Theory Of Equations Research Articles

Fenomena Phubbing: Peran Teknologi Komunikasi Dalam Perubahan Interaksi Sosial

The rapid advances in communication technology have an impact on our daily lives, careers, and modes of communication. IoT (Internet of Things), e-learning, AI (Artificial Intelligence), cloud computing, mobile apps, virtual reality (VR), and augmented reality (AR) communication are some of the key aspects in the development of communication technology. These trends explain how advancements in communication technology could impact daily interactions and lifestyle choices. Even while these developments create opportunities for efficiency and connectivity, it's essential to understand and deal with the societal problems and consequences that these developments also bring with it. Phubbing has become a thing as a consequence of technology use gone wrong. "Phubbing" is the practice of someone spending excessive amounts of time, especially during social interactions, attached to an electronic gadget, such as a smartphone. The goal of this research is to determine how phubbing affects social relationships and how advancements in technology contributed to this trend. Media Dependency Theory and Media Equation Theory analysis are used to support this research, which uses a qualitative literature review approach from multiple relevant journals. The findings of this study demonstrate that the phenomenon of phubbing and its effects on social interaction are the outcome of media dependency caused by technological advancements.

Mathematical modelling of COVID-19 outbreak using caputo fractional derivative: stability analysis

The novel coronavirus SARS-Cov-2 is a pandemic condition and poses a massive menace to health. The governments of different countries and their various prohibitory steps to restrict the virus's expanse have changed individuals' communication processes. Due to physical and financial factors, the population's density is more likely to interact and spread the virus. We establish a mathematical model to present the spread of the COVID-19 in worldwide. In this article, we propose a novel mathematical model (‘ S L I I q I h R P ’) to assess the impact of using hospitalization, quarantine measures, and pathogen quantity in controlling the COVID-19 pandemic. We analyse the boundedness of the model's solution by employing the Laplace transform approach to solve the fractional Gronwall's inequality. To ensure the uniqueness and existence of the solution, we rely on the Picard-Lindelof theorem. The model's basic reproduction number, a crucial indicator of epidemic potential, is determined based on the greatest eigenvalue of the next-generation matrix. We then employ stability theory of fractional differential equations to qualitatively examine the model. Our findings reveal that both locally and globally, the endemic equilibrium and disease-free solutions demonstrate symptomatic stability. These results shed light on the effectiveness of the proposed interventions in managing and containing the COVID-19 outbreak.

Efficient Full-Frequency GW Calculations Using a Lanczos Method.

The GW approximation is widely used for reliable and accurate modeling of single-particle excitations. It also serves as a starting point for many theoretical methods, such as its use in the Bethe-Salpeter equation (BSE) and dynamical mean-field theory. However, full-frequency GW calculations for large systems with hundreds of atoms remain computationally challenging, even after years of efforts to reduce the prefactor and improve scaling. We propose a method that reformulates the correlation part of the GW self-energy as a resolvent of a Hermitian matrix, which can be efficiently and accurately computed using the standard Lanczos method. This method enables full-frequency GW calculations of material systems with a few hundred atoms on a single computing workstation. We further demonstrate the efficiency of the method by calculating the defect-state energies of silicon quantum dots with diameters up to 4nm and nearly 2,000 silicon atoms using only 20 computational nodes.

Dynamics of Rabies Transmission Model in Human and Dog Populations with Time Delay

Rabies is a fatal zoonotic disease caused by a virus through bites or saliva of an infected animal. Dogs are the main reservoir of Rabies and are responsible for most Human cases worldwide. In this research, a delay differential equations model for assessing the effects of controls and time delay as an incubation period on the transmission dynamics of Rabies in human and dog populations is formulated and analyzed. Basic properties of the model as par theories of delay differential equations are established, and the model is well-posed mathematically and biologically. Analysis of the model shows that there is a locally and globally asymptotically stable rabies-free equilibrium whenever the epidemiological threshold (the control reproduction number,) is less than unity. Furthermore, the model has a unique endemic equilibrium point when the control reproduction number, exceeds unity. Time delay is found to have an influence on the endemicity of rabies. Treatment and Vaccination of humans and dogs, coupled with an annual crop of puppies, are imposed to curtail the spread of Rabies in the populations. Numerical experiments are conducted to illustrate the theoretical results and control strategies. Delay differential equations, Effective reproduction number, Equilibria, Rabies, Stability

