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The increasing demand for low voltage, power efficient, high-speed analog-to-digital converters (ADCs) results in the improvement of speed and power of regenerative dynamic comparator. In this paper, a dual-tail dynamic comparator is used with two extra transistors in the latch stage. These extra transistors help in the increase of transconductance of the latch stage, which helps decrease the delay of the proposed comparator. Mathematical analysis is done for the proposed architecture; this gives the idea of reducing the delay of the comparator with an increase in the transconductance of the comparator. The simulation and layout of the proposed comparator are done on the Cadence software with 90 nm CMOS technology. This proposed design is simulated with a 2 GHz clock frequency at supply voltage of 1 V. The proposed architecture consumes a power of 39.19 μ W and a delay of 143.12 ps at 1 V supply voltage, 5 mV input difference voltage and 0.9 V common mode voltage. The Monte Carlo simulation of the proposed architecture for power, delay, power delay product (PDP) and offset is also demonstrated in this paper. Process corner analysis is done for power, delay and PDP. [ABSTRACT FROM AUTHOR]

At present, the informatization of basic education quality assessment has become a hot topic in the field of education and is playing an increasingly important role. Based on the theory of deep convolutional neural network, this paper adopts the methods of mathematical analysis and experimental research to construct a regional basic education quality assessment model. The model solves the data informatization problem of education quality assessment. In the simulation process, two key modules of data self-assessment and expert assessment of the deep convolutional neural network are realized by ASENET+SQL SERVER, and the assessment results are integrated by using the weighted average method and the fuzzy comprehensive assessment method. The experimental results show that the quantitative analysis of the quality assessment is carried out by using the logic and support relationship, and the results of comprehensive qualitative analysis and quantitative analysis are realized and segmented when the threshold level is 9, the MIOU obtains the highest value of 0.7501, and the MIOU of the multi-stage method of the quality evaluation model proposed in this paper is 0.8116, which is 6.15% points higher than the traditional multi-stage algorithm, which effectively improves the current stage area quality of basic education. [ABSTRACT FROM AUTHOR]

The sterile insect technique (SIT) has been applied as an alternative method to reduce or eradicate mosquito-borne diseases. To explore the impact of the sterile mosquitoes on controlling the wild mosquito populations, in this paper, we further extend the work in [J. Li, New revised simple models for interactive wild and sterile mosquito populations and their dynamics, J. Biol. Dyn. 11(S2) (2017) 316–333] and formulate delayed models for interactive wild and sterile mosquitoes, which can depict wild mosquito population undergoing distinct stages of development during a lifetime. By performing mathematical analysis, the threshold dynamics of the proposed models are explored, respectively. In particular, Hopf bifurcation phenomena are observed as the delay τ is varying. Numerical examples illustrate our findings. [ABSTRACT FROM AUTHOR]

When people interact, their behavior tends to become synchronized, a mutual coordination process that fosters short-term adaptations, like increased affiliation, and long-term adaptations, like increased bonding. This paper addresses for the first time how such short-term and long-term adaptivity induced by synchronization can be modeled computationally by a second-order multi-adaptive neural agent model. It addresses movement, affect and verbal modalities and both intrapersonal synchrony and interpersonal synchrony. The behavior of the introduced neural agent model was evaluated in a simulation paradigm with different stimuli and communication-enabling conditions. Moreover, in this paper, mathematical analysis is also addressed for adaptive network models and their positioning within the landscape of adaptive dynamical systems. The first type of analysis addressed shows that any smooth adaptive dynamical system has a canonical representation by a self-modeling network. This implies theoretically that the self-modeling network format is widely applicable, which also has been found in many practical applications using this approach. Furthermore, stationary point and equilibrium analysis was addressed and applied to the introduced self-modeling network model. It was used to obtain verification of the model providing evidence that the implemented model is correct with respect to its design specifications. [ABSTRACT FROM AUTHOR]

The security of mobile wireless sensor networks has captivated extensive attention of researchers because of their wide range of applications and vulnerability to attacks caused by malware. In this paper, we investigate a delayed malware propagation model on mobile wireless sensor network incorporating nonlinear incidence rate, logistic growth rate and recovery rate. Local asymptotic stability of the endemic equilibrium and existence of Hopf bifurcation at crucial value of the time delay are analyzed. Then, properties of Hopf bifurcation are explored. Specifically, global exponential stability is investigated via linear matrix inequality. An example is presented finally to underline the effectiveness of findings in our paper numerically and graphically. [ABSTRACT FROM AUTHOR]

This paper describes a theoretical framework and computational methods of a thin layer coating of a non-Newtonian polymeric material while it moves through a tiny space among two inverted rollers. Order of magnitude is accustomed to clarify the nondimensional forms of the governing equations. Semi-analytical solutions of pressure gradient, velocity profile and rate of the flow are acquired via optimal homotopy asymptotic method (OHAM). The graphical representation depicts the physical quantities of the effects of velocity profile ratio k and Weissenberg number We. It is observed that by increasing the values of k and We, velocity profile decreases while pressure distribution increases. [ABSTRACT FROM AUTHOR]

Linear complementarity problems are fundamental in various mathematical fields, and it is widely recognized that these problems have a unique solution if and only if the matrix related to them is a P-matrix. However, determining whether a matrix is a P-matrix can be extremely challenging or even impossible, especially for large matrices. In this paper, we present a method for establishing the existence and uniqueness of the solution to linear complementarity problems without the need for P-matrix verification. [ABSTRACT FROM AUTHOR]

