number of clusters was 3, the clustering accuracy of the three learners was the highest. In similarity calculation, the calculation method used in the study was at the minimum in terms of root mean square error and absolute error average index, which were 0.048% and 0.01% respectively. This indicated that the model proposed by the research had better classification effect on the difficulty of knowledge points for learners of different cognitive levels, and had certain application potential. [ABSTRACT FROM AUTHOR]

This work investigates novel fractional Hadamard integral inequalities by utilizing extended convex functions and generalized Riemann-Liouville operators. By carefully using extended integral formulations, we not only find novel inequalities but also improve the accuracy of error bounds related to fractional Hadamard integrals. Our study broadens the applicability of these inequalities and shows that they are useful for a variety of convexity cases. Our results contribute to the advancement of mathematical analysis and provide useful information for theoretical comprehension as well as practical applications across several scientific directions. [ABSTRACT FROM AUTHOR]

While natural communities can contain hundreds of species, modern coexistence theory focuses primarily on species pairs. Alternatively, the structural stability approach considers the feasibility of equilibria, gaining scalability to larger communities but sacrificing information about dynamic stability. Three‐species competitive communities are a bridge to more‐diverse communities. They display novel phenomena while remaining amenable to mathematical analysis, but remain incompletely understood. Here, we combine these approaches to identify the key quantities that determine three‐species competition outcomes. We show that pairwise niche overlap and fitness differences are insufficient to completely characterize competitive outcomes, which requires a strictly triplet‐wise quantity: cyclic asymmetry, which underlies intransitivity. Low pairwise niche overlap stabilizes the triplet, while high fitness differences promote competitive exclusion. The effect of cyclic asymmetry on stability is complex and depends on pairwise niche overlap. In summary, we elucidate how pairwise niche overlap, fitness differences and cyclic asymmetry determine three‐species competition outcomes. [ABSTRACT FROM AUTHOR]

Holden described, without mathematical analysis, a kinematical method for constructing from platonic solids polylinks with flat or solid polygonal links. No statement was made about the number of polylinks. Geometric parameters of examples shown were found by trial and error. In the present paper, it is shown that each platonic solid defines a one-parametric manifold of polylinks. The geometry of flat links and of links with circular cross section is expressed in terms of the free parameter. The solution is based on a theorem which generalizes known solutions of special cases. [ABSTRACT FROM AUTHOR]

An approach is presented to employ two different types of converters in bridgeless configuration for supply side power factor enhancement of the system. The isolated single‐stage electric vehicle battery charger uses two different converters in a bridgeless configuration to extract the advantages of both converters for supply‐side power factor enhancement. For the negative and positive semi‐cycles of the supply voltage, the power factor‐enhanced asymmetrical alternating current–direct current converter utilises a fourth order single‐ended primary‐inductor converter and a second order buck‐boost converter, respectively. The use of single‐ended primary‐inductor converter and buck‐boost converter in bridgeless configuration reduces the net order of the system with respect to conventional bridgeless‐single‐ended primary‐inductor converter schemes. The buck‐boost converter also needs the supply‐side filter to eradicate the unwanted harmonics in the supply current which increases the order of the system. The usage of both converters presents many benefits like input inductance of the single‐ended primary‐inductor converter can be utilised as a filtering element with a capacitor for the buck‐boost converter. The anti‐parallel diode conduction operation of both switches facilitates the elimination of extra reverse feed diodes (generally used in bridgeless schemes). The single‐stage charger itself comes with the benefit of elimination of extra stages and thus the losses associated with it. The presented charger also witnesses the elimination of the rectifier due to usage of bridgeless configuration. The isolated single‐stage electric vehicle battery charger is also garnished with electrical isolation which adds to the safety standard of the system. To attain power factor enhancement, the asymmetrical alternating current–direct current converter functions in discontinuous current conduction mode in the present work. The elimination of extra‐stages (with respect to two stage charger), a filter, a rectifier, two extra reverse‐feeding diodes, one voltage sensor, one current sensor (with respect to continuous current conduction mode), and electrical isolation not only makes the system compact and safer but also makes the system cheaper. Elaborated mathematical modelling and stability analysis of the presented alternating current–direct current converter using a pole‐zero map and bode plot have been included in the article. The prototype and MATLAB/Simulink model of isolated single‐stage electric vehicle battery charger system with discontinuous current conduction mode control has been built and results of both prototype and MATLAB/Simulink are deployed to verify isolated single‐stage electric vehicle battery charger system's performance during dynamic and steady‐state conditions. [ABSTRACT FROM AUTHOR]

