Computational Mathematics and Mathematical Physics

Papers
(The TQCC of Computational Mathematics and Mathematical Physics is 1. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2021-09-01 to 2025-09-01.)
ArticleCitations
Ideal-Fluid Flow through a Fixed Near-Wall Granular Layer in the Form of Semi-Infinite Step48
Difference Operator Approximations on Nonstandard Rectangular Grid21
Reflection of Detonation Wave from the Symmetry Plane within a Cylindrical Target for Controlled Thermonuclear Fusion18
Analysis of the Boundary Conditions for Rarefied Molecular Gases with Partial Accommodation Coefficients and Energy Exchange16
On a Boundary Problem for a Fourth-Order Elliptic Equation on a Plane13
On the Radial Basis Function Interpolation I: Spectral Analysis of the Interpolation Matrix and the Related Operators13
Functionals of Eigenvalues on the Manifold of Potentials12
Symmetries and Decomposition of Systems of Partial Differential Equations and Control Systems with Distributed Parameters11
Singular Nonlinear Problems for Self-Similar Solutions of Boundary-Layer Equations with Zero Pressure Gradient: Analysis and Numerical Solution10
Triple Series Evaluated in π and $$\ln 2$$ as Well as Catalan’s Constant G9
Generalization of the Penalized Wall Function Method for Modeling of Turbulent Flows with Adverse Pressure Gradient9
Modeling the Motion of an Elongated Contour under Free Surface of a Heavy Fluid under Large Froude Numbers8
Lower Bounds for Column Matrix Approximations8
Finding Complex-Valued Solutions of Brent Equations Using Nonlinear Least Squares8
Formulas for Analytic Continuation of Horn Functions of Two Variables8
Algorithm for Mesh Adaptation to a Flow Field with a Bow Shock Wave7
Three-Level Schemes with Double Change in the Time Step7
Memory Response on Thermoelastic Behavior with Temperature Dependent Material Moduli under Mechanical Strip Load7
High-Order Energy-Preserving Compact Difference Schemes for the Improved Boussinesq Equation7
New Results on Generalized Quaternions for Hyper-Numbers with Fibonacci and Lucas Numbers Components6
Lagrange Interpolation and the Newton–Cotes Formulas on a Bakhvalov Mesh in the Presence of a Boundary Layer6
Adaptation of the Finite Element Method to the Stieltjes String Deformation Problem with Nonlinear Condition6
On the Solvability of an Essentially Nonlinear Elliptic Differential Equation with Nonlocal Boundary Conditions6
Accuracy Estimation for a Class of Iteratively Regularized Gauss–Newton Methods with a posteriori Stopping Rule6
Solving Some Inverse Problems of Gravimetry and Magnetometry Using an Algorithm That Improves Matrix Conditioning6
The Avalos–Triggiani Problem for the Linear Oskolkov System and a System of Wave Equations6
Stability Analysis of Polymerization Fronts6
Conformal Mapping of a Z-Shaped Domain6
Existence of Bounded Soliton Solutions in the Problem of Longitudinal Oscillations of an Elastic Infinite Rod in a Field with a Nonlinear Potential of General Form6
State Space Approach to Characterize Rayleigh Waves in Nonlocal Thermoelastic Medium with Double Porosity under Three-Phase-Lag Model6
Adaptive Block Algebraic Multigrid Method for Multiphysics Problems6
Explicit Numerically Implementable Formulas for Poincaré–Steklov Operators6
Local Solvability, Blow-Up, and Hölder Regularity of Solutions to Some Cauchy Problems for Nonlinear Plasma Wave Equations: III. Cauchy Problems6
Problems of Determining Quasi-Stationary Electromagnetic Fields in Weakly Inhomogeneous Media5
Gradient-type Approaches to Inverse and Ill-Posed Problems of Mathematical Physics5
Multizonal Boundary and Internal Layers in the Singularly Perturbed Problems for a Stationary Equation of Reaction–Advection–Diffusion Type with Weak and Discontinuous Nonlinearity5
FAD Technique and Differentiation of a Composite Function5
A Fast Method for Determining the Forces and Moments Acting on Aircraft in a Vortex Wake5
An Approach to Improving the Accuracy and Efficiency of the ROMB Method for Solving the Nonstationary Heat Equation5
Application of Mosaic-Skeleton Approximations of Matrices in the Physical Optics Method for Electromagnetic Scattering Problems5