Currently, diabetic retinopathy is still screened as a three-stage classification, which is a tedious strategy and along these lines of this paper focuses on developing an improved methodology. In this methodology, we taught a convolutional neural network form on a major dataset, which includes around 45 depictions to do mathematical analysis and characterization. In this paper, DR is constructed, which takes the enter parameters as the HRF fundus photo of the eye. Three classes of patients are considered — healthy patients, diabetic's retinopathy patients and glaucoma patients. An informed convolutional neural system without a fully connected model will also separate the highlights of the fundus pixel with the help of the enactment abilities like ReLu and softmax and arrangement. The yield obtained from the convolutional neural network (CNN) model and patient data achieves an institutionalized 97% accuracy. Therefore, the resulting methodology is having a great potential benefiting ophthalmic specialists in clinical medicine in terms of diagnosing earlier the symptoms of DR and mitigating its effects. [ABSTRACT FROM AUTHOR]

The aim of this research paper is to model the effects of misidentification in the transmission dynamics of the super yeast, Candida auris (or C. auris), among patients receiving treatment in the Intensive Care Units (ICUs). The mathematical analysis is carried out by obtaining the reproduction number of the C. auris model using the next generation matrix and utilizing it as a threshold value to establish the local and global stability properties at the points of equilibria. The numerical investigations carried out in this paper establish the outcomes of the effect of variations in the values of important parameters on the dynamics of C. auris colonization and infections in the health care settings. The corresponding results from the numerical simulations are illustrated graphically. [ABSTRACT FROM AUTHOR]

A nonclassical model known as the guava model with the conformable derivative describing the interaction of guava pests and natural enemies is studied in this paper. To this end, first the Adams–Bashforth–Moulton predictor–corrector (ABM-PC) scheme is adopted to numerically solve the guava model with the conformable derivative such that its performance is examined using the finite-difference (FD) method. The truncation error of the ABM-PC scheme is then presented in a detailed way. The effect of the order of the conformable derivative on the dynamical characteristics of guava pests and natural enemies is investigated by considering a series of graphical representations. In the end, based on the results given in this study, it is shown which day is more beneficial to harvest the guava. [ABSTRACT FROM AUTHOR]

In this paper, we establish the validity of the so-called Bounded Approximation Property (BAP) for a comprehensive class of translation and modulation invariant Banach spaces (B, ∥ · ∥B) of tempered distributions on the Euclidean space ℝ d . In fact, such spaces have a double module structure, over some Beurling algebra with respect to convolution, and with respect to pointwise multiplication over some Fourier Beurling algebra. Combining this double module structure with functional analytic arguments which describe the approximation of convolution operators by discrete convolutions we are able to verify the BAP, in fact, for most cases even the Metric Approximation Property (MAP) for such Banach space. The family of spaces under consideration is very rich and contains virtually all the classical function spaces relevant for mathematical analysis, as long as the Schwartz space (ℝ d) is dense in (B, ∥ · ∥B). In particular, all the reflexive spaces in this family are included. Moreover, this family of Banach spaces is closed with respect to intersections, sums and various interpolation methods. [ABSTRACT FROM AUTHOR]

In this paper, we use a previously developed measles model to forecast measles in Turkey for the period 1970–2021. We study the structural identifiability of the model both by hand and using software. By hand, we assume the prevalence and the total population size are given. Using software, we assume the incidence and the total population size are given. The model is structurally identifiable if one of the three parameters is fixed. We notice that Turkey has a significant change in time of the immigration rate and vaccination proportions, so we assume these two quantities are time-dependent. We fit the nonautonomous model to the measles incidences in Turkey for 1970–2021. We perform practical identifiability of the fitted model, and find that all parameters but one are practically identifiable. When fixing the unidentifiable parameter to a value derived from additional data, we obtain that all parameters are practically identifiable. [ABSTRACT FROM AUTHOR]

The growing demand for maintaining secure communication channels with the advancements in digital technologies has led to an intensified interest in designing reliable image encryption schemes. Despite various encryption schemes that have been used, some are considered to have insecurity regarding data transmission and multimedia. Motivated by this concern, this paper proposes a new color image encryption algorithm of a multi-key generation-based nD-Hyperchaotic (HC) system. The new algorithm achieves Shannon’s confusion and diffusion principles using a two S-box generation approach, where the first S-box is generated from the proposed nD-HC system and the resulting sequence is used to increase encryption complexity, while the second S-box is generated from (n + i)D-HC system. Afterward, mathematical analysis is carried out to showcase the robustness and efficiency of the proposed algorithm, as well as its resistance to visual, statistical, differential, and brute-force attacks. The proposed scheme successfully passes all NIST SP 800 suite tests. The cryptographic system demonstrated by the proposed scheme has proven to have outstanding performance through simulation tests, which indicates promising potential applicability aspects in secure and real-time image communication settings. [ABSTRACT FROM AUTHOR]