The Internet of Things (IoT) is the underlying technology that has enabled connecting daily apparatus to the Internet and enjoying the facilities of smart services. IoT marketing is experiencing an impressive 16.7% growth rate and is a nearly USD 300.3 billion market. These eye-catching figures have made it an attractive playground for cybercriminals. IoT devices are built using resource-constrained architecture to offer compact sizes and competitive prices. As a result, integrating sophisticated cybersecurity features is beyond the scope of the computational capabilities of IoT. All of these have contributed to a surge in IoT intrusion. This paper presents an LSTM-based Intrusion Detection System (IDS) with a Dynamic Access Control (DAC) algorithm that not only detects but also defends against intrusion. This novel approach has achieved an impressive 97.16% validation accuracy. Unlike most of the IDSs, the model of the proposed IDS has been selected and optimized through mathematical analysis. Additionally, it boasts the ability to identify a wider range of threats (14 to be exact) compared to other IDS solutions, translating to enhanced security. Furthermore, it has been fine-tuned to strike a balance between accurately flagging threats and minimizing false alarms. Its impressive performance metrics (precision, recall, and F1 score all hovering around 97%) showcase the potential of this innovative IDS to elevate IoT security. The proposed IDS boasts an impressive detection rate, exceeding 98%. This high accuracy instills confidence in its reliability. Furthermore, its lightning-fast response time, averaging under 1.2 s, positions it among the fastest intrusion detection systems available. [ABSTRACT FROM AUTHOR]

This study explores the advanced mathematical modeling of electromagnetic energy harvesting in vehicle suspension systems, addressing the pressing need for sustainable transportation and improved energy efficiency. We focus on the complex challenge posed by the non-linear behavior of magnetic flux in relation to displacement, a critical aspect often overlooked in conventional approaches. Utilizing Taylor expansion and Fourier analysis, we dissect the intricate relationship between oscillation and electromagnetic damping, crucial for optimizing energy recovery. Our rigorous mathematical methodology enables the precise calculation of the average power per cycle and unit mass, providing a robust metric for evaluating the effectiveness of energy harvesting. Further, the study extends to the practical application in a combined system of passive and electromagnetic suspension, demonstrating the real-world viability of our theoretical findings. This research not only offers a comprehensive solution for enhancing vehicle efficiency through advanced suspension systems but also sets a precedent for the integration of complex mathematical techniques in solving real-world engineering challenges, contributing significantly to the future of energy-efficient automotive technologies. The cases reviewed in this article and listed as references are those commonly found in the literature. [ABSTRACT FROM AUTHOR]

Component failures can lead to performance degradation or even failure in multi-agent systems, thus necessitating the development of fault diagnosis methods. Addressing the distributed fault diagnosis problem in a class of partial differential multi-agent systems with actuators, a fault estimator is designed under the introduction of virtual faults to the agents. A P-type iterative learning control protocol is formulated based on the residual signals, aiming to adjust the introduced virtual faults. Through rigorous mathematical analysis utilizing contraction mapping and the Bellman–Gronwall lemma, sufficient conditions for the convergence of this protocol are derived. The results indicate that the learning protocol ensures the tracking of virtual faults to actual faults, thereby facilitating fault diagnosis for the systems. Finally, the effectiveness of the learning protocol is validated through numerical simulation. [ABSTRACT FROM AUTHOR]

Accurate assessment of the intrinsic period of the human circadian pacemaker is essential for a quantitative understanding of how our circadian rhythms are synchronized to exposure to natural and man-made light-dark (LD) cycles. The gold standard method for assessing intrinsic period in humans is forced desynchrony (FD) which assumes that the confounding effect of lights-on assessment of intrinsic period is removed by scheduling sleep-wake and associated dim LD cycles to periods outside the range of entrainment of the circadian pacemaker. However, the observation that the mean period of free-running blind people is longer than the mean period of sighted people assessed by FD (24.50 ± 0.17 h vs 24.15 ± 0.20 h, p < 0.001) appears inconsistent with this assertion. Here, we present a mathematical analysis using a simple parametric model of the circadian pacemaker with a sinusoidal velocity response curve (VRC) describing the effect of light on the speed of the oscillator. The analysis shows that the shorter period in FD may be explained by exquisite sensitivity of the human circadian pacemaker to low light intensities and a VRC with a larger advance region than delay region. The main implication of this analysis, which generates new and testable predictions, is that current quantitative models for predicting how light exposure affects entrainment of the human circadian system may not accurately capture the effect of dim light. The mathematical analysis generates new predictions which can be tested in laboratory experiments. These findings have implications for managing healthy entrainment of human circadian clocks in societies with abundant access to light sources with powerful biological effects. [ABSTRACT FROM AUTHOR]

