yusuke1997/dblp-id-title huggingface dataset:
Analyzing Dynamical Behaviors of a Stochastic Competitive Model with a Holling Type-II Functional Response Under Diffusion and the Ornstein-Uhlenbeck Process
Nonrelativistic Approximation in the Theory of a Spin-2 Particle with Anomalous Magnetic Moment
Dynamic Analysis of a Stochastic Delayed SEIRS Epidemic Model with Lévy Jumps and the Impact of Public Health Education
A New Type of Generalization on W - Asymptotically J λ - Statistical Equivalence with the Number of α
A Short Note on Integral Transformations and Conversion Formulas for Sequence Generating Functions
Acoustic Drift: Generating Helicity and Transferring Energy
Global Weak Solution in a p-Laplacian Attraction-Repulsion Chemotaxis System with Nonlinear Sensitivity and Signal Production
Stability of Anisotropy Pressure in Self-Gravitational Systems in f(G) Gravity
Measuring Profitable Efficiency, Technical Efficiency, Technological Innovation of Waste Management Companies Using Negative Super-SBM-Malmquist Model
Non-Resonant Non-Hyperbolic Singularly Perturbed Neumann Problem
Simulation of the Advection Process of Stokes Flow Inside a Rectangular Cavity Under Constant Velocities
Incentive Compatible Decision Making: Real Options with Adverse Incentives
Simultaneous Method for Solving Certain Systems of Matrix Equations with Two Unknowns
Impact of Auxiliary Information and Measurement Errors on Mean Estimation with Mixture Optional Enhanced Trust (MOET) Randomized Response Model
Analysis of Novel Oscillations of Quantized Mechanical Energy in Mass-Accreting Nano-Oscillator Systems
A Characterization of Normal Injective and Normal Projective Hypermodules
On One Problems of Spectral Theory for Ordinary Differential Equations of Fractional Order
Failure Cause Analysis Under Progressive Type-II Censoring Using Generalized Linear Exponential Competing Risks Model with Medical and Industrial Applications
Characteristic Number: Theory and Its Application to Shape Analysis
A Novel Robust Transformation Approach to Finite Population Median Estimation Using Monte Carlo Simulation and Empirical Data
Razy: A String Matching Algorithm for Automatic Analysis of Pathological Reports
Existence of Mild Solutions for Multi-Term Time-Fractional Random Integro-Differential Equations with Random Carathéodory Conditions
Evolutionary Dynamics of Stochastic Q Learning in Multi-Agent Systems
Establishing Effective Remedial Instruction Grouping Using the Rough Set Theory and Grey Structural Modeling
Optimization of General Power-Sum Connectivity Index in Uni-Cyclic Graphs, Bi-Cyclic Graphs and Trees by Means of Operations
Uniform Stabilization and Asymptotic Behavior with a Lower Bound of the Maximal Existence Time of a Coupled System's Semi-Linear Pseudo-Parabolic Equations
Connections between Some Extremization Problems and Associated Inequalities
Spatial Decay Estimates for the Moore-Gibson-Thompson Heat Equation Based on an Integral Differential Inequality
Three Problems for Decision Rule Systems from Closed Classes
Non-Abelian Pseudocompact Groups
A Statistical Dependence Framework Based on a Multivariate Normal Copula Function and Stochastic Differential Equations for Multivariate Data in Forestry
Equivalent Base Expansions in the Space of Cliffordian Functions
Advancements in Gevrey Regularity for a Coupled Kadomtsev-Petviashvili II System: New Insights and Findings
Representations, Translations and Reductions for Ternary Semihypergroups
TOPSIS Method Based on Hamacher Choquet-Integral Aggregation Operators for Atanassov-Intuitionistic Fuzzy Sets and Their Applications in Decision-Making
Families of Ramanujan-Type Congruences Modulo 4 for the Number of Divisors
Queueing System with Two Phases of Service and Service Rate Degradation
Surface Pencil Couple with Bertrand Couple as Joint Principal Curves in Galilean 3-Space
The Classification of All Singular Nonsymmetric Macdonald Polynomials
Pseudo Overlap Functions, Fuzzy Implications and Pseudo Grouping Functions with Applications