In this paper, we construct and analyze a mathematically reasonable and simplest population dynamics model based on Mark Granovetter’s idea for the spread of a matter (rumor, innovation, psychological state, etc.) in a population. The model is described by a one-dimensional difference equation. Individual threshold values with respect to the decision-making on the acceptance of a spreading matter are distributed throughout the population ranging from low (easily accepts it) to high (hardly accepts). Mathematical analysis on our model with some general threshold distributions (uniform; monotonically decreasing/increasing; unimodal) shows that a critical value necessarily exists for the initial frequency of acceptors. Only when the initial frequency of acceptors is beyond the critical, the matter eventually spreads over the population. Further, we give the mathematical results on how the equilibrium acceptor frequency depends on the nature of threshold distribution. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the classical SIR epidemic model by replacing the simple bilinear transmission rate by a nonlinear one. Our results show that in the presence of environmental fluctuations represented by Brownian motion and that mainly act on the transmission rate, the generalized non-concave force of infection adopted here, greatly affects the long-time behavior of the epidemic. Employing the Markov semigroup theory, we prove that the model solutions do not admit a unique stationary distribution but converge to 0 in p th moment for any p > 0. Furthermore, we prove that the disease extinguishes asymptotically exponentially with probability 1 without any restriction on the model parameters and we also determine the rate of convergence. This is an unexpected qualitative behavior in comparison with the existing literature where the studied epidemic models have a threshold dynamics behavior. It is also a very surprising behavior regarding the deterministic counterpart that can exhibit a rich qualitative dynamical behaviors such as backward bifurcation and Hopf bifurcation. On the other hand, we show by several numerical simulations that as the intensity of environmental noises becomes sufficiently small, the epidemic tends to persist for a very long time before dying out from the host population. To solve this problem and to be able to manage the pre-extinction period, we construct a new process in terms of the number of infected and recovered individuals which admits a unique invariant stationary distribution. Finally, we discuss the obtained analytical results through a series of numerical simulations. [ABSTRACT FROM AUTHOR]

Quantitative phase imaging (QPI) technology is one of the important techniques for nondestructive imaging of a cell's morphology. In QPI, the decoupling of refractive index (RI) and thickness of a cell is a key problem. We aim at the multiple hypothesis constraints (MHC) shortcomings of the traditional method in the decoupling of multi-media and nonspherical cells. A method is proposed to decouple the RI and the thickness of a cell under three-wavelength phase imaging in this paper. In this method, the sample's RI and thickness distributions can be obtained by solving three-wavelength phase equations using the approximate setting under dispersion based on the optical dispersion theories. In simulation experiments, the results show that the method can effectively decouple the RI and thickness for homogeneous and multi-media nonspherical cells and has high accuracy. Because the method in this paper is obtained by using few approximate assumptions and strict mathematical analysis, it can decouple the RI and thickness of nuclear cells with any shape, and moreover, it provides an important basis for the technological development of cell morphology analysis. [ABSTRACT FROM AUTHOR]

This paper presents a survey and critical analysis of the mathematical literature on modeling and simulation of human crowds taking into account behavioral dynamics. The main focus is on research papers published after the review [N. Bellomo and C. Dogbè, On the modeling of traffic and crowds: A survey of models, speculations, and perspectives, SIAM Rev. 53 (2011) 409–463], thus providing important research perspectives related to new, emerging trends. The presentation addresses the scaling problem corresponding to microscopic (individual-based), mesoscopic (kinetic), and macroscopic (hydrodynamic) modeling and analysis. A multiscale vision guides the overall content of the paper. The critical analysis of the overall content naturally leads to research perspectives. A selection of them is brought to the attention of the interested reader together with hints on how to deal with them. [ABSTRACT FROM AUTHOR]

This paper is concerned with the mathematical analysis of terminal value problems (TVP) for a stochastic nonclassical diffusion equation, where the source is assumed to be driven by classical and fractional Brownian motions (fBms). Our two problems are to study in the sense of well-posedness and ill-posedness meanings. Here, a TVP is a problem of determining the statistical properties of the initial data from the final time data. In the case 0 < β ≤ 1 , where β is the fractional order of a Laplace operator, we show that these are well-posed under certain assumptions. We state a definition of ill-posedness and obtain the ill-posedness results for the problems when β > 1. The major analysis tools in this paper are based on properties of stochastic integrals with respect to the fBm. [ABSTRACT FROM AUTHOR]

Waterborne diseases are illnesses caused by pathogenic bacteria that spread through water and have a negative influence on human health. Due to the involvement of most countries in this vital issue, accurate analysis of mathematical models of such diseases is one of the first priorities of researchers. In this regard, in this paper, we turn to a waterborne disease model for solution's existence, HU-stability, and computational analysis. We transform the model to an analogous fractal-fractional integral form and study its qualitative analysis using an iterative convergent sequence and fixed-point technique to see whether there is a solution. We use Lagrange's interpolation to construct numerical algorithms for the fractal-fractional waterborne disease model in terms of computations. The approach is then put to the test in a case study, yielding some interesting outcomes. [ABSTRACT FROM AUTHOR]

This paper is concerned with a reaction–diffusion–advection chemostat model with two species growing and competing for a single-limited resource. By taking the growth rates of the two species as variable parameters, we study the effect of growth rates on the dynamics of this system. It is found that there exist several critical curves, which may classify the dynamics of this system into three scenarios: (1) extinction of both species; (2) competitive exclusion; (3) coexistence. Moreover, we take numerical approaches to further understand the potential behaviors of the above critical curves and observe that the bistable phenomenon can occur, besides competitive exclusion and coexistence. To further study the effect of advection and diffusion on the dynamics of this system, we present the bifurcation diagrams of positive equilibrium solutions of the single species model and the two-species model with the advection rates and the diffusion rates increasing, respectively. These numerical results indicate that advection and diffusion play a key role in determining the dynamics of two species competing in a flow reactor. [ABSTRACT FROM AUTHOR]