Modeling Flexible Manipulators without Inverting Their Mass Matrices5
Analytical and Numerical Solution of Kinetic Interaction Problems for Groups of Fast Particles5
Comparative Analysis of Gradient Methods for Source Identification in a Diffusion-Logistic Model5
On Asymptotics of Eigenvalues of Seven-Diagonal Toeplitz Matrices5
Extended Launch Pad Method for the Pareto Frontier Approximation in Multiextremal Multiobjective Optimization Problems5
Inverse Problem for Quasi-Stationary Complex Heat Transfer Equations with Fresnel Matching Conditions5
Review of the Theory of Stable Matchings and Contract Systems5
Generating Functions Involving the Fox-Wright Functions5
Singularity Formation in an Incompressible Boundary Layer on an Upstream Moving Wall under Given External Pressure5
Approximate Solution of Inverse Problems for the Heat Equation with a Singular Perturbation5
Nonlinear Method of Corner Boundary Functions with the Influence of an Inflection Point5
Boundary Layer Mesh Generation with Fast Collision Detection5
Statement of the Beamforming Problem and a Method of Its Solution for the Localization of an Acoustic Source Based on Computational Experiment Data5
Elliptic Differential-Difference Equations with Nonlocal Potentials in a Half-Space5
Complex Narayana Quaternions5
Sample Size Determination: Likelihood Bootstrapping4
Comparison of Upwind and Symmetric WENO Schemes in Large Eddy Simulation of Basic Turbulent Flows4
Sequence Transformations in Proofs of Irrationality of Some Fundamental Constants4
Economic Growth Models with Heterogeneous Discounting4
On Numerical Damping of String Vibrations Using Several Stationary Actuators4
On the Redundancy of Hessian Nonsingularity for Linear Convergence Rate of the Newton Method Applied to the Minimization of Convex Functions4
Gaps in the Spectrum of Thin Waveguides with Periodically Locally Deformed Walls4
A Discrete Nine-Velocity Model of the Boltzmann Equation: Solution in the Form of Wild Sum and Applications to Simulating Incompressible Flows4
Convergence of Some Difference Schemes of the Support Operator Method for Repeated Rotational Operations4
Estimation of the Remainder Terms of Certain Horn Hypergeometric Series4
Grid Convergence Analysis of Grid-Characteristic Method on Chimera Meshes in Ultrasonic Nondestructive Testing of Railroad Rail4
Decomposition–Composition Schemes for Systems of Second-Order Evolution Equations4
Approximation of Optimal Control Problems for Semilinear Elliptic Convection–Diffusion Equations with Boundary Observation of the Conormal Derivative and with Controls in Coefficients of the Convectiv4
Calculation of a Strong Resonance Condition in a Hamiltonian System4
Conditional Gradient Method for Optimization Problems with a Constraint in the Form of the Intersection of a Convex Smooth Surface and a Convex Compact Set4
Quadrature Formulas for Singular Integrals Containing the Values of a Function and Its Derivatives4
Formulas for Computing Euler-Type Integrals and Their Application to the Problem of Constructing a Conformal Mapping of Polygons4
Results of Symmetry Classification of 2-Field Third-Order Evolutionary Systems with a Constant Separant4
Determination of the Thermal Conductivity from the Heat Flux on the Surface of a Three-Dimensional Body3
Regular Approximations of the Fastest Motion of Mobile Robot under Bounded State Variables3
Optimal Control of Quasi-Stationary Equations of Complex Heat Transfer with Reflection and Refraction Conditions3
Optimization Approach to Determining the Velocity Field in Image Processing Problems3
Numerical Analysis for a Singularly Perturbed Parabolic Differential Equation with a Time Delay3
Transparent Boundary Conditions for the Wave Equation with Variable Speed of Sound3
Two-Dimensional Mathematical Models of Strict Plasma Equilibrium in Galatea Magnetic Traps and Numerical Analysis of Stability3
On the Accuracy of Shock-Capturing Schemes Calculating Gas-Dynamic Shock Waves3
On L2-Dissipativity of a Linearized Scheme on Staggered Meshes with a Regularization for 1D Barotropic Gas Dynamics Equations3