Cauchy Problem with Summable Initial-Value Functions for Parabolic Equations with Translated Potentials

We study the Cauchy problem for differential–difference parabolic equations with potentials undergoing translations with respect to the spatial-independent variable. Such equations are used for the modeling of various phenomena not covered by the classical theory of differential equations (such as nonlinear optics, nonclassical diffusion, multilayer plates and envelopes, and others). From the viewpoint of the pure theory, they are important due to crucially new effects not arising in the case of differential equations and due to the fact that a number of classical methods, tools, and approaches turn out to be inapplicable in the nonlocal theory. The qualitative novelty of our investigation is that the initial-value function is assumed to be summable. Earlier, only the case of bounded (essentially bounded) initial-value functions was investigated. For the prototype problem (the spatial variable is single and the nonlocal term of the equation is single), we construct the integral representation of a solution and show its smoothness in the open half-plane. Further, we find a condition binding the coefficient at the nonlocal potential and the length of its translation such that this condition guarantees the uniform decay (weighted decay) of the constructed solution under the unbounded growth of time. The rate of this decay (weighted decay) is estimated as well.

Island density scaling in reversible submonolayer growth with attachment barriers.

Island nucleation and growth play an important role in thin-film growth. One quantity of particular interest is the exponent χ, which describes the dependence of the saturation island density N_{sat}∼(D_{h}/F)^{-χ} on the ratio D_{h}/F of the monomer hopping rate D_{h} to the deposition rate F. While standard rate equation(RE) theory predicts that χ=i/(i+2) (where i is the critical island size), more recently it has been predicted that in the presence of a strong barrier to the attachment of monomers to islands, a significantly larger value χ=2i/(i+3) may be observed. While this prediction has recently been tested using kinetic Monte Carlo simulations for the case of irreversible growth corresponding to i=1, it has not been tested for the case of reversible island growth corresponding to i>1. Here we present a mean-field self-consistent RE method which we have used to study the dependence of the effective value of χ on D_{h}/F and barrier-strength for i=1,2,3, and 6. Both the no-nucleation-barrier case in which there exists a barrier for monomers to attach to islands larger than the critical island size (but not to smaller islands) and the nucleation-barrier case in which there is a barrier for monomers to attach to islands of all sizes are studied. In all cases, we find that the existence of attachment barriers significantly increases the effective value of χ for a given barrier strength. In addition, for i=1 we find good agreement between our extrapolated asymptotic value of χ and the theoretical strong-barrier prediction both with and without a nucleation barrier. In contrast, for i>1 the value of χ is significantly larger in the presence of a nucleation barrier than in its absence. In particular, while an asymptotic analysis of our results for i>1 also leads to excellent agreement with the strong barrier prediction in the presence of a nucleation barrier, in the absence of a nucleation barrier the asymptotic values are significantly lower.

Estimating Baryon Density through the CAMB and Assessing its Reliability

The Cosmic Microwave Background Radiation and its anisotropies allow us to analyze many properties and phenomena of the early universe. One such important property is the Baryon Density(Ω_b), a cosmological constant for the density of Baryons in the universe in comparison to its critical density. Baryon Density affects the interactions of matter in the early universe and therefore the analysis of CMB Anisotropies to study how matter interacts allows for the estimation of the Baryon Density in the Early Universe. Understanding Ω_b, is crucial as it reveals information about the composition of the universe, such as the amount of dark matter and dark energy, the early formation of celestial bodies and matter-antimatter asymmetry. This paper aimed to test the reliability of CAMB, a simulation algorithm for CMB anisotropies, by estimating Ω_b h^2. The CAMB mainly utilizes a combination of field equations, the Friedmann-Lemaître-Robertson-Walker metric, Fluid Equations, the Boltzmann Equation and Linear Perturbation theory in order to compute the CMB power spectra. We estimated the value of Ω_b h^2, maintaining other cosmological parameters constant and changing Ω_b h^2 from 0.01 to 0.03 in increments of 0.000625. The peaks, troughs, positions, damping scale and amplitudes of the resultant TT and TE power spectra were compared with data from the Planck Satellite. We use chi-square minimization and find the best fit value and uncertainty forΩ_b h^2 to be 0.02325 ± 0.00015. The estimated value of the baryon density from our study was compared to existing estimates to evaluate the reliability of CAMB as a simulation and source of information for further CMB Anisotropy related research, where it was confirmed to be accurate. However, further developments using wider sets of data was acknowledged with deep learning being a potential step forward.

