Radius Of Convergence Research Articles

3-D density structure of the upper-mantle in the eastern Mediterranean Sea and surrounding region using gravity inversion constrained by seismic velocity model

A 3D density structure of the lithosphere and upper mantle beneath the eastern Mediterranean Sea (EMS) and its adjacent region was constructed based on gravity anomaly inversion constrained by a seismic tomography model. Gravity effects of terrain and crust were removed from the observed gravity field (EIGEN-6C4) to obtain the residual mantle gravity anomaly (RMGA). The density distribution of the lithosphere and upper mantle was investigated. The 3D inversion process was constrained by an initial density model projected from the shear-wave velocity model (SL2013sv). The results show some characteristics of the density distribution in the lithosphere and in the upper mantle that could be related to the tectonic importance of the Mediterranean Sea and the surrounding region. A low-density zone dominates the lithosphere beneath the Sea except for the area around the Arabia Shield and North Anatolian Fault belt. A thinner, high-density layer beneath the southwest of the Sea may be related to the older oceanic lithospheric fragments. The high-density anomalies appear at depths below 280 km beneath the Sea and the Turkish Aegean Sea Plate. However, the low-density anomalies appear on the upper mantle under the trenches of the southwestern part of the Mediterranean Sea, the eastern part of the Aegean Sea, the Red Sea, the Black Sea, and the middle of the Arabia shield. The deep structure under the Eratosthenes seamount in the Mediterranean Sea is the source of the intensity and genesis of tectonic activity. Furthermore, the convergence region of two low-density anomaly zones (Africa-Anatolia) may be interpreted as a significant tectonic unit (Eratosthenes seamount) caused by the arrival of the relatively thick and buoyant Eratosthenes block to its present location south of Cyprus in Holocene time based on the density model interpretation beneath the Mediterranean Sea during the Late Cretaceous and early Tertiary period.

High-order analytical solutions of bounded relative motions for Coulomb formation flying

Close-proximity Coulomb formation flying offers attractive prospects in multiple astronautical missions. A semi-analytical method of constructing the series solution up to an arbitrary order for the relative motion near the equilibrium of Coulomb formation systems is proposed to facilitate the design of Coulomb formations based on a Lindstedt–Poincaré method. The details of the series expansion and coefficient solution for arbitrary $$m\!:\!n$$ -period orbits are discussed. To verify the effectiveness of the proposed method, the practical convergence domain of the high-order series solution is computed by comparing it with corresponding numerical solutions that satisfy the specified boundary conditions. Simulation results demonstrate the efficacy of the Lindstedt–Poincaré method in constructing series solutions for the relative motion of Coulomb formation systems.

Mutual impedance computation using spherical harmonics between two closely spaced antennas

Mutual coupling between two identical radiators is computed using vector spherical harmonics and reaction theorem for small element spacing cases. For closely spaced antennas, the minimum spheres that enclose the antennas overlap, and the vector spherical harmonic expansions do not converge on the surface that separates the two antennas. The proposed method mainly uses addition theorems to translate the vector spherical harmonic expansions to a different center. These operations on spherical waves enable to redefine the minimum spheres and convergence regions. The proposed method has been validated by analyzing the coupling between two half-wave dipoles in a side-by-side configuration. The results clearly show excellent agreement with that obtained from induced EMF method. The theory is also tested experimentally. A printed dipole antenna is designed, and its spherical harmonic coefficients are obtained by spherical near field measurement. Mutual impedance between two such dipoles is computed using the proposed method. The computed results for different element spacings in a side-by-side configuration are compared to those obtained from s-parameter measurements.

GKZ hypergeometric systems of the three-loop vacuum Feynman integrals

We present the Gel’fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems of the Feynman integrals of the three-loop vacuum diagrams with arbitrary masses, basing on Mellin-Barnes representations and Miller’s transformation. The codimension of derived GKZ hypergeometric systems equals the number of independent dimensionless ratios among the virtual masses squared. Through GKZ hypergeometric systems, the analytical hypergeometric series solutions can be obtained in neighborhoods of origin including infinity. The linear independent hypergeometric series solutions whose convergent regions have non-empty intersection can constitute a fundamental solution system in a proper subset of the whole parameter space. The analytical expression of the vacuum integral can be formulated as a linear combination of the corresponding fundamental solution system in certain convergent region.

Properties of the multipole fields formed by round electrodes

The aim of the work is to study the properties of multipole electric fields formed by round rods. We consider the problem of finding the convergence radius of the series obtained by expansion of the potential into spatial harmonics, as well as the calculation of the complex potential for the case of the optimal configuration of cylindrical electrodes. A method is given for finding the real potential, which allows to obtain expansion of potential into power series with high precision.