Approximation of Functions Defined in Tabular Form. II3
Exact Solution of a Bicompact Difference Scheme for Maxwell’s Equations3
On Asymptotics of the Solution to the Cauchy Problem for a Singularly Perturbed Operator-Differential Transport Equation with Weak Diffusion in the Case of Several Space Variables3
Differential-Difference Equations with Optimal Parameters3
Numerical Analysis of the Blow-Up of One-Dimensional Polymer Fluid Flow with a Front3
Existence and Stability of the Solution to a System of Two Nonlinear Diffusion Equations in a Medium with Discontinuous Characteristics3
On Using the Shell Theory in Stability Analysis of Fluid Flows in Compliant Pipes3
Rational Arithmetic with a Round-Off3
Calculation of Radiated Sound from Finite Rectangular Thin Plate Excited by Plane Wave3
Constructing Solutions of Cauchy Type Integral Equations by Using Four Kinds of Basis3
Optimal Disturbances of Stationary and Periodic Solutions to Delay Systems in Mathematical Immunology3
A Formula for the Linking Number in Terms of Isometry Invariants of Straight Line Segments3
Asymptotics of Long Waves Generated by Time-Harmonic Spatially Localized Sources in Basins with Gently Sloping Shores3
Smooth Solution of the Second Initial-Boundary Value Problem for a Model Parabolic System in a Semibounded Nonsmooth Domain on the Plane3
Computation of Unsteady Swirling Flows in Nozzles and Pipes by Applying a New Locally Implicit Godunov-Type Scheme3
On the Probabilistic-Statistical Approach to the Analysis of Nonlocality Parameters of Plasma Density3
Discontinuity Structures and Solitary Waves in Electromagnetic Hydrodynamics Associated with Linear and Nonlinear Alfvén Wave Resonances3
Local Wavelet Adaptation of Cartesian Grids in Computational Fluid Dynamics3
Analytical-Numerical Method for Analyzing Small Perturbations of Geostrophic Ocean Currents with a General Parabolic Vertical Profile of Velocity3
Approximation of Continuous Functions by Classical Sincs and Values of Operators Cλ3
Structured Pseudospectra in Problems of Spatial Stability of Boundary Layers3
Verification of a Numerical Algorithm Based on Quasi-Hydrodynamic Equations as Applied to Thermal Convection Problems3
Shock-Capturing Exponential Multigrid Methods for Steady Compressible Flows3
Choice of an Algorithm for Broadband Monitoring of the Optical Coating Deposition Process Taking into Account the Effect of Error Self-Compensation3
Mathematical Simulation of Nonequilibrium Shock Layer Flow around a Rotating Body3
Cubic–Quartic Optical Solitons and Conservation Laws with Kudryashov’s Law of Refractive Index by Extended Trial Function3
Blow-Up of the Solution to the Equation for Nonlinear Beam Vibrations with Allowance for Transverse Deformation Effects3
Density Gradient Model in Spherically Symmetric Formulation and Its Explicit-Implicit Dissipative Discretization for the Study of Phase Boundary Dynamics3
On Numerical Solution of One Class of Integral Equations of the Third Kind3
A Posteriori Error Estimates of Approximate Solutions to Elliptic Boundary Value Problems in Terms of Local Norms and Cost Functionals3
Higher-Order Trotter–Suzuki Implementation on Tight Binding Propagation Method for Calculating the Density of States and Optical Conductivity of Disordered Graphene2
Non-Simplicial Delaunay Meshing via Approximation by Radical Partitions2
Numerical Construction of Parametrized Potentials for Nucleon-Alpha Inverse Scattering Using Variational Monte Carlo and Phase Function Method2
Analytical Study on the Generalized q-Deformed Sinh–Gordon (Eleuch) Equation2
Asymptotic Expansion for the Solution of an Optimal Boundary Control Problem in a Doubly Connected Domain with Different Control Intensity on Boundary Segments2
Variational Data Assimilation Methods in Geophysical Hydrodynamics Problems2
Deriving Known Particular Solutions of the σ-Commutation Problem (σ ≠ 0, ±1) for a Toeplitz and a Hankel Matrix within a Unified Approach2
Fast Solution Algorithm for a Three-Dimensional Inverse Multifrequency Problem of Scalar Acoustics with Data in a Cylindrical Domain2
On Normal Modes of a Waveguide2