Concentrated aqueous solutions of multivalent macroions enhance the electrical double layer capacitance and differential capacitance of a planar supercapacitor

The electrostatic properties of the ionic cloud, or electrical double layer, neutralizing a charged electrode are relevant to improve the storage of electrical energy and the efficiency of supercapacitors and/or batteries using coulombic fluids. In this work, we study the microscopic profiles of charged particles, integrated surface charge density, and the mean electrostatic potential associated to a pair of infinite parallel plates uncharged or, else, with opposite charge, in the presence of a salt-free aqueous solution constituted by big positive macroions and small anions, which interact via an explicit electrostatic coulombic potential and are dissolved in an implicit solvent. The particle profiles and the integrated surface charge density associated to Monte Carlo simulations and integral equations theory display an oscillatory or non-monotonic behaviour producing the phenomena of charge inversion and charge reversal. These phenomena are not predicted by the non-linear Poisson-Boltzmann equation, which highlights the importance of ion correlations and ionic volume excluded effects. The phenomenon of surface charge amplification is observed near the point of zero charge, which is yielded by the particle size-asymmetry. For a fixed concentration of macroions, a monotonic increase of the mean electrostatic potential difference between the charged parallel plates is predicted by simulations and theories as a function of the electrodes' charge. For a fixed surface charge density, the capacitance of the parallel plates capacitor increases when the ionic strength of the macroion's solution increases. A concavity inversion and an augment of the differential capacitance is also observed for an electrode near the point of zero charge as function of the macroion's concentration.

Power Analyses for Estimation of Complier Average Causal Effects Under Random Encouragement Designs in Education Research: Theory and Guidance

Random encouragement designs evaluate treatments that aim to increase participation in a program or activity. These randomized controlled trials (RCTs) can also assess the mediated effects of participation itself on longer term outcomes using a complier average causal effect (CACE) estimation framework. This article considers power analysis methods for such CACE analyses for a range of RCT designs, including nonclustered, clustered, and random block designs. The focus is on behavioral encouragements to promote action, such as text messaging, that are increasingly being tested in education trials. We derive asymptotic distributions of the CACE estimators using generalized estimating equations theory, which underlie the power formulas. We incorporate noncompliance from both the actual receipt of the encouragement and participation itself. An illustrative power analysis provides sample size guidance using an available Shiny R dashboard.

Existence of solutions by coincidence degree theory for Hadamard fractionaldifferential equations at resonance

Existence of solutions by coincidence degree theory for Hadamard fractionaldifferential equations at resonance

Influence of media campaigns efforts to control spread of COVID-19 pandemic with vaccination: A modeling study

Abstract The outbreak of coronavirus disease 2019 (COVID-19) has been declared a pandemic by the world health organization on March 11, 2020,. Here, a nonlinear mathematical model is proposed and analyzed to study the spread of coronavirus disease in a human habitat. In modeling the dynamics, the total population is divided into five subclasses: susceptible population, asymptomatic infective population, symptomatic infective population, recovered population, and vaccinated population. It is assumed that the disease is transmitted directly from infectives. It is further assumed that due to the effect of media, susceptible individuals become aware about the disease and avoid contact with the infectives. The analysis of the model is performed using the stability theory of differential equations. Furthermore, conditions that influence the persistence of the system are obtained. We have also conducted numerical simulations to validate the analytical results. The model analysis shows that with an increase in media awareness, the spread of coronavirus disease decreases with a decrease in the number of infective populations.

A Test for Global Attractivity of Linear Dynamic Equations with Delay

In this paper, we consider the delay dynamic equation Based on Lyapunov’s method, we study global attractivity of the trivial solution of (∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$*$$\\end{document}). Our new result generalizes some well-known results in the theory of difference and differential equations to dynamic equations of the form (∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$*$$\\end{document}). We also present some examples on nonstandard time scales to illustrate the importance of the new result.

