Axioms

32 pages, 515 KiB

Open AccessArticle

New Flexible Asymmetric Log-Birnbaum–Saunders Nonlinear Regression Model with Diagnostic Analysis

by Guillermo Martínez-Flórez, Inmaculada Barranco-Chamorro and Héctor W. Gómez

Axioms 2024, 13(9), 576; https://doi.org/10.3390/axioms13090576 - 23 Aug 2024

Viewed by 139

A nonlinear log-Birnbaum–Saunders regression model with additive errors is introduced. It is assumed that the error term follows a flexible sinh-normal distribution, and therefore it can be used to describe a variety of asymmetric, unimodal, and bimodal situations. This is a novelty since there are few papers dealing with nonlinear models with asymmetric errors and, even more, there are few able to fit a bimodal behavior. Influence diagnostics and martingale-type residuals are proposed to assess the effect of minor perturbations on the parameter estimates, check the fitted model, and detect possible outliers. A simulation study for the Michaelis–Menten model is carried out, covering a wide range of situations for the parameters. Two real applications are included, where the use of influence diagnostics and residual analysis is illustrated. Full article

(This article belongs to the Special Issue Probability, Statistics and Estimations, 2nd Edition)

23 pages, 469 KiB

Open AccessArticle

Uniform Stabilization and Asymptotic Behavior with a Lower Bound of the Maximal Existence Time of a Coupled System’s Semi-Linear Pseudo-Parabolic Equations

by Nian Liu

Axioms 2024, 13(9), 575; https://doi.org/10.3390/axioms13090575 - 23 Aug 2024

Viewed by 142

Abstract

This article discusses the initial boundary value problem for a class of coupled systems of semi-linear pseudo-parabolic equations on a bounded smooth domain. Global solutions with exponential decay and asymptotic behavior are obtained when the maximal existence time has a lower bound for both low and overcritical energy cases. A sharp condition linking these phenomena is derived, and it is demonstrated that global existence also applies to the case of the potential well family. Full article

(This article belongs to the Special Issue Differential Equations and Related Topics, 2nd Edition)

24 pages, 6021 KiB

Open AccessArticle

Combined Compact Symplectic Schemes for the Solution of Good Boussinesq Equations

by Zhenyu Lang, Xiuling Yin, Yanqin Liu, Zhiguo Chen and Shuxia Kong

Axioms 2024, 13(9), 574; https://doi.org/10.3390/axioms13090574 - 23 Aug 2024

Viewed by 164

Abstract

Good Boussinesq equations are considered in this work. First, we apply three combined compact schemes to approximate spatial derivatives of good Boussinesq equations. Then, three fully discrete schemes are developed based on a symplectic scheme in the time direction, which preserves the symplectic structure. Meanwhile, the convergence and conservation of the fully discrete schemes are analyzed. Finally, we present numerical experiments to confirm our theoretical analysis. Both our analysis and numerical tests indicate that the fully discrete schemes are efficient in solving the spatial derivative mixed equation. Full article

(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)

45 pages, 492 KiB

Open AccessArticle

Lagrange Duality and Saddle-Point Optimality Conditions for Nonsmooth Interval-Valued Multiobjective Semi-Infinite Programming Problems with Vanishing Constraints

by Balendu Bhooshan Upadhyay, Shivani Sain and Ioan Stancu-Minasian

Axioms 2024, 13(9), 573; https://doi.org/10.3390/axioms13090573 - 23 Aug 2024

Viewed by 148

Abstract

Thisarticle deals with a class of nonsmooth interval-valued multiobjective semi-infinite programming problems with vanishing constraints (NIMSIPVC). We introduce the VC-Abadie constraint qualification (VC-ACQ) for NIMSIPVC and employ it to establish Karush–Kuhn–Tucker (KKT)-type necessary optimality conditions for the considered problem. Regarding NIMSIPVC, we formulate interval-valued weak vector, as well as interval-valued vector Lagrange-type dual and scalarized Lagrange-type dual problems. Subsequently, we establish the weak, strong, and converse duality results relating to the primal problem, NIMSIPVC, and the corresponding dual problems. Moreover, we introduce the notion of saddle points for the interval-valued vector Lagrangian and scalarized Lagrangian of NIMSIPVC. Furthermore, we derive the saddle-point optimality criteria for NIMSIPVC by establishing the relationships between the solutions of NIMSIPVC and the saddle points of the corresponding Lagrangians of NIMSIPVC, under convexity assumptions. Non-trivial illustrative examples are provided to demonstrate the validity of the established results. The results presented in this paper extend the corresponding results derived in the existing literature from smooth to nonsmooth optimization problems, and we further generalize them for interval-valued multiobjective semi-infinite programming problems with vanishing constraints. Full article

(This article belongs to the Special Issue Optimization, Operations Research and Statistical Analysis)

15 pages, 283 KiB

Open AccessArticle

Sufficient Efficiency Criteria for New Classes of Non-Convex Optimization Models

by Savin Treanţă and Omar Mutab Alsalami

Axioms 2024, 13(9), 572; https://doi.org/10.3390/axioms13090572 - 23 Aug 2024

Viewed by 158

Abstract

In this paper, we introduce and study a new class of minimization models driven by multiple integrals as cost functionals. Concretely, we formulate and establish some sufficient efficiency criteria for a feasible point in the considered optimization problem. To this end, we introduce [...] Read more.

(Γ, ψ)

-invexity and generalized

(Γ, ψ)

-invexity for the involved real-valued controlled multiple integral-type functionals. More precisely, we extend the notion of (generalized)

(Γ, ψ)

-invexity to the multiple objective control models driven by multiple integral functionals. In addition, innovative proofs are considered for the principal results derived in the paper. Full article

(This article belongs to the Special Issue Recent Developments in Stability and Control of Dynamical Systems)

14 pages, 317 KiB

Open AccessArticle

Limit Property of an L²-Normalized Solution for an L²-Subcritical Kirchhoff-Type Equation with a Variable Exponent

by Xincai Zhu and Hanxiao Wu

Axioms 2024, 13(9), 571; https://doi.org/10.3390/axioms13090571 - 23 Aug 2024

Viewed by 153

Abstract

This paper is concerned with the following

L^{2}

-subcritical Kirchhoff-type equation [...] Read more.

This paper is concerned with the following

L^{2}

-subcritical Kirchhoff-type equation

- (a + b {(\int_{R^{2}} {| \nabla u |}^{2} d x)}^{s}) Δ u + V (x) u = μ u + β {| u |}^{2} u, x \in R^{2}

, with

\int_{R^{2}} {| u |}^{2} d x = 1

. We give a detailed analysis of the limit property of the

L^{2}

-normalized solution when exponent s tends toward 0 from the right (i.e.,

s ↘ 0

). Our research extends previous works, in which the authors have displayed the limit behavior of

L^{2}

-normalized solutions when

s = 1

a ↘ 0

b ↘ 0

. Full article

(This article belongs to the Special Issue Advances in Differential Equations and Its Applications)

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Axioms, Volume 13, Issue 9 (September 2024) – 6 articles

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