In this paper, we consider the inverse scattering problem of identifying a two-layered cavity by internal acoustic measurements under the condition that the interior interface has a mixed transmission boundary condition. We focus on the mathematical analysis of recovering the shape of the interior interface by using the linear sampling method, including reconstructing the surface conductivity by the same measurements. [ABSTRACT FROM AUTHOR]

The analysis of the mathematical and mechanical properties of thermoelastic coupling tensors in anisotropic laminates is the topic of this paper. Some theoretical results concerning the compliance tensors are shown and their mechanical consequences analyzed. Moreover, the case of thermally stable laminates, important for practical applications, is also considered. The study is carried out in the framework of the polar method, a mathematical formalism particularly well-suited for the analysis of planar anisotropic problems, introduced by Prof. G. Verchery in 1979. [ABSTRACT FROM AUTHOR]

This study investigates the drying of ginger cubes using three different techniques: electrohydrodynamic drying, electrohydrodynamic-hot air drying, and hot air drying. The main objective is to assess how these drying methods affect drying times, effective diffusion coefficients, color, and microstructure. Additionally, the study includes fitting ten different thin-layer models to the experimental data for mathematical analysis. It was observed that increasing temperature and voltage values led to a reduction in the drying times of the ginger samples. After conducting statistical tests, it was determined that the Midilli et al. and Wang and Singh models were the most suitable for describing the experimental drying curves. Effective diffusion coefficient values increased with the rise in temperature and voltage values. The L* values of the dried ginger samples decreased due to temperature and voltage applications. Notably, ginger samples dried using the electrohydrodynamic method exhibited better preservation of their original appearance, particularly in terms of microstructure and starch particle integrity, compared to other drying methods. The findings of the study suggest that integrating electrohydrodynamic technology with hot air drying reduces overall drying time. This innovative approach shows promise for producing high-quality end products in the future. [ABSTRACT FROM AUTHOR]

In this work, a new optimal iterative algorithm is presented with fourth-order accuracy for root-finding of real functions. It uses only function as well as derivative evaluation. The algorithm is obtained as a combination of existing third-order methods by specifying a parameter involved. The algorithm is based on local and semilocal analysis and has been specifically designed to improve efficiency and accuracy. The proposed algorithm represents a significant improvement over existing iterative algorithms. In particular, it is tested on a range of polynomial functions and was found to produce accurate and efficient results, with improved performance over existing algorithms in terms of both speed and accuracy. The results demonstrate the effectiveness of the proposed algorithm and suggest that it has great potential for use in a wide range of applications in polynomiography and other areas of mathematical analysis. [ABSTRACT FROM AUTHOR]

For expensive problems, as the number of objectives and the number of decision variables increase, the number of non-dominated solutions in the population increases dramatically, and the population does not have enough convergence pressure to converge to the true pareto frontier. A Kriging-assisted Multi-stage Evolutionary Algorithm (K-MSEA) is proposed to enhance the exploratory capacity of populations in expensive many-objective optimization problems. A multi-stage strategy is used in K-MSEA. Mating selection and environmental selection of populations are divided into three stages based on convergence and diversity indices. Targeted selection of individuals should be conducted at each stage of population development. The population independently chooses the appropriate stage in accordance with the current demands of convergence and diversity. Differential evolutionary algorithm is used to improve the search ability of the population. To guide the population in the correct direction, K-MSEA employs an elite retention strategy in environmental selection. The population utilizes individual renewal, where underperforming parents are replaced by better-performing offspring. The surrogate model is then updated with the uncertainty information supplied by the Kriging model. Finally, K-MSEA is benchmarked against five other algorithms in experiments on two benchmark problems and two realistic expensive problems. Mathematical analysis demonstrates that K-MSEA is more competitive than others. [ABSTRACT FROM AUTHOR]