Southern gains and northern losses: Regional variation in the evolution of black/white earnings differences in the United States, 1976–2017

AbstractWe document large differences among regions of the United States in the trends of the black/white earnings gap among full‐time workers from 1976 to 2017. Outside the South, the earnings of black workers grew more slowly than those of non‐Hispanic white workers. These relative decreases were much larger for women than for men. However, in the South, the racial earnings gap shrank for men, and changed little for women. Thus, we find a substantial convergence across regions in the black/white earnings gap. The most important explanations of the racial earnings gaps are persistent racial differences in educational attainment and persistent occupational segregation. However, differences in observables leave much of the racial earnings gaps unexplained. The regional convergence in the racial earnings gap is evident in both explained and unexplained gaps for both women and men.

An ROI Optimization Method Based on Dynamic Estimation Adjustment Model

An important research direction in the field of traffic light recognition of autonomous systems is to accurately obtain the region of interest (ROI) of the image through the multi-sensor assisted method. Dynamic evaluation of the performance of the multi-sensor (GNSS, IMU, and odometer) fusion positioning system to obtain the optimum size of the ROI is essential for further improvement of recognition accuracy. In this paper, we propose a dynamic estimation adjustment (DEA) model construction method to optimize the ROI. First, according to the residual variance of the integrated navigation system and the vehicle velocity, we divide the innovation into an approximate Gaussian fitting region (AGFR) and a Gaussian convergence region (GCR) and estimate them using variational Bayesian gated recurrent unit (VBGRU) networks and a Gaussian mixture model (GMM), respectively, to obtain the GNSS measurement uncertainty. Then, the relationship between the GNSS measurement uncertainty and the multi-sensor aided ROI acquisition error is deduced and analyzed in detail. Further, we build a dynamic estimation adjustment model to convert the innovation of the multi-sensor integrated navigation system into the optimal ROI size of the traffic lights online. Finally, we use the YOLOv4 model to detect and recognize the traffic lights in the ROI. Based on laboratory simulation and real road tests, we verify the performance of the DEA model. The experimental results show that the proposed algorithm is more suitable for the application of autonomous vehicles in complex urban road scenarios than the existing achievements.

Nozzle Thrust Eccentricity Calculation Based on FLUENT Software

Thrust eccentricity refers to the phenomenon that the thrust vector deviates from the axis of symmetry. This phenomenon will produce lateral force and torque around the aircraft, which affects the normal flight of the aircraft, increases the required control torque, and reduces the density of uncontrolled rockets. There are three sources of thrust eccentricity: mass eccentricity, geometric eccentricity, and aerodynamic eccentricity. The aerodynamic eccentricity is caused by the asymmetrical flow of combustion gas in the nozzle. This paper uses FLUENT software to carry out a numerical simulation of a cone-shaped nozzle. By changing different factors such as the structure of the inner surface of the nozzle and the convergence radius, the influence law of the inner surface structure of different nozzles on the lateral force of the pneumatic eccentricity of the nozzle is explored. The following conclusions were drawn: With the expansion of the expansion half-angle, the second zero point moves toward the nozzle outlet. The relative radius of curvature has little effect on the main thrust of the nozzle but has a certain influence on the eccentricity of its thrust, and as the relative radius of curvature increases, the first and second zeros move toward the throat.

On the analyticity of the pressure for a non-ideal gas with high density boundary conditions

We consider a continuous system of classical particles confined in a cubic box Λ interacting through a stable and finite range pair potential with an attractive tail. We study the Mayer series of the grand canonical pressure of the system pΛω(β,λ) at inverse temperature β and fugacity λ in the presence of boundary conditions ω belonging to a very large class of locally finite particle configurations. This class of allowed boundary conditions is the basis for any probability measure on the space of locally finite particle configurations satisfying the Ruelle estimates. We show that the pΛω(β,λ) can be written as the sum of two terms. The first term, which is analytic and bounded as the fugacity λ varies in a Λ-independent and ω-independent disk, coincides with the free-boundary-condition pressure in the thermodynamic limit. The second term, analytic in a ω-dependent convergence radius, goes to zero in the thermodynamic limit. As far as we know, this is the first rigorous analysis of the behavior of the Mayer series of a non-ideal gas subjected to non-free and non-periodic boundary conditions in the low-density/high-temperature regime when particles interact through a non-purely repulsive pair potential.

Measurement of the Self-Sensing Capability of Synchronous Machines for High Frequency Signal Injection Sensorless Drives

Signal injection sensor-less control for synchronous machines is known to be afflicted by an estimation error dependent on the load current. The estimation error is related to the cross-saturarion and the saliency of the adopted synchronous machine. A motor can be more or less suitable for signal injection sensorless control compared to other motors with different designs or sizes. A sensorless drive can even be afflicted by the control divergence when the machine is highly saturated, resulting in a useless drive. Moreover, even when the control converges, the actual current control trajectory is different from the given reference. In this paper, a measurement procedure of the convergence region, i.e. the operating points where the motor can be successfully controlled without a position sensor is presented and validated. In particular, two different synchronous motors are considered, a permanent magnet assisted synchronous reluctance motor (PMA-SynRM) and a synchronous reluctance motor (SynRM).