q-Modified Differential Transform Method2
First Initial-Boundary Value Problem for Parabolic Systems in a Semibounded Domain with Curvilinear Lateral Boundary2
Convergence of Continuous Analogues of Numerical Methods for Solving Degenerate Optimization Problems and Systems of Nonlinear Equations2
Mathematical Modeling of Unsteady Combustion of Coke Sedimentations in a Catalyst Layer with Spherical Grains2
Smooth Lyapunov Manifolds for Autonomous Systems of Nonlinear Ordinary Differential Equations and Their Application to Solving Singular Boundary Value Problems2
A Uniform Numerical Method for Solving a Singularly Perturbed Neutral Delay Differential Equation2
The Method of Optical Paths for the Numerical Solution of Integrated Photonics Problems2
Accuracy of Bicompact Schemes in the Problem of Taylor–Green Vortex Decay2
Determination of the Thermal Conductivity and Volumetric Heat Capacity of Substance from Heat Flux2
KP1-Scheme for Acceleration of Upscatter Iterations over the Neutron Thermalization Region and the Fission Source in Solving a Subcritical Boundary Value Problem2
On Analytic Continuation of Conformal Mapping of a Circular Triangle2
New Mixed Variational Problem and the Stokes System with a Singular Right-Hand Side2
Monotone Decomposition of the Cauchy Problem for a Hyperbolic Equation Based on Transport Equations2
Numerical-Analytical Decomposition-Autocompensation Method for Signal Recognition from Incorrect Observations2
Nonlinear Evolution of Stationary Perturbations in a Spatially Evolving Round Submerged Jet2
Constructing Circulants and Skew-Circulants with Prescribed Properties2
Three Boundary Value Problems for Complex Partial Differential Equations in the Lens Domain2
Another Approach to Build Lyapunov Functions for the First Order Methods in the Quadratic Case2
Size Gradation Control for Anisotropic Mixed-Element Mesh Adaptation2
Analytical Solution for the Cavitating Flow over a Wedge. II2
Influence of the Shock Wave Intensity on Instability Development at Rough Interfaces of a Three-Layer Gas System2
Solving Nonlinear Volterra Integral Equations of the First Kind with Discontinuous Kernels by Using the Operational Matrix Method2
On the Number of Solutions to Linear Diophantine Equation and Frobenius Problem2
Quadrature Formula for a Double Layer Potential in the Case of the Helmholtz Equation2
Integral Representations for Second-Order Elliptic Systems in the Plane2
Numerical Algorithm for Source Determination in a Diffusion–Logistic Model from Integral Data Based on Tensor Optimization2
Convergence Analysis of the ADI Scheme for Parabolic Problems using Discrete Harmonic Functions2
Splitting Schemes for One Class of Operator Differential Equations2
On Accuracy of the Lattice Boltzmann Equations of Low and High Orders as Applied to Slow Isothermal Microflows2
Cauchy Problem for the One-Dimensional Equation of Motion in a Metamaterial2
Singular Part of the Electromagnetic Field in Problems of Diffraction by Bodies with Edges for Different Types of Boundary Conditions2
Non-Quadratic Proxy Functions in Mirror Descent Method Applied to Designing of Robust Controllers for Nonlinear Dynamic Systems with Uncertainty2
Numerical and Analytical Investigation of Shock Wave Processes in Elastoplastic Media2
Fault-Tolerant Families of Production Plans: Mathematical Model, Computational Complexity, and Branch-and-Bound Algorithms2
Conditions for Solvability of the Cauchy Problem for One Pseudohyperbolic System2
Monotone Schemes of Conditional Approximation and Arbitrary Order of Accuracy for the Transport Equation2
Instability of Gas–Liquid Interface in Porous Media Flow Governed by Forchheimer’s Law2
Coordinated Control of Multiple Surface Unmanned Vehicle Clusters under the Influence of Wind Field and Tides2
Numerical Solution of Ionization Equations by the Fractional Step Method2
On the Difference Solution of a Nonlocal Boundary Value Problem for a Fractional Diffusion Equation2
Quantum Markovian Dynamics after the Bath Correlation Time2
Generalization of the Method of Scattering Matrices to Problems in Nonlinear Dispersion Media2