Local Structure of Convex Surfaces near Regular and Conical Points
Competing Risks in Accelerated Life Testing: A Study on Step-Stress Models with Tampered Random Variables
Tuberculosis in Ethiopia: Optimal Intervention Strategies and Cost-Effectiveness Analysis
New Flexible Asymmetric Log-Birnbaum-Saunders Nonlinear Regression Model with Diagnostic Analysis
An Improved Tikhonov-Regularized Variable Projection Algorithm for Separable Nonlinear Least Squares
Fixed Point Results for New Types of Fuzzy Contractions via Admissible Functions and FZ -Simulation Functions
Noncommutative Multi-Parameter Subsequential Wiener-Wintner-Type Ergodic Theorem
Deterministic and Random Generalized Complex Numbers Related to a Class of Positively Homogeneous Functionals
Controllability Results for First Order Impulsive Fuzzy Differential Systems
Construction of Fractional Pseudospectral Differentiation Matrices with Applications
Geometry of Harmonic Nearly Trans-Sasakian Manifolds
A Novel Methodology for Forecasting Business Cycles Using ARIMA and Neural Network with Weighted Fuzzy Membership Functions
A New Family of Lifetime Models: Theoretical Developments with Applications in Biomedical and Environmental Data
On the Regularized Asymptotics of a Solution to the Cauchy Problem in the Presence of a Weak Turning Point of the Limit Operator
Existence and Properties of the Solution of Nonlinear Differential Equations with Impulses at Variable Times
On Certain Properties of Parametric Kinds of Apostol-Type Frobenius-Euler-Fibonacci Polynomials
Golden Ratio and a Ramanujan-Type Integral
Stability and Hyperstability of Ternary Hom-Multiplier on Ternary Banach Algebra
pth Moment Exponential Synchronization of Fuzzy Stochastic Cellular Neural Networks with Discrete and Infinite Delays
Localization Operators for the Linear Canonical Dunkl Windowed Transformation
Convex (α, β)-Generalized Contraction and Its Applications in Matrix Equations
On the Čech-Completeness of the Space of τ-Smooth Idempotent Probability Measures
On an Indefinite Metric on a Four-Dimensional Riemannian Manifold
Practical Consequences of Quality Views in Assessing Software Quality
Turbulent Free Convection and Thermal Radiation in an Air-Filled Cabinet with Partition on the Bottom Wall
Notes on Cauchy-Stieltjes Kernel Families
Applying the Fuzzy BWM to Determine the Cryptocurrency Trading System under Uncertain Decision Process
Congruence Representations via Soft Ideals in Soft Topological Spaces
Evaluation of Digital Marketing Technologies with Fuzzy Linguistic MCDM Methods
Numerical Reconstruction of the Source in Dynamical Boundary Condition of Laplace's Equation
Stability of the Split-Step θ-Method for Stochastic Pantograph Systems with Markovian Switching and Jumps
Parameter Estimation of the Exponentiated Pareto Distribution Using Ranked Set Sampling and Simple Random Sampling
Synthetic Tableaux with Unrestricted Cut for First-Order Theories
Novel Expressions for Certain Generalized Leonardo Polynomials and Their Associated Numbers
Fixed Point Theory for Multi-Valued Feng-Liu-Subrahmanyan Contractions
Chaos in Topological Modules
Some Chen Inequalities for Submanifolds in Trans-Sasakian Manifolds Admitting a Semi-Symmetric Non-Metric Connection
Interval Type-3 Fuzzy Inference System Design for Medical Classification Using Genetic Algorithms
The Cauchy-Optimal Stability Results for Cauchy-Jensen Additive Mappings in the Fuzzy Banach Space and the Unital Fuzzy Banach Space
Score-Guided Generative Adversarial Networks
Nonoscillation and Oscillation Criteria for a Class of Second-Order Nonlinear Neutral Delay Differential Equations with Positive and Negative Coefficients
Influence of Heat Transfer on Stress Components in Metallic Plates Weakened by Multi-Curved Holes
Abelian Function Fields on Jacobian Varieties
The Invariant Subspace Problem for Separable Hilbert Spaces
Comparing Regional Attitudes toward Immigrants in Six European Countries
Capital Asset Pricing Model and Ordered Weighted Average Operator for Selecting Investment Portfolios