Regional convergence of environmental quality in Indonesia: an empirical spatial analysis

This study aims to determine the extent to which the convergence of environmental quality in 34 provinces in Indonesia by considering spatial dependence between one province and another. The data are drawn from the environmental quality index of 34 provinces and processed using spatial econometric methods. The results of the study revealed the existence of convergence and strong spatial dependence. The implication is that changes in environmental quality originating in one province can spillover into surrounding provinces, potentially complicating the transitional dynamics of the convergence process.

The Homotopy Analysis Method to Solve the Nonlinear System of Volterra Integral Equations and Applying the Genetic Algorithm to Enhance the Solutions

This paper presents the application of the Homotopy Analysis Method (HAM) for solving nonlinear system of Volterra integral equations used to obtain a reasonably approximate solution. The HAM contains the auxiliary parameter h which provides a simple way to adjust and control the convergence region of the solution series. The results show that the HAM is a very effective method as well. The results were compared with the solutions obtained by developing a homotopy analysis method using the genetic algorithm (HAM-GA), considering the residual error function as a fitness function of the genetic algorithm.

Perturbative boundaries of quantum advantage: Real-time evolution for digitized λϕ4 lattice models

The real time evolution of quantum field theory models can be calculated order by order in perturbation theory. For $\ensuremath{\lambda}{\ensuremath{\phi}}^{4}$ models, the perturbative series have a zero radius of convergence which in part motivated the design of digitized versions suitable for quantum computing. In agreement with general arguments suggesting that a large field cutoff modifies Dyson's reasoning and improves convergence properties, we show that the harmonic digitizations of $\ensuremath{\lambda}{\ensuremath{\phi}}^{4}$ lattice field theories lead to weak coupling expansions with a finite radius of convergence. Similar convergence properties are found for strong coupling expansions. We compare the resources needed to calculate the real-time evolution of the digitized models with perturbative expansions to those needed to do so with universal quantum computers. Unless new approximate methods can be designed to calculate long perturbative series for large systems efficiently, it appears that the use of universal quantum computers with digitizations involving a few qubits per site has the potential for more efficient calculations of the real-time evolution for large systems at intermediate coupling.

GKZ-system of the 2-loop self energy with 4 propagators

Applying the system of linear partial differential equations derived from the Mellin–Barnes representation and the Miller transformation, we present the GKZ-system of the Feynman integral of the 2-loop self energy diagram with 4 propagators. The codimension of the derived GKZ-system equals the number of independent dimensionless ratios among the external momentum squared and virtual mass squared. In total 536 hypergeometric functions are obtained in the neighborhoods of the origin and infinity, in which 30 linearly independent hypergeometric functions whose convergent regions have nonempty intersection constitute a fundamental solution system in a proper subset of the whole parameter space.

A novelty Multi-Step Associated with Laplace Transform Semi Analytic Technique for Solving Generalized Non-linear Differential Equations

In this work, a novel technique to obtain an accurate solutions to nonlinear form by multi-step combination with Laplace-variational approach (MSLVIM) is introduced. Compared with the traditional approach for variational it overcome all difficulties and enable to provide us more an accurate solutions with extended of the convergence region as well as covering to larger intervals which providing us a continuous representation of approximate analytic solution and it give more better information of the solution over the whole time interval. This technique is more easier for obtaining the general Lagrange multiplier with reduces the time and calculations. It converges rapidly to exact formula with simply computable terms with few time. To investigate of this technique, selected examples to show the ability, validity, accurately and effectiveness.

Adaptive finite-time fault-tolerant control for nano-satellite attitude tracking under actuator constraints

In this paper, a finite-time fault-tolerant control method is developed for attitude tracking of a nano-satellite with three magnetorquers and one reaction wheel in the presence of actuator faults, inertia uncertainties, external distribution, and actuator constraints. For this purpose, the modified non-singular fast terminal sliding mode control is used due to the ability of robustness against uncertainties and finite-time convergence. In this approach, the modified sliding surface variable is constructed based on angular velocity and attitude error to converge the attitude error to zero in a finite time. In addition, three adaptive parameters are employed to reduce the adverse effect of uncertain expressions and to track the attitude commands with high control accuracy. The adaptive parameters and sliding surface variable are used in the reaching phase of the controller to decrease the chattering phenomenon. The dynamics of adaptive parameters, with regard to the angular velocities of the nano-satellite and reaction wheel and the sliding surface variable, are obtained during the stability proof of the closed-loop system. Also, the finite-time convergence of sliding surface and attitude variables are proved by the extended Lyapunov condition, and the convergence regions of attitude tracking errors are obtained. The simulations are accomplished and compared with an existing adaptive sliding mode control approach to evaluate the performance of the proposed controller. The results verify that the proposed controller performs better than the mentioned controller in terms of finite-time convergence, the accuracy of attitude tracking, and the reduction of the chattering phenomenon.