This paper represents a new integrable trans-admittance mode universal filter employing an active building block, i.e., Voltage Differencing Current Conveyor, and all grounded passive elements. The proposed circuit can easily realize all five, widely used, filter responses, i.e., bandpass, high pass, low pass, all pass and band-reject. The designed circuit configuration provides favorable impedances at the input as well as output ports. Independent tunability of its gain parameter and orthogonal tunability of its quality factor and operating frequency are some of the noteworthy features of the designed circuit. The simulations of the designed filter are verified by 180-nm Complementary Metal Oxide Semiconductor (CMOS) technology in the SPICE simulation environment. Validation of the proposed design is done by experimental work along with the regular mathematical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we present a brief history of artificial intelligence (AI) research for more than 70 years since its inception. We begin with an analysis of the mathematical, engineering, psychological and philosophical foundations enabling modern AI. We then outline and give examples of the three primary research thrusts the discipline has taken over its existence. We conclude offering both important criticisms as well as describing the future promise for current AI research and practice. [ABSTRACT FROM AUTHOR]

In this paper, we study a mathematical model of Hepatitis C Virus (HCV) infection. We present a compartmental mathematical model involving healthy hepatocytes, infected hepatocytes, non-activated dendritic cells, activated dendritic cells and cytotoxic T lymphocytes. The derivative used is of non-local fractional order and with non-singular kernel. The existence and uniqueness of the system is proven and its stability is analyzed. Then, by applying the Laplace Adomian decomposition method for the fractional derivative, we present the semi-analytical solution of the model. Finally, some numerical simulations are performed for concrete values of the parameters and several graphs are plotted to reveal the qualitative properties of the solutions. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamical behavior of the modified May–Holling–Tanner model in the presence of dynamic alternative resources. We study the role of dynamic alternative resources on the survival of the species when there is prey rarity. Detailed mathematical analysis and numerical evaluations, including the situation of ecosystem collapsing, have been presented to discuss the coexistence of species', stability, occurrence of different bifurcations (saddle-node, transcritical, and Hopf) in three cases in the presence of prey and alternative resources, in the absence of prey and in the absence of alternative resources. It has been obtained that the multiple coexisting states and their stability are outcomes of variations in predation rate for alternative resources. Also, the occurrence of Hopf bifurcation, saddle-node bifurcation, and transcritical bifurcation are due to variations in the parameters of dynamic alternative resources. The impact of dynamic alternative resources on species' density reveals the fact that if the predation rate for alternative resources increases, then the prey biomass increases (under some restrictions), and variations in the predator's biomass widely depend upon the quality of food items. This study also points out that the survival of predators is possible in the absence of prey. In the theme of ecological balance, this study suggests some theoretical points of view for the eco-managers. [ABSTRACT FROM AUTHOR]

Influenced by seasonal changes, the infection rate of many infectious diseases fluctuates in cycles. In this paper, we propose and investigate an SIRS model on a scale-free network. To model seasonality, we assume that the infection rate is periodic. The existence and positivity of solutions of the proposed model are proved and the basic reproduction number ℜ 0 is defined. The global stability of steady states is determined by rigorous mathematical analysis. When ℜ 0 < 1 , the disease-free equilibrium E 0 is globally asymptotically stable. When ℜ 0 > 1 , the system has a unique positive periodic solution E * , and E * is globally asymptotically stable. Numerical simulations are performed to support our theoretic results, and the effects of various parameters on the amplitude and mean of infected individuals are studied. The sensitivity of parameters of the basic reproduction number ℜ 0 is solved by the Sobol global sensitivity analysis method, and the results show that the effects of the parameters β 0 and α on ℜ 0 are remarkable. [ABSTRACT FROM AUTHOR]

In this paper, we analyze a new Ito stochastic differential equation model for untreated human glioblastomas. The model was the best fit of the average growth and variance of 94 pairs of a data set. We show the existence and uniqueness of solutions in the positive spatial domain. When the model is restricted in the finite domain (0 , b) , we show that the boundary point 0 is unattainable while the point b is reflecting attainable. We prove there is a unique ergodic stationary distribution for any non-zero noise intensity, and obtain the explicit probability density function for the stationary distribution. By using Brownian bridge, we give a representation of the probability density function of the first passage time when the diffusion process defined by a solution passes the point b firstly. We carry out numerical studies to illustrate our analysis. Our mathematical and numerical analysis confirms the soundness of our randomization of the deterministic model in that the stochastic model will set down to the deterministic model when the noise intensity approaches zero. We also give physical interpretation of our stochastic model and analysis. [ABSTRACT FROM AUTHOR]

Enlightened by the Caputo type of fractional derivative, this research paper is the analysis of a mathematical model of generalized thermoelastic diffusion with memory-dependent derivative (MDD) for an isotropic infinite medium with a cylindrical cavity in the context of dual-phase lag model. The surface of the cavity is traction free and subjected to harmonically heat sources with constant angular frequency of thermal vibration. Laplace transform technique has been used to solve the problem. Later eigenvalue approach is used to obtain the analytical expressions for different physical fields in the transformed domain. Finally to obtain the solutions in the real-time domain, the Riemann-sum approximation method is used. According to the graphical representations corresponding to the numerical results, the effect of heat source speed on temperature, displacement, stress, mass concentration and chemical potential are studied. The effect of memory-dependent parameters, as well as in the absence of MDD on physical quantities are also demonstrated. [ABSTRACT FROM AUTHOR]