Resolution of an Isolated Case of a Quadratic Hypergeometric 2F1 Transformation
A Crank-Nicolson Compact Difference Method for Time-Fractional Damped Plate Vibration Equations
Basic Core Fuzzy Logics and Algebraic Routley-Meyer-Style Semantics
Reliability and Performance Optimization of Multi-Subsystem Systems Using Copula-Based Repair
The Reduced-Dimension Method for Crank-Nicolson Mixed Finite Element Solution Coefficient Vectors of the Extended Fisher-Kolmogorov Equation
Decision-Making with Fermatean Neutrosophic Vague Soft Sets Using a Technique for Order of Preference by Similarity to Ideal Solution
Finite Time Blowup in a Fourth-Order Dispersive Wave Equation with Nonlinear Damping and a Non-Local Source
New Results on Start-Points for Multi-Valued Maps
A Unified Approach to Aitchison's, Dually Affine, and Transport Geometries of the Probability Simplex
Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials
Complex Riemannian Spacetime: Removal of Black Hole Singularities and Black Hole Paradoxes
Fixed Point of Modified F-Contraction with an Application
Stability and Bifurcation Analysis for the Transmission Dynamics of Skin Sores with Time Delay
Fuzzy H-Quasi-Contraction and Fixed Point Theorems in Tripled Fuzzy Metric Spaces
Stability Analysis of Fixed-Wing UAV Swarms Under Time-Delayed Tracking Control Law
Diffeomorphism Spline
The Difference of Zagreb Indices of Halin Graphs
Asymptotic Analysis of Spectrum and Stability for One Class of Singularly Perturbed Neutral-Type Time-Delay Systems
Applications of Shell-like Curves Connected with Fibonacci Numbers
Pseudo-Quasi Overlap Functions and Related Fuzzy Inference Methods
Graphs in an Intuitionistic Fuzzy Soft Environment
Maximizing the Index of Signed Complete Graphs Containing a Spanning Tree with k Pendant Vertices
Fractional Singular Differential Systems of Lane-Emden Type: Existence and Uniqueness of Solutions
Extension of an Eighth-Order Iterative Technique to Address Non-Linear Problems
Limiting Approach to Generalized Gamma Bessel Model via Fractional Calculus and Its Applications in Various Disciplines
Green Financing Efficiency and Influencing Factors of Chinese Listed Construction Companies against the Background of Carbon Neutralization: A Study Based on Three-Stage DEA and System GMM
The Fourfold Way to Gaussianity: Physical Interactions, Distributional Models and Monadic Transformations
Solution Method for Systems of Nonlinear Fractional Differential Equations Using Third Kind Chebyshev Wavelets
An Accelerated Dual-Integral Structure Zeroing Neural Network Resistant to Linear Noise for Dynamic Complex Matrix Inversion
Approximation by Power Series of Functions
Statistical Inference of Truncated Cauchy Power-Inverted Topp-Leone Distribution under Hybrid Censored Scheme with Applications
On Some Branched Continued Fraction Expansions for Horn's Hypergeometric Function H4(a, b;c, d;z1, z2) Ratios
Conditional Tail Expectation and Premium Calculation under Asymmetric Loss
Analysis of Tandem Queue with Multi-Server Stages and Group Service at the Second Stage
Stability Analysis of a Stage-Structure Predator-Prey Model with Holling III Functional Response and Cannibalism
Elliptic Problems with Additional Unknowns in Boundary Conditions and Generalized Sobolev Spaces
Statistical Convergence via q-Calculus and a Korovkin's Type Approximation Theorem
Managing Interacting Criteria: Application to Environmental Evaluation Practices
On the Laplacian, the Kirchhoff Index, and the Number of Spanning Trees of the Linear Pentagonal Derivation Chain
On the Spatiotemporal Pattern Formation in Nonlinear Coupled Reaction-Diffusion Systems
A Fast Novel Recursive Algorithm for Computing the Inverse of a Generalized Vandermonde Matrix
A Comparative Study of Several Classical, Discrete Differential and Isogeometric Methods for Solving Poisson's Equation on the Disk
On a Harmonic Univalent Subclass of Functions Involving a Generalized Linear Operator
Notes on Semiprime Ideals with Symmetric Bi-Derivation
Prediction of the Share of Solar Power in China Based on FGM (1, 1) Model