The Singularity Set of Optimal Transportation Maps2
The Simultaneous Reduction of a Pair of Unitoid Matrices to Diagonal Form Revisited2
Modeling Epidemics: Neural Network Based on Data and SIR-Model2
On Boundary Properties of Conformal Mappings2
Aggregation Kinetics in Sedimentation: Effect of Diffusion of Particles2
Projector Approach to the Butuzov–Nefedov Algorithm for Finding Asymptotic Solutions for a Class of Discrete Problems with a Small Step2
Local Solvability and Blow-Up of Classical Solution to Some Initial-Boundary Value Problem for a Nonlinear Equation Governing Ion-Acoustic Waves in a Plasma2
Optimal Control of Investment in a Collective Pension Insurance Model: Study of Singular Nonlinear Problems for Integro-Differential Equations2
Fast Automatic Differentiation Technique and Control of Thermal Dynamical Systems2
Adaptive Interpolation Algorithm Using TT-Decomposition for Modeling Dynamical Systems with Interval Parameters2
An Approach to the Implementation of the Multigrid Method with Full Approximation for CFD Problems2
Lavrent’ev-Type Equations and Systems in the Inverse Problem of Reconstructing Viscoelastic Medium Memory2
Symbolic-Numerical Modeling of the Propagation of Adiabatic Waveguide Mode in a Smooth Waveguide Transition2
Erratum to: On the Construction of an Optimal Network of Observation Points when Solving Inverse Linear Problems of Gravimetry and Magnetometry2
h-, p-, and hp-Versions of the Least-Squares Collocation Method for Solving Boundary Value Problems for Biharmonic Equation in Irregular Domains and Their Applications2
Grid-Characteristic Numerical Method on an Irregular Grid with Extending the Interpolation Stencil2
Rational Coefficients of Orthogonal Expansions of Some Functions2
A Fast Single-Pass Method for Solving the Generalized Eikonal Equation in a Moving Medium2
Reconstruction of Two Functions in the Model of Vibrations of a String One End of Which Is Placed in a Moving Medium2
On the Uniform Convergence of Approximations to the Tangential and Normal Derivatives of the Single-Layer Potential Near the Boundary of a Two-Dimensional Domain2
On Numerical Beamforming for Correlated Dipole-Type Sources1
MHD Cattaneo–Christov Heat and Mass Fluxes with Nanofluid Flow in a Porous Medium between Dual Stretchable Rotating Disks1
Optimization of Control and Parameters in Systems with Phase Constraints1
On the Reconstruction of an Input Disturbance in a Reaction–Diffusion System1
Testing of Quadrature Formulas for the Direct Value of the Normal Derivative of a Single-Layer Potential at the Boundary of a Thin Body1
Gas Well Injectivity in Different Regimes of Reservoir Fluid Displacement1
A Mixed Finite Element Approximation for Fluid Flows of Mixed Regimes in Porous Media1
On Lavrent’ev-Type Integral Equations in Coefficient Inverse Problems for Wave Equations1
Finite Fourier Series in Hyperbolic Initial-Boundary Value Problems for Domains with Curved Boundaries1
Stability Analysis of Nonclassical Difference Schemes for Nonlinear Volterra Integral Equations of the Second Kind1
Efficient and Stable Time Integration of Cahn–Hilliard Equations: Explicit, Implicit, and Explicit Iterative Schemes1
On the Simultaneous Determination of the Distribution Density of Sources Equivalent in the External Field and the Spectrum of the Useful Signal1
Time Dependence of Stability of the Water–Vapor Phase Transition Front in High-Temperature Rocks1
Efficient Method for Solving the Boltzmann Equation on a Uniform Mesh1
Perturbation Method and Regularization of the Lagrange Principle in Nonlinear Constrained Optimization Problems1
Stability Indicators of Nonnegative Matrices: Parametric and Sparse Cases1
Accelerated Algorithms for Growing Segments from Image Regions1
Subsonic Rarefied Gas Flow over a Rectangular Cylinder1
An Adaptive Variant of The Frank–Wolfe Method for Relative Smooth Convex Optimization Problems1
Numerical Investigation of the Properties of Remainder in Gauss’s Circle Problem1
Quasi-Isometric Mesh Movement and Deformation with Geometrically Adaptive Metric1
Direct and Inverse Problems in the Generalized Logarithmic Boussinesq Equation1