This paper proposes new cointegration tests based on instrumental variable (IV) estimation. An important property of our tests is that the asymptotic distribution remains standard normal (orChi-square) regardless of the number of regressors, differing deterministic terms, structural dummies, and inclusion of stationary covariates. Thus, our IV cointegration tests have the operational advantage that they do not depend on nuisance parameters. As such, we can incorporate stationary covariates into a model to enhance power without affecting the asymptotic distribution of the test. This is important because it alleviates the need to tabulate the critical values for every possible case or to bootstrap the critical values. [ABSTRACT FROM AUTHOR]

In this paper, we unify the Riesz transform with the Teager–Kaiser energy operator (TKEO) and monogenic multi-resolution analysis in comparison to conventional gradient and Riesz transform-based approaches. We show that benefits of our approach maintain the following aspects of different known estimators: the stability of mixed (higher) order of derivatives, like given in TKEO, the all-pass filter characteristics featuring the Riesz transform and the scale-based analysis. Furthermore, we demonstrate the ability of the considered technique for extracting structural defects at different scales, estimating orientation or being used for 2D demodulation of amplitude- and phase modulated signals, like interferometric fringe patterns. Additionally, the abilities of orientation estimation of 3D data is demonstrated. From the viewpoint of mathematical analysis, we will emphasize the connection to monogenic higher dimensional signals, Clifford frames, and monogenic multi-resolution signal analysis. Furthermore, we will discuss higher order Riesz transform. [ABSTRACT FROM AUTHOR]

This paper studies the capability of digital architecture to mimic fractal behavior. As chaotic attractors realized digitally had opened many tracks, digital designs mimicking fractals may ultimately achieve the same. This study is based on a complex single-dimensional discrete chaotic system known as the generalized positive logistic map. The fractals realized from this system are linked to the results of the mathematical analysis to understand the fractal behavior with different variations. A digital hardware architecture manifesting the fractal behavior is achieved on FPGA, showing a fractal entity experimentally. With this digital realization, it is hoped that fractals can follow the example of chaotic attractors digital applications. [ABSTRACT FROM AUTHOR]

Chikungunya fever, caused by Chikungunya virus (CHIKV) and transmitted to humans by infected Aedes mosquitoes, has posed a global threat in several countries. In this paper, we investigated a modified within-host Chikungunya virus (CHIKV) infection model with antibodies where two routes of infection are considered. In a first step, the basic reproduction number ℛ 0 was calculated and the local and global stability analysis of the steady states is carried out using the local linearization and the Lyapunov method. It is proven that the CHIKV-free steady-state E 0 is globally asymptotically stable when ℛ 0 ≤ 1 , and the infected steady-state E 1 is globally asymptotically stable when ℛ 0 > 1. In a second step, we applied an optimal strategy in order to optimize the infected compartment and to maximize the uninfected one. For this, we formulated a nonlinear optimal control problem. Existence of the optimal solution was discussed and characterized using some adjoint variables. Thus, an algorithm based on competitive Gauss–Seidel-like implicit difference method was applied in order to resolve the optimality system. The theoretical results are confirmed by some numerical simulations. [ABSTRACT FROM AUTHOR]

As generalization of semigroups, Karl Menger introduced in the 1940th algebras of multiplace operations. Such algebras satisfy the superassociative law, a generalization of the associative law. Menger algebras are defined as models of this superassociative law. Cayley's theorem for semigroups says that any model of the associative law is isomorphic to a transformation semigroup. R. M. Dicker proved in 1963 that every Menger algebra of rank n is isomorphic to a Menger algebra of n -ary operations on some set. The composition of terms in which each variable occurs at most r -times, so-called r -terms, leads to partial algebras where the superassociative law is satisfied as a weak identity. In this paper, we introduce the concepts of a partial Menger algebra, a unitary partial Menger algebra and of a generalized partial Menger algebra. We prove that r -terms of some type form a generalized partial Menger algebra with infinitely many nullary operations. Using weak identities and weak isomorphisms, Dicker's result will be extended to partial Menger algebras and to unitary partial Menger algebras. [ABSTRACT FROM AUTHOR]

Enhancing traffic flow plays an important role in the traffic management of urban arterial networks. The policy of prohibiting left-turn (PLT) at selected highly demanded intersections has been adopted as an attempt to increase the efficiency at these intersections. In this paper, we study the impact of PLT by mathematical analysis and simulations based on the cellular automaton model. Using the flow-density relation, three system performance indexes are examined: the average trip completion rate, the average traffic flow, and the average velocity of vehicles. Different route guidance strategies, including the shortest path and the quickest path, are investigated. We show that when left turn is prohibited, vehicles are distributed more homogeneously in the road network, and the system performs better and reaches a higher capacity. We also derive a critical length of link, above which the benefit of PLT will decrease. [ABSTRACT FROM AUTHOR]