Asymptotic Representation of Vorticity and Dissipation Energy in the Flux Problem for the Navier-Stokes Equations in Curved Pipes
Solving Feasibility Problems with Infinitely Many Sets
Finite and Symmetric Euler Sums and Finite and Symmetric (Alternating) Multiple T-Values
A Learning Path Recommendation Approach in a Fuzzy Competence Space
Zero-Aware Low-Precision RNS Scaling Scheme
Sustainable Integrated Fuzzy Optimization for Multimodal Petroleum Supply Chain Design with Pipeline System: The Case Study of Vietnam
Optimized Self-Similar Borel Summation
Formation and Evolution of Ideal Interfirm Collaborative Innovation Networks Based on Decision-Making Rules for Partner Selection
Optimal Treatment Strategy for Cancer Based on Mathematical Modeling and Impulse Control Theory
New Results for Multivalued Mappings in Hausdorff Neutrosophic Metric Spaces
Euclidean Algorithm for Extension of Symmetric Laurent Polynomial Matrix and Its Application in Construction of Multiband Symmetric Perfect Reconstruction Filter Bank
Net-Compact Hausdorff Topologies and Continuous Multi-Utility Representations for Closed Preorders
Hölder-Type Inequalities for Power Series of Operators in Hilbert Spaces
Ground State for a Schrödinger-Born-Infeld System via an Approximating Procedure
A Comprehensive Study on the Applications of NTIM and OAFM in Analyzing Fractional Navier-Stokes Equations
On the Existence of (p,q)-Solutions for the Post-Quantum Langevin Equation: A Fixed-Point-Based Approach
Extension of Chu-Vandermonde Identity and Quadratic Transformation Conditions
Determining COVID-19 Dynamics Using Physics Informed Neural Networks
On the Normalized Laplacian Spectrum of the Linear Pentagonal Derivation Chain and Its Application
Fractional Dynamical Behavior of an Elastic Magneto Piezo Oscillator Including Non-Ideal Motor Excitation
Fourier Transform of the Orthogonal Polynomials on the Unit Ball and Continuous Hahn Polynomials
Expanded Rough Approximation Spaces Using Grill and Maximal Rough Neighborhoods for Medical Applications
On the Acoustic Radiation Force Affecting Two Liquid Drops Located in the Wave Field
A Logic for Quantum Register Measurements
Factor Prioritization for Effectively Implementing DevOps in Software Development Organizations: A SWOT-AHP Approach
Research on Repeated Quantum Games with Public Goods under Strong Reciprocity
Evaluation of Cryptocurrencies for Investment Decisions in the Era of Industry 4.0: A Borda Count-Based Intuitionistic Fuzzy Set Extensions EDAS-MAIRCA-MARCOS Multi-Criteria Methodology
A Selection Principle and Products in Topological Groups
Modified Heisenberg Commutation Relations, Free Schrödinger Equations, Tunnel Effect and Its Connections with the Black-Scholes Equation
New Generalization of Geodesic Convex Function
On the Dynamics of a Modified van der Pol-Duffing Oscillator
Refined Discontinuous Trigger Scheme for Event-Based Synchronization of Chaotic Neural Networks
A Survey on the k-Path Vertex Cover Problem
Fuzzy Hom-Lie Ideals of Hom-Lie Algebras
Computational Algebra, Coding Theory, and Cryptography: Theory and Applications
A q-Analog of the Class of Completely Convex Functions and Lidstone Series
Some Model Theoretic Properties for Pavelka-Style Gödel Logic, RGL* and Gödel Logic with Δ
On the Natural Density of Sets Related to Generalized Fibonacci Numbers of Order r
Homotopy Analysis Method and Physics-Informed Neural Networks for Solving Volterra Integral Equations with Discontinuous Kernels
Oscillation of Emden-Fowler-Type Neutral Delay Differential Equations
Estimation Methods of the Multiple-Group One-Dimensional Factor Model: Implied Identification Constraints in the Violation of Measurement Invariance
Two New Tests for the Relationships of Stochastic Dominance
On the Structure of Quantum Markov Chains on Cayley Trees Associated with Open Quantum Random Walks
A New Perspective on Intuitionistic Fuzzy Structures in Sheffer Stroke BCK-Algebras
Research on PDF Shape Control for Nonlinear Stochastic System Using an Approximate Solution of FPK Equation