Grain refinement mechanism in adiabatic shear band of solution treated Ti–10V–2Fe–3Al alloy under high strain rate

The grain refinement mechanism in the adiabatic shear band (ASB) of solution treated Ti–10V–2Fe–3Al alloy was investigated under high strain rates using a split Hopkinson pressure bar and hat-shaped specimens. The TEM results show that elongated and parallel grains are the major characteristics of the transition region between the matrix and the centre of the ASB. The central region of the ASB consists of ultrafine and equiaxed recrystallized grains with a typical size of 100 nm. According to the classical one-dimensional Fourier heat conduction equation and recrystallization theory calculations, it is proved that ultrafine and equiaxed recrystallized grains did not undergo significant growth during the cooling stage after deformation. The thermodynamics and kinetics calculated results indicate that instant grain refinement within the ASB is due to the rotational dynamic recrystallization (RDR) that occurs during the deformation process.

Fractional Lindley distribution generated by time scale theory, with application to discrete-time lifetime data

ABSTRACT The fractional Lindley distribution is used to model the distribution of perturbations in count data regressions, which allow for dealing with widely dispersed data. It is obtained from the non-fractional Lindley distribution by replacing the support T = R + by T = N ∖ { 0 } and applying time scale theory, whose ambition is to unify the theories of difference equations and differential equations, integral and differential calculus, and the calculus of finite differences. It thus provides a framework for the study of dynamical systems in discrete-continuous time. Delta moments are discrete-time Laplace transforms of the frequency function of the fractional Lindley distribution. The parameter of the fractional Lindley distribution is estimated by least squares, weighted least squares, maximum likelihood, moments, and proportions. The moment estimator always exists, so that delta moments result from the nabla Laplace transform of the frequency function of the fractional Lindley distribution. The maximum likelihood estimates have the least mean-square errors. The proportion method works satisfactorily only when the mode of the distribution is null and the proportion of zeros is high. A simulation allows for quantifying the mean-square errors associated with the estimators. A count regression based on the fractional Lindley distribution with data on the total number of stays after hospital admission among U.S. residents aged 65 and over shows that the Akaike information criteria is significantly lower than with the uniform Poisson and Poisson regressions.

Magneto-optical anisotropies of two-dimensional antiferromagnetic MPX3 from first principles

Here we systematically investigate the impact of the spin direction on the electronic and optical properties of transition metal phosphorus trichalcogenides (MPX3, M=Mn, Ni, Fe; X=S, Se) exhibiting various antiferromagnetic arrangements within the 2D limit. Our analysis based on the density functional theory and versatile formalism of Bethe-Salpeter equation reveals larger exciton binding energies for MPS3 (up to 1.1 eV in air) than MPSe3 (up to 0.8 eV in air), exceeding the values of transition metal dichalcogenides (TMDs). For the (Mn,Fe)PX3, we determine the optically active band-edge transitions, revealing that they are sensitive to in-plane magnetic order, irrespective of the type of chalcogen atom. We predict the anistropic effective masses and the type of linear polarization as important fingerprints for sensing the type of magnetic AFM arrangements. Furthermore, we identify the spin-orientation-dependent features such as the valley splitting, the effective mass of holes, and the exciton binding energy. In particular, we demonstrate that for MnPX3 (X=S, Se), a pair of nonequivalent K+ and K− points exists yielding the valley splittings that strongly depend on the direction of AFM aligned spins. Notably, for the out-of-plane direction of spins, two distinct peaks are expected to be visible below the absorption onset, whereas one peak should emerge for the in-plane configuration of spins. These spin-dependent features provide an insight into spin flop transitions of 2D materials. Finally, we propose a strategy for how the spin valley polarization can be realized in 2D AFM within a honeycomb lattice. Published by the American Physical Society 2024

Simulation of optoelectronic oscillator injection locking, pulling & spiking phenomena

Complex envelope and reduced phase simulation models describing the dynamical behaviour of an optoelectronic oscillator (OEO) under injection by an external source are described. The models build on the foundations of a previously reported delay integral/differential equation (DDE) theory of injection locking of time delay oscillators (TDO) such as the OEO. The DDE formulation is particularly amenable to high precision simulation using the Simulink™ block diagram environment. The correspondence between the blocks and the oscillator components offers intuition and considerable freedom to explore different circuit architectures and design variations with minimal coding effort. The simulations facilitate the study of the profound effect the multimode nature of a TDO has on its dynamical behavior. The reduced phase models that make use of the Leeson approximation are generally successful in reproducing the results of complex envelope models for established oscillations except for spiking phenomena for which the Leeson approximation fails. Simulation results demonstrating phenomena not captured by classical injection theory are presented, including multimode oscillation, the appearance of sidemodes in the RF and phase noise spectrum, and persistent spike trains redolent of recent experimental observations of 2π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2\\pi $$\\end{document} phase pulse trains in a broadband OEO under injection.