Dengue is among the most important infectious diseases in the world. The main contribution of our paper is to present a mixed system of partial and ordinary differential equations. This combined model is a generalization of the two presented mathematical models (A. L. de Araujo, J. L. Boldrini and B. M. Calsavara, An analysis of a mathematical model describing the geographic spread of dengue disease, J. Math. Anal. Appl.444 (2016) 298–325) and (L. Cai, X. Li, N. Tuncer, M. Martcheva and A. A. Lashari, Optimal control of a malaria model with asymptomatic class and superinfection, Math. Biosci.288 (2017) 94–108), describing the geographic spread of dengue disease. Our model has the ability to consider the possibility of asymptomatic infection, which leads to investigate the effect of dengue asymptomatic individuals on disease dynamics and to go into the possibility of superinfection of asymptomatic individuals. In the light of considering these factors, as well as the movements of human and mature female mosquitoes, more realistic modeling of dengue disease can be achieved. We present a mathematical analysis and show the global existence of a unique non-negative solution to this model and then establish ways to control dengue disease using numerical simulations and sensitivity analysis of model parameters (which are related to the contact rates and death rate of winged mosquitoes). To show different biological behaviors, we provide several numerical results, showing the role of parameters in controlling dengue disease transmission. From our numerical simulations, it can also be concluded that local control of dengue transmission can be done at a lower cost. [ABSTRACT FROM AUTHOR]

The ellipsoidal magnetization model has a wide range of application scenarios. For example, in aviation magnetic field prospecting, mineral prospecting, seabed prospecting, and UXO (unexploded ordnance) detection. However, because the existing ellipsoid magnetization formula is relatively complicated, the detection model is usually replaced by a dipole. Such a model increases the error probability and poses a significant challenge for subsequent imaging and pattern recognition. Based on the distribution of ellipsoid gravity potential and magnetic potential, the magnetic anomaly field distribution equation generated by the ellipsoid is deduced by changing the aspect ratio, making the ellipsoid equivalent to a sphere. The result of formula derivation shows that the two magnetic anomaly fields are consistent. This paper uses COMSOL finite element software to model UXO, ellipsoids, and spheres and analyzes magnetic anomalies. The conclusion shows that the ellipsoid model can completely replace the UXO model when the error range of 1nT is satisfied. Finally, we established two sets of ellipsoids and calculated the magnetic anomalous field distributions on different planes using deduction formulas and finite element software. We compared the experimental results and found that the relative error of the two sets of data was within ± 0. 2 5 ‰. Error analysis found that the error distribution is standardized and conforms to the normal distribution. The above mathematical analysis and finite element simulation prove that the calculation method is simple and reliable and provides a magnetic field distribution equation for subsequent UXO inversion. [ABSTRACT FROM AUTHOR]

In this paper, we propose detailed and reasonable viral dynamics by using a multi-compartment model that incorporating the age since the infection of multiple infected cells, multiple target cells (Langerhans-cells and CD4 + T-cells), multiple viral strains (CCR5 and CXR4 HIV) and multiple infection routes (cell-to-cell and cell-to-virus). The basic reproduction number, R 0 , of the whole model is derived from two transmission mechanisms: one is the potential trigger from the infection routes for a single target cell and other is the joint effect of multiple viral infections for multi-target cells. Accordingly, we study the global stability of the steady states for the single target model. For the whole model, we prove that the infection-free steady state is globally asymptotically stable if R 0 < 1 , whereas viruses persist uniformly if R 0 > 1. Numerical simulations are carried out to illustrate the theoretical results. Sensitive analyses expound the effect of model parameters on the comprehensive reproduction number. It is remarkable to find that simultaneous control of HIV infection for two target cells can effectively reduce the viral loads within-host. Finally, our work suggests that the synergetic mechanism of multi-target cells and multi-strain cannot be ignored during treatment. [ABSTRACT FROM AUTHOR]

In this paper, we propose and investigate an SIRS model with age structure and two delays. Both the infected and the recovered individuals have age structure, the infection rate (from the infective to the susceptible) and the immune loss rate (from the recovered to the susceptible) are related to two independent time delays, respectively. We prove that the proposed age structured SIRS model is well-posed by using the C 0 -semigroup theory. The basic reproduction number ℜ 0 is given, and the unique endemic equilibrium exists when ℜ 0 > 1 , while the disease-free equilibrium always exists. A rigorous mathematical analysis for the stability of two equilibria is provided. The disease-free equilibrium is local asymptotically stable if ℜ 0 < 1 , and the endemic equilibrium is local asymptotically stable if ℜ 0 > 1 and τ l = 0. Finally, we give numerical simulations to verify our results. [ABSTRACT FROM AUTHOR]

Reduced population growth at low density has important implications for conservation, colonization success, and wildlife management. In this context, the Allee effect, i.e. the positive relationship between per capita growth rate and biomass of small population density, is a crucial biological phenomenon since it is directly related to population extinction. The present paper deals with a two-species interacting model with a predator–prey relationship, where the prey population experiences the mate-finding Allee effect caused by the predator. We assume that the searching efficiency of prey individuals decreases linearly with predator density due to predation fear and investigate how predation intensity affects predator–prey dynamics. Moreover, we consider the Monod–Haldane type functional response for predator–prey interactions, which shows group defense of prey against the predator. We provide detailed mathematical analyses, including the positivity and boundedness of solutions, all biologically feasible equilibria, and their local and global stabilities. From our detailed mathematical analyses, we observe that when the carrying capacity of prey is low, at most one interior equilibrium exists, and system dynamics is simple compared to the case with high carrying capacity in which multiple coexistence equilibria may exist. We discuss three codimension-one bifurcations mathematically, e.g. Hopf bifurcation, transcritical bifurcation, saddle-node bifurcation. We notice bistability in the system when there are two interior equilibria with high carrying capacity. However, a unique attractor exists when there is only a single interior equilibrium and both populations persist. We perform extensive numerical simulations by varying two parameters simultaneously and explore how the system dynamics become complex when carrying capacity is high compared to low carrying capacity. Moreover, we discuss other important biological phenomena, e.g. the paradox of enrichment, bubbling phenomenon, etc. [ABSTRACT FROM AUTHOR]