Hybrid Deduction-Refutation Systems
Applications of Fuzzy Logic and Probabilistic Neural Networks in E-Service for Malware Detection
Resolvent-Free Method for Solving Monotone Inclusions
Interval-Valued Pseudo Overlap Functions and Application
Minor and Major Strain: Equations of Equilibrium of a Plane Domain with an Angular Cutout in the Boundary
Fractional Dynamical Systems Solved by a Collocation Method Based on Refinable Spaces
Infinitely Many Solutions for a Perturbed Partial Discrete Dirichlet Problem Involving ϕc-Laplacian
Analyzing Uniqueness of Solutions in Nonlinear Fractional Differential Equations with Discontinuities Using Lebesgue Spaces
Change Point Detection Using Penalized Multidegree Splines
Existence of Sign-Changing Solutions for a Class of p(x)-Biharmonic Kirchhoff-Type Equations
On Order Degree Problem for Moore Bound
Numerical Model for Simulation of the Laser Thermal Forming Process
Bayesian Sensitivity Analysis for VaR and CVaR Employing Distorted Band Priors
Conditions of Functional Null Controllability for Some Types of Singularly Perturbed Nonlinear Systems with Delays
Local Grey Predictor Based on Cubic Polynomial Realization for Market Clearing Price Prediction
A PDE Model Approach to Formation Control of Large-Scale Mobile Sensor Networks with Boundary Uncertainties
Infinite Horizon Irregular Quadratic BSDE and Applications to Quadratic PDE and Epidemic Models with Singular Coefficients
Conformally Flat Siklos Metrics Are Ricci Solitons
Crossed Modules and Non-Abelian Extensions of Differential Leibniz Conformal Algebras
George-Veeramani Fuzzy Metrics Revised
Diversity Constraint and Adaptive Graph Multi-View Functional Matrix Completion
Boolean Subtypes of the U4 Hexagon of Opposition
Cuntz Semigroups of Compact-Type Hopf C*-Algebras
On the Impact of Some Fixed Point Theorems on Dynamic Programming and RLC Circuit Models in R-Modular b-Metric-like Spaces
Product of Spacing Estimation of Stress-Strength Reliability for Alpha Power Exponential Progressively Type-II Censored Data
Operator Smith Algorithm for Coupled Stein Equations from Jump Control Systems
New Fuzzy Extensions on Binomial Distribution
A Nonconstant Gradient Constrained Problem for Nonlinear Monotone Operators
Modeling High-Frequency Zeros in Time Series with Generalized Autoregressive Score Models with Explanatory Variables: An Application to Precipitation
Complex Numbers Related to Semi-Antinorms, Ellipses or Matrix Homogeneous Functionals
Optimal Minimax Rate of Smoothing Parameter in Distributed Nonparametric Specification Test
Existence of Solutions for Nonlinear Choquard Equations with (p, q)-Laplacian on Finite Weighted Lattice Graphs
Ergodicity and Mixing Properties for SDEs with α-Stable Lévy Noises
A Comprehensive Study of Generalized Lambert, Generalized Stieltjes, and Stieltjes-Poisson Transforms
Longitudinal Data Analysis Based on Bayesian Semiparametric Method
Fractional Evolution Equation with Nonlocal Multi-Point Condition: Application to Fractional Ginzburg-Landau Equation
Optimization of Convolutional Neural Networks Architectures Using PSO for Sign Language Recognition
On Two Intuitionistic Fuzzy Modal Topological Structures
Smart Competence Management Using Business Analytics with Fuzzy Predicates
Group Acceptance Sampling Plan Based on New Compounded Three-Parameter Weibull Model
Kropina Metrics with Isotropic Scalar Curvature
Accelerated Modified Tseng's Extragradient Method for Solving Variational Inequality Problems in Hilbert Spaces
Axiomatic Processes for Asymmetric Allocation Rules under Fuzzy Multicriteria Situations
Composition and Decomposition of Positive Linear Operators (VIII)
A Second-Order Numerical Method for a Class of Optimal Control Problems
Recent Advances in Fractional Calculus
An Efficient Non-Standard Numerical Scheme Coupled with a Compact Finite Difference Method to Solve the One-Dimensional Burgers' Equation
Numbers of Mutations within Multicellular Bodies: Why It Matters
Identification of Chaotic Dynamics in Jerky-Based Systems by Recurrent Wavelet First-Order Neural Networks with a Morlet Wavelet Activation Function