Capabilities of Sounding at a Finite Set of Frequencies1
Solution of the Exterior Boundary Value Problem for the Helmholtz Equation Using Overlapping Domain Decomposition1
The New is the Well-Forgotten Old—F4 Algorithm Optimization1
Solvability Theory for Singular Integro-Differential Equations in the Class of Generalized Functions1
On Higher-Order Gaussian Fibonacci Quaternions and Their Properties1
Exact Formula for Solving a Degenerate System of Quadratic Equations1
Some Aspects of Numerical Modeling of Shock-Wave Processes in a Two-Phase Gas-Dispersed Mixture1
On One Method for Calculating Nonstationary Heat Transfer between a Gas Flow and a Solid Body1
Existence of Bounded Soliton Solutions in the Problem of Longitudinal Vibrations of an Infinite Elastic Rod in a Field with a Strongly Nonlinear Potential1
Incompressible Boundary Layer with Counterflows at a Given Pressure Gradient1
Hodograph Method for Solving the Overturned Shallow Water Problem1
K-Optimal Preconditioners Based on Approximation of Inverse Matrices1
Study of the Gardner Equation with Homogeneous Boundary Conditions via Fourth Order Modified Cubic B-Spline Collocation Method1
Sparse and Transferable Universal Singular Vectors Attack1
Sensitivity of Functionals of the Solution to the Variational Assimilation Problem to the Input Data on the Heat Flux for a Model of Sea Thermodynamics1
New Classes of Solutions of the σ-Commutation Problem ($$\sigma \ne 0,\; \pm 1$$) for Toeplitz and Hankel Matrices within a Unified Approach1
Provably High Degree Polynomial Representation Learning with FreeNets1
Development of Methods of Asymptotic Analysis of Transition Layers in Reaction–Diffusion–Advection Equations: Theory and Applications1
Application of the Finite Element Method (FEM) to a Class of Nonlocal Elliptic and Parabolic Equations1
Study and Optimization of N-Particle Numerical Statistical Algorithm for Solving the Boltzmann Equation1
Duality Method for Solving 3D Contact Problems with Friction1
Supplement to the Classical Result of A.N. Tikhonov on Electromagnetic Sensing for a Medium with Thin Layers1
A Parallel RBF-VerBSS Hybrid Method for Mesh Deformation1
On a Flow Around a Cylinder Over Uneven Bottom1
Turbulent Kinetic Energy in an Approximate Riemann Solver1
New Technique for Solving System of Variable-Order Fractional Partial Integro Differential Equations1
On the Stability of a Central Difference Scheme with a Stabilizing Correction for the 3D Transport Equation1
Differential Epidemic Models and Scenarios of Restrictive Measures1
Convective Cahn–Hilliard–Oono Equation1
Influence of Vibration on the Onset of Convection in Second Grade Fluid1
Dualism in the Theory of Soliton Solutions II1
On Favard Local Parabolic Interpolating Splines with Additional Knots1
On a Nonlinear Problem for a System of Integro-Differential Equations of Radiative Transfer Theory1
A Class of Singularly Perturbed Equations with Discontinuous Right-Hand Side in the Critical Case1
Alternative Direction Implicit Method for Solving First Order 2D Hyperbolic Delay Differential Equations1
Solution to a Two-Dimensional Nonlinear Parabolic Heat Equation Subject to a Boundary Condition Specified on a Moving Manifold1
Four Classes of Definite Integrals about Hyperbolic and Trigonometric Functions1
Asymptotic Solution of the Boundary Control Problem for a Burgers-Type Equation with Modular Advection and Linear Gain1
Localizing the Initial Condition for Solutions of the Cauchy Problem for the Heat Equation1
On the Unique Solvability of Initial-Boundary Value Problems for Parabolic Systems in a Semibounded Plane Domain with a Nonsmooth Lateral Boundary1
On the Solution of a Conformal Mapping Problem by Means of Weierstrass Functions1
Derivation of the Equations of Electrodynamics and Gravity from the Principle of Least Action1
On the Set of Stable Matchings in a Bipartite Graph1
New Computer Efficient Approximations of Random Functions for Solving Stochastic Transport Problems1
Three-Dimensional Numerical Transfer Model Using a Monotonized Z-Scheme1
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