This paper presents an inductor less wideband low noise amplifier (LNA) with an area of 0.3 mm2, using 130 nm SiGe BiCMOS technology targeted for 5G WiGig wireless application. A g m boosting amplifier used at the intermediate node of the cascode topology to reduce the noise contribution of the common base (CB) transistor for the first time in SiGe HBT technology. Mathematical analysis shows that the proposed high frequency g m boosting technique on the CB transistor can be optimally tuned for either low NF or high linearity. Furthermore, the circuit incorporates variable capacitors for multimode capability, ensuring optimal performance in all four WiGig channels. Post layout EM simulation of the circuit shows that the resultant LNA has a maximum gain of 21.08 dB with the − 3 dB frequency over 56 GHz to 67.3 GHz. The proposed LNA exhibits a minimum noise figure of 4.3 dB and shows high linearity with an input referred I P 3 of − 2.7 dB. The designed when operated using supply voltage of 1.2 V consumes a total dc power of 8.9 mW. [ABSTRACT FROM AUTHOR]

We propose a mathematical model studying a within-host infection dynamics of SARS-CoV-2 in pneumocytes. This model incorporates immune response, vaccination and antiviral drugs. The crucial properties of the model — the existence, positivity and boundary of solutions — are established. Equilibrium points and the basic reproduction number are calculated. The stability of each equilibrium point is analyzed. Optimal control is applied to the model by adding three control variables: vaccination, treatment by Favipiravir and treatment by Molnupiravir. Numerical results show that each individual control could reduce SARS-CoV-2 infection in some aspects; however, with a combination of three controls, we obtain the best results in reducing SARS-CoV-2 infection. This study has emphasized the importance of prevention by vaccine and the antiviral treatments. [ABSTRACT FROM AUTHOR]

Green's ∗-relations on semirings satisfying additional identities x n ≈ x and 2 (x + y) ≈ 2 x + 2 y are studied. Equivalent characterizations of ℋ ∗ + ∧ ℒ ∗ • , ℋ ∗ + ∧ ℛ ∗ • , ℋ ∗ + ∧ ∗ • , ℋ ∗ + ∧ ℋ ∗ • , ℋ ∗ + ∨ ℒ ∗ • , ℋ ∗ + ∨ ℛ ∗ • , ℋ ∗ + ∨ ∗ • and ℋ ∗ + ∨ ℋ ∗ • are obtained and equivalent conditions are given for the above relations to be congruences. It is proved that semiring classes determined by these congruences are varieties. [ABSTRACT FROM AUTHOR]

A model for assessing the impact of key population at risk in spreading HIV/ AIDS is designed. The model is shown to have a globally asymptotically stable (GAS) disease-free equilibrium whenever the associated reproduction number is less than unity. It has a unique GAS endemic equilibrium whenever reproduction number exceeds unity, if there is no back and forth movement in susceptible classes. It is shown that if infected individuals with high risk abandon their risky behavioral practices, then the disease burden will reduce. Furthermore, if infected individuals with low risk do not adopt risky behaviors then the transmission of the disease will decrease. Partial Rank Correlation Coefficient (PRCC) indices are assessed using all the infection-related classes and basic reproduction number of the model. Uncertainty and sensitivity analysis results show that controlling the effective contact rate, disease-induced death rate in AIDS stage with low and high risk classes will help controlling the transmission of the disease. [ABSTRACT FROM AUTHOR]

Ergodic properties of a stochastic medium complexity model for atmosphere and ocean dynamics are analyzed. More specifically, a two-layer quasi-geostrophic model for geophysical flows is studied, with the upper layer being perturbed by additive noise. This model is popular in the geosciences, for instance to study the effects of a stochastic wind forcing on the ocean. A rigorous mathematical analysis however meets with the challenge that in the model under study, the noise configuration is spatially degenerate as the stochastic forcing acts only on the top layer. Exponential convergence of solutions laws to the invariant measure is established, implying a spectral gap of the associated Markov semigroup on a space of Hölder continuous functions. The approach provides a general framework for generalized coupling techniques suitable for applications to dissipative SPDEs. In case of the two-layer quasi-geostrophic model, the results require the second layer to obey a certain passivity condition. [ABSTRACT FROM AUTHOR]

The article introduce a generalized viscosity method which includes a sequence of contractive mappings for approximating solutions of fixed point problem of finitely many resolvents of a lower semi-continuous function together with a fixed point problem of countable infinite family of L-Lipschitzian and quasi-pseudocontractive mappings in Hadamard spaces.

