1,523 Results Found

The main contribution of this paper is to prove the existence of extremal solutions for a novel class of $\mathsf{\psi }$-Caputo fractional differential equation with nonlinear boundary conditions. For this purpose, we utilize the well-known monotone iterative tech...

The main crux of this work is to study the existence of extremal solutions for a new class of nonlinear sequential fractional differential equations (NSFDEs) with nonlinear boundary conditions (NBCs) under the $\psi$-Caputo operator. The obtained outc...

Condition indicators derived from multivariate monitoring signals are widely used to characterize ordered changes in machine operating states. However, an indicator constructed in one operating state may fluctuate or even reverse its direction when t...

We study the sufficient optimality conditions for a class of fractional variational control problems involving data uncertainty in the cost functional. Concretely, by using the parametric technique, we prove the sufficiency of the robust necessary op...

We obtained results on the existence and uniqueness of a mild solution for a fractional-order semi-linear differential inclusion in a Hilbert space whose right-hand side contains an unbounded linear monotone operator and a Carathéodory-type mu...

In this paper, the authors review and survey some results published since 2020 about (complete) monotonicity, inequalities, and their necessary and sufficient conditions for several newly introduced functions involving polygamma functions and origina...

The aim of the present work is to study a class of singular perturbed nabla fractional problems coupled with Dirichlet conditions. Under sufficient conditions we show that the related Green’s function that can be expressed as an infinite series...

In this paper, we study the solvability of various two-point boundary value problems for $x^{\left(4\right)}=f(t,x,x^{\prime },x^{″},x^{‴}),t\in (0,1),$ where f may be defined and continuous on a suitable bounded...

In this paper, we study a nonlinear Riemann-Liouville fractional a q-difference system with multi-strip and multi-point mixed boundary conditions under the Caputo fractional q-derivative, where the nonlinear terms contain two coupled unknown function...

Under the uniform Hörmander hypothesis, we study the smoothness and exponential bounds of the density of the law of the solution of a stochastic differential equation (SDE) with locally Lipschitz drift that satisfies a monotonicity condition. We...

In this paper, a general class of time-symmetric mean-field stochastic systems, namely the so-called mean-field forward-backward doubly stochastic differential equations (mean-field FBDSDEs, in short) are studied, where coefficients depend not only o...

In the paper, the authors find a sufficient and necessary condition for the power-exponential function ${\left(1+\frac{1}{x}\right)}^{\alpha x}$ to be a Bernstein function, derive closed-form formulas for the nth derivatives of the power-exponential functions ${\left(1+\frac{1}{x}\right)}^{\alpha x}$ and ${(1}^{}$...

Solid oxide fuel cell (SOFC) systems in shipboard power plants exhibit strong thermal–electrochemical coupling and are highly sensitive to both balance-of-plant and stack-related faults under changing operating conditions. In this study, a mech...

The classical Eneström–Kakeya Theorem restricts the location of the complex zeros of polynomials with real, positive, monotone increasing coefficients. That is, for ${\displaystyle p\left(z\right)=\sum _{v=0}^n{a}_v{z}^v}$, where $0\le a_0\le a_1\le \cdots \le a_n$, the zeros of p l...

Motivated by results on the location of the zeros of a complex polynomial with monotonicity conditions on the coefficients (such as the classical Eneström–Kakeya theorem and its recent generalizations), we impose similar conditions and giv...

The classical Eneström–Kakeya theorem states that an n-degree polynomial ${\displaystyle p\left(z\right)={\displaystyle \sum _{k=0}^n}{a}_k{z}^k}$ with real coefficients satisfying $0\le a_0\le a_1\le \cdots \le a_n$ has all of its zeros in $|z|\le 1$ in the complex plane. Numerous generalizations of...

Background/Objectives: Mental fatigue during driving, whether passive (arising from monotony) or active (caused by cognitive overload), is a critical factor for road safety. Despite the growing interest in monitoring techniques based on neurophysiolo...

A suction pile is a promising option when floating offshore structures are deployed at deep and distant locations. A suction pile is typically used for the foundation system of a mooring system subjected to horizontal loading with a load inclination....

In this work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci–Mann iteration process, introduced recently...

The relaxed inertial Tseng-type method for solving the inclusion problem involving a maximally monotone mapping and a monotone mapping is proposed in this article. The study modifies the Tseng forward-backward forward splitting method by using both t...

A Bayesian approach was developed, tested, and applied to model ordinal response data in monotone non-decreasing processes with measurement errors. An inhomogeneous hidden Markov model with continuous state-space was considered to incorporate measure...

In this paper, we investigate a class of nonlinear Schrödinger systems containing a nonlinear operator under Osgood-type conditions. By employing the iterative technique, the existence conditions for entire positive radial solutions of the above...