A new graph theoretic analytical method for nonlinear distributed order fractional ordinary differential equations by clique polynomial of cocktail party graph

In this paper, we presented a new analytical method for one of the rapidly emerging branches of fractional calculus, the distributed order fractional differential equations (DFDE). Due to its significant applications in modeling complex physical systems, researchers have shown profound interest in developing various analytical and numerical methods to study DFDEs. With this motivation, we proposed an easy computational technique with the help of graph theoretic polynomials from algebraic graph theory for nonlinear distributed order fractional ordinary differential equations (NDFODE). In the method, we used clique polynomials of the cocktail party graph as an approximation solution. With operational integration and fractional differentiation in the Caputo sense, the NDFODEs transformed into a system of algebraic equations and then solved by Newton–Raphson's method to determine the unknowns in the Clique polynomial approximation. The proficiency of the proposed Clique polynomial collocation method (CCM) is illustrated with four numerical examples. The convergence and error analysis are discussed in tabular and graphical depictions by comparing the CCM results with the results of existing numerical methods.

Dynamics analysis and optimal control study of uncertain information dissemination model triggered after major emergencies

In order to effectively prevent and combat online public opinion crises triggered by major emergencies, this paper explores the dissemination mechanism of uncertain information on online social platforms. According to the decision-making behavior of netizens after receiving uncertain information, they are divided into eight categories. Considering that there will be a portion of netizens who clarify uncertain information after receiving it, this paper proposes a SEFTFbTbMR model of uncertain information clarification behavior. The propagation dynamics equations of the model are given based on the theory of differential equations, the basic regeneration number R0 of the model is calculated, and the existence and stability of the equilibrium point of the model are analyzed. The theoretical analysis of the model is validated using numerical simulation software, and sensitivity analysis is performed on the parameters related to R0. In order to reduce the influence caused by uncertain information, the optimal control strategy of the model is proposed using the Hamiltonian function. It is found that the dissemination of uncertain information among netizens can be suppressed by strengthening the regulation of social platforms, improving netizens’ awareness of identifying the authenticity of information, and encouraging netizens to participate in the clarification of uncertain information. The results of this work can provide a theoretical basis for future research on the uncertain information dissemination mechanism triggered by major emergencies. In addition, the results can also provide methodological support for the relevant government departments to reduce the adverse effects caused by uncertain information in the future.

Research on the Temperature Distribution in Electrically Heated Offshore Heavy Oil Wellbores

The electric heating process for lifting heavy oil has been widely applied. However, research on its temperature field laws mostly focuses on onshore heavy oil wells, while research offshore is limited. Therefore, based on the energy conservation equation and heat transfer theory, a transient one-dimensional wellbore temperature model coupled with the temperature and viscosity of heavy oil and considering the effect of time was developed. In order to verify the accuracy of the model, the results of the previous model were used for comparison with the present model, and the results showed that the model has good accuracy. The results show that a reasonable selection of the process parameters of electric heating can increase the production of heavy oil while saving development costs and improving the economic benefits of the oilfield. The conclusions and recommendations of this paper can provide a theoretical basis and guiding suggestions for the optimal design of process parameters for lifting heavy oil using an offshore electric heating process.

Prescribed‐time sensor fault estimation for linear systems with unknown inputs by periodic delayed observers

SummaryThis paper studies the problem of sensor fault estimation for linear systems in the presence of unknown inputs in both input and output channels. Relying on matrix equation theory, the unknown inputs are first removed from the output channel. Second, an augmented descriptor system is constructed by treating both system state and sensor fault as (pseudo)‐state variables. Third, the augmented descriptor system is transformed into a regular one, followed by the elimination of the unknown input from the state equation. Finally, a reduced‐order prescribed‐time sensor fault estimator is obtained by using periodic delayed observers. This matrix equation based approach is then complemented by an alternative one, which relies on successive transformations of state, input and outputs. This approach sheds light on the adopted solvability conditions throughout the paper and on the role of different directions in the output space in handling unknown inputs, sensor faults and the core state estimation problem. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed methodologies.