The re-emergence of the Ebola virus disease has pushed researchers to investigate more on this highly deadly disease in order to better understand and control the outbreak and recurrence of epidemics. It is in this perspective that we formulate a realistic mathematical model for the dynamic transmission of Ebola virus disease, incorporating relevant control measures and factors such as ban on eating bush-meat, social distancing, observance of hygiene rules and containment, waning of the vaccine-induced, imperfect contact tracing and vaccine efficacy, quarantine, hospitalization and screening to fight against the spread of the disease. First, by considering the constant control parameters case, we thoroughly compute the control reproduction number ℛ 0 c from which the dynamics of the model is analyzed. The existence and stability of steady states are established under appropriate assumptions on ℛ 0 c . Also, the effect of all the control measures is investigated and the global sensitivity analysis of the control reproduction number is performed in order to determine the impact of parameters and their relative importance to disease transmission and prevalence. Second, in the time-dependent control parameters case, an optimal control problem is formulated to design optimal control strategies for eradicating the disease transmission. Using Pontryagin's Maximum Principle, we derive necessary conditions for optimal control of the disease. The cost-effectiveness analysis of all combinations of the control measures is made by calculating the infection averted ratio and the incremental cost-effectiveness ratio. This reveals that combining the four restrictive measures conveyed through educational campaigns, screening, safe burial and the care of patients in health centers for better isolation is the most cost-effective among the strategies considered. Numerical simulations are performed to illustrate the theoretical results obtained. [ABSTRACT FROM AUTHOR]

This article introduces temporally stochastic cellular automata where a cell of the cellular system can be updated using one of the two elementary cellular automata rules, say f and g. The f is the default rule and g is temporally applied to the overall system with some probability that acts as noise to the system. As the mathematical analysis of such system is a difficult task, we use qualitative and quantitative simulations to study the dynamics of these temporally stochastic cellular automata. We are specially interested to exploring if it is possible that two periodic (resp. chaotic) rules together depict chaotic (resp. periodic) dynamics. To answer these questions, we fully classify temporally stochastic cellular automata. The study further observes phase transition and various types of class transition in the temporally stochastic cellular automata. [ABSTRACT FROM AUTHOR]

A mathematical analysis method is employed to solve the bending problem of slip clamped shallow spherical shell on elastic foundation. Using the slip clamped boundary conditions, the differential equations of the problem are simplified to a biharmonic equation. Using the R -function, the fundamental solution and the boundary equation of the biharmonic equation, a function is established. This function satisfies the homogeneous boundary condition of the biharmonic equation. The biharmonic equation of the slip clamped shallow spherical shell bending problem on elastic foundation is transformed to Fredholm integral equation of the second kind by using Green's formula. The vector expression of the integral equation kernel is derived. Choosing a suitable form of the normalized boundary equation, the singularity of the integral equation kernel is overcome. To obtain the numerical results, the discretization of the integral equation of the bending problem is conducted. The treatment of singular term in the discretization equation is to use the integration by parts. Numerical results of rectangular, trapezoidal, pentagonal, L-shaped and concave shape shallow spherical shells show high accuracy of the proposed method. The numerical results show fine agreement with the ANSYS finite element method (FEM) solution, which shows the proposed method is an effective mathematical analysis method. [ABSTRACT FROM AUTHOR]

Measles is a highly transmissible disease in children around the world. According to the World Health Organization (WHO), 73% of deaths of children were due to measles in 2018. This study describes the physical solution of the SIQR model for measles spread under the effect of natural delay amongst different compartments. By three different numerical techniques, the efficacies of solutions of the underlying system have been compared and a clear preference of nonstandard finite-difference (NSFD) scheme over the rest has been established. It has also been observed, on principle, that the NSFD formulation recovers all the essential traits of a continuous model namely the boundedness, positivity and stability of equilibriums of populations. The numerical results have also been supported by a very strong classical analysis of the model where the existence of a solution vector in explicit subsets of the function spaces has been guaranteed which leads to optimization of fixed-point methods. [ABSTRACT FROM AUTHOR]

This work presents an effective and straightforward frequency compensation scheme in CMOS three-stage amplifiers. Using a differential block in the compensation network, the proposed circuit shows independent and large first dominant pole regarding the DC gain path. The presented three-stage architecture is frequency-compensated just by a single Miller capacitor. Mathematical analysis is presented along with ample simulations that are performed using TSMC 0.18- μ m CMOS technology. According to the results, the proposed circuit shows DC gain equal to 118 dB, GBW equal to 466 MHz, PM equal to 74.3∘ and 1.2 mW as power consumption, respectively. The high values of DC gain and GBW make the proposed amplifier appropriate for more speedy operations such as high-speed modulators and data converters. [ABSTRACT FROM AUTHOR]

Atherosclerosis, a long-term inflammatory affliction, occurs due to plaque accumulation in the intima, the innermost layer of artery. It is one of the prime causes of deaths from several cardio-vascular diseases. The primary interaction between oxidized low density lipoprotein (LDL) and macrophages in forming fatty steak is presented here in terms of a nonlinear reaction-diffusion system in one spatial dimension under Neumann boundary conditions. Both the spatio-temporal and the temporal models are analyzed qualitatively. Numerical simulations of both the model systems lead to three significant model parameters with respect to which bifurcations are found. Bifurcating parameters indicate possible developments of various therapeutic strategies in order to establish any preventative measures for an individual or group of patients. It has been found that ingestion rate of oxidized LDL by macrophages has a great impact on the plaque forming process. [ABSTRACT FROM AUTHOR]