Riemann-Liouville Operator in Weighted L p Spaces via the Jacobi Series Expansion
Quantum Fisher Information Dynamics in Squeezed Reservoirs: Mathematical Insights and Quantum Applications
A Novel Lorenz-like Attractor and Stability and Equilibrium Analysis
A Novel Color Recognition Model for Improvement on Color Differences in Products via Grey Relational Grade
A Novel PM2.5 Concentration Forecasting Method Based on LFIG_DTW_HC Algorithm and Generalized Additive Model
Discrete Analogue of Fishburn's Fractional-Order Stochastic Dominance
Starlikeness and Convexity of Generalized Bessel-Maitland Function
Modeling Bland-Altman Limits of Agreement with Fractional Polynomials - An Example with the Agatston Score for Coronary Calcification
The Synchronization of a Class of Time-Delayed Chaotic Systems Using Sliding Mode Control Based on a Fractional-Order Nonlinear PID Sliding Surface and Its Application in Secure Communication
An MDL-Based Wavelet Scattering Features Selection for Signal Classification
Dynamical Analysis of a Modified Epidemic Model with Saturated Incidence Rate and Incomplete Treatment
Robust Semi-Infinite Interval Equilibrium Problem Involving Data Uncertainty: Optimality Conditions and Duality
An Exponentiated Inverse Exponential Distribution Properties and Applications
A New Advanced Class of Convex Functions with Related Results
Some Implicational Semilinear Gaggle Logics: (Dual) Residuated-Connected Logics
High-Order Compact Difference Method for Solving Two- and Three-Dimensional Unsteady Convection Diffusion Reaction Equations
Impossibility of Quantum Bit Commitment, a Categorical Perspective
Numerical Analysis of Heat Transfer through Hollow Brick Using Finite-Difference Method
Multi-Task Deep Learning Games: Investigating Nash Equilibria and Convergence Properties
Modulation Transfer between Microwave Beams: A Hypothesized Case of a Classically-Forbidden Stochastic Process
Classical Probability and Quantum Outcomes
Fractional Whitham-Broer-Kaup Equations within Modified Analytical Approaches
Solving Biharmonic Equations with Tri-Cubic C1 Splines on Unstructured Hex Meshes
Gamma-Nabla Hardy-Hilbert-Type Inequalities on Time Scales
On the Polynomial Solution of Divided-Difference Equations of the Hypergeometric Type on Nonuniform Lattices
New Fixed Point Theorem on Triple Controlled Metric Type Spaces with Applications to Volterra-Fredholm Integro-Dynamic Equations
Join Spaces and Lattices
Recent Results on Expansive-Type Evolution and Difference Equations: A Survey
An Alternative to Real Number Axioms
Analytical and Numerical Simulations of a Delay Model: The Pantograph Delay Equation
On Certain Axiomatizations of Arithmetic of Natural and Integer Numbers
Novel Frequency-Based Approach to Analyze the Stability of Polynomial Fractional Differential Equations
Malliavin Regularity of Non-Markovian Quadratic BSDEs and Their Numerical Schemes
Applications in Integral Equations through Common Results in C*-Algebra-Valued Sb-Metric Spaces
Partial Sums of the Normalized Le Roy-Type Mittag-Leffler Function
On a Resolution of Another Isolated Case of a Kummer's Quadratic Transformation for 2F1
Federated Learning Incentive Mechanism Design via Shapley Value and Pareto Optimality
Existence Results for a Multipoint Fractional Boundary Value Problem in the Fractional Derivative Banach Space
The Maximal Complexity of Quasiperiodic Infinite Words
Exact Solutions to the Fractional Differential Equations with Mixed Partial Derivatives
Modern Problems of Mathematical Physics and Their Applications
Searching for New Integrals in the Euler-Poisson Equations
Barotropic-Baroclinic Coherent-Structure Rossby Waves in Two-Layer Cylindrical Fluids
Elliptic Quaternion Matrices: A MATLAB Toolbox and Applications for Image Processing
Tactical Size Unit as Distribution in a Data Farming Environment
The Mean and the Variance as Dual Concepts in a Fundamental Duality
Multi-Criteria Group Decision-Making Models in a Multi-Choice Environment