In this paper, we derived a modified conjugate gradient (CG) parameter by adopting the Birgin and Mart$\acute{i}$nez strategy using the descent three-term CG direction and the Newton direction. The proposed CG parameter is applied and suggests a robust...

In this paper, we consider local Dirichlet problems driven by the $\left(r\right(u),s(u\left)\right)$-Laplacian operator in the principal part. We prove the existence of nontrivial weak solutions in the case where the variable exponents $r,s$ are real continuous functions and...

Currently, two-level Mokken scale analysis for clustered test data is being developed. This paper contributes to this development by providing model-fit procedures for two-level Mokken scale analysis. New theoretical insights suggested that the exist...

Rotating machinery prognostics is essential for ensuring the reliability and operational safety of industrial systems. Although gated recurrent units (GRUs) have achieved competitive performance in remaining useful life (RUL) prediction, whether thei...

The 2008 fixed point result on rs-relational metric spaces due to Jachymski is equivalent with the classical 1922 Banach Contraction Principle. This is also valid for the 1961 statement in metric spaces due to Edelstein, or the 2005 fixed point resul...

Polyamide 66 reinforced with 25 wt.% short glass fibres (PA66-GF25) is widely used in engineering applications requiring long-term operation under combined thermal and lubricated conditions, including polymer bearing cage applications. However, the l...

We show that there is a one-to-one correspondence between positive operator-monotone functions on the positive reals, monotone Riemannian metrics, and finite positive Borel measures on the unit interval. This correspondence appears as an integral rep...

The null-continuity of monotone measures is a weaker condition than continuity from below and possesses many special properties. This paper further studies this structure characteristic of monotone measures. Some basic properties of null-continuity a...

Experiments with gypsum as a model rock material were conducted to investigate the characteristics of crack growth under monotonic and cyclic loading. The specimens had two pre-existing flaws that were placed at different inclination angle, spacing a...

We study convergence in multi-agent reinforcement learning (MARL) through the lens of sufficient conditions, using a single-point-of-failure analysis applied to multi-agent policy iteration integrated with linear programming (MAPI-LP), where results...

We study a relaxed inertial forward–backward–half-forward splitting approach with variable step size to solve a monotone inclusion problem involving a maximal monotone operator, a cocoercive operator, and a monotone Lipschitz operator. Th...

Since the monotonicity of the best approximant is crucial to establish partial ordering methods, in this paper, we, respectively, characterize the best approximants in Banach function spaces and Lorentz spaces ${\mathrm{\Gamma }}_{p,w}$, in which we especially focus...

In this paper, the necessary and sufficient conditions for the upper strict monotonicity point and the upper local uniform monotonicity point are given in the case of Musielak–Orlicz spaces equipped with the Mazur–Orlicz F-norm. Moreover,...

The class of symmetric function interacts extensively with other types of functions. One of these is the class of positivity of functions, which is closely related to the theory of symmetry. Here, we propose a positive analysis technique to analyse a...

Positivity analysis is used with some basic conditions to analyse monotonicity across all discrete fractional disciplines. This article addresses the monotonicity of the discrete nabla fractional differences of the Riemann–Liouville type by con...

Monotonicity is a prevalent feature in natural language. Notably, determiners such as every, some, and no induce monotonic (upward) or antitonic (downward) entailments. The Monotonicity Calculus is a proof system that formalizes such reasoning in nat...

The monotonic and cyclic deformation behavior of ultrafine-grained metastable austenitic steel AISI 304L, produced by severe plastic deformation, was investigated. Under monotonic loading, the martensitic phase transformation in the ultrafine-grained...

A square matrix is said to have property n if there exists a positive integer w such that $A^w$ is nonnegative. In this paper, we study the core-EP monotonicity for property-n matrices. Some necessary and sufficient conditions for a property-n matrix to...

In this manuscript, we study the unified integrals recently defined by Rahman et al. and present some new double generalized weighted type fractional integral inequalities associated with increasing, positive, monotone and measurable function $\mathcal{F}$. Also...

In this manuscript, we propose an efficient algorithm for solving a class of nonlinear operator equations. The algorithm is an improved version of previously established method. The algorithm’s features are as follows: (i) the search direction...

In this paper, under some new appropriate conditions imposed on the parameters and mappings involved in the proximal mapping associated with a general H-monotone operator, its Lipschitz continuity is proved and an estimate of its Lipschitz constant i...

This study investigates the monotonic and cyclic performance of composite bucket foundation breakwater in clay through centrifuge modeling. The application of monotonic loads simulates extreme wave conditions, and cyclic load corresponds to long-term...

In recent years, the fractional Laplacian has attracted