Finite-time synchronization control scheme for underactuated satellite formation reconfiguration

A synchronization control scheme for underactuated satellite formation reconfiguration in circular orbits is proposed in this paper. The main idea of the synchronization scheme is to control the satellite without radial or along-track thrust to track its desired configuration while synchronizing its motion with that of other underactuated satellites to maintain the predefined or time-varying formation. Firstly, a new underactuated control approach is presented for either underactuated case. Based on the inherent coupling of the system states, the finite-time convergence of the system trajectory could be guaranteed by the sliding mode-based underactuated controller. Secondly, to synchronize the reconfiguration motion between followers, the sum of the sliding mode errors of every two neighbor followers is defined as the synchronization control. The Lyapunov-based method proves the finite-time convergence of synchronization control. More importantly, the minimum nonzero eigenvalue of the Laplace matrix can reduce the system state convergence region. Numerical simulations also verify the performance of the proposed underactuated synchronization controller.

Recurrence property for Galton–Watson processes in which individuals have variable lifetimes

This paper is concerned with an extended Galton–Watson process in which individuals are allowed to live and reproduce for more than one unit time. We assume that each individual can live k seasons (time-units) with probability hk, and produce m offspring with probability pm at the end of each season. It can be viewed as Galton–Watson processes with countably infinitely many types in which particles of type i may only have offspring of type i+1 and type 1. Let M be its mean progeny matrix and γ be the convergence radius of the power series ∑k≥0rk(Mk)ij. We first derive formula of calculating γ and show that γ, in supercritical case, is actually the extinction probability of a Galton–Watson process. Next, we give clear criteria for M to be γ-transient, γ-positive and γ-null recurrent from which the ergodic property of the process is discussed. The criteria for γ-recurrence of M rely on the properties of lifetime distribution which are easier to be verified than current results. Finally, we show the asymptotic behavior of the total population size of each type of individuals under certain conditions which illustrates the evolution of Galton–Watson process in which individuals have variable lifetimes.

A multiconsistent computational methodology to resolve a diffusive epidemiological system with effects of migration, vaccination and quarantine

BackgroundWe provide a compartmental model for the transmission of some contagious illnesses in a population. The model is based on partial differential equations, and takes into account seven sub-populations which are, concretely, susceptible, exposed, infected (asymptomatic or symptomatic), quarantined, recovered and vaccinated individuals along with migration. The goal is to propose and analyze an efficient computer method which resembles the dynamical properties of the epidemiological model. Materials and methodsA non-local approach is utilized for finding approximate solutions for the mathematical model. To that end, a non-standard finite-difference technique is introduced. The finite-difference scheme is a linearly implicit model which may be rewritten using a suitable matrix. Under suitable circumstances, the matrices representing the methodology are M-matrices. ResultsAnalytically, the local asymptotic stability of the constant solutions is investigated and the next generation matrix technique is employed to calculate the reproduction number. Computationally, the dynamical consistency of the method and the numerical efficiency are investigated rigorously. The method is thoroughly examined for its convergence, stability, and consistency. ConclusionsThe theoretical analysis of the method shows that it is able to maintain the positivity of its solutions and identify equilibria. The method’s local asymptotic stability properties are similar to those of the continuous system. The analysis concludes that the numerical model is convergent, stable and consistent, with linear order of convergence in the temporal domain and quadratic order of convergence in the spatial variables. A computer implementation is used to confirm the mathematical properties, and it confirms the ability in our scheme to preserve positivity, and identify equilibrium solutions and their local asymptotic stability.

Norm-dependent convergence and stability of the inverse scattering series for diffuse and scalar waves

This work analyzes the forward and inverse scattering series for scalar waves based on the Helmholtz equation and the diffuse waves from the time-independent diffusion equation, which are important partial differential equations (PDEs) in various applications. Different from previous works, which study the radius of convergence for the forward and inverse scattering series, the stability, and the approximation error of the series under the L p norms, we study these quantities under the Sobolev H s norm, which associates with a general class of L 2-based function spaces. The H s norm has a natural spectral bias based on its definition in the Fourier domain: the case s < 0 biases towards the lower frequencies, while the case s > 0 biases towards the higher frequencies. We compare the stability estimates using different H s norms for both the parameter and data domains and provide a theoretical justification for the frequency weighting techniques in practical inversion procedures. We also provide numerical inversion examples to demonstrate the differences in the inverse scattering radius of convergence under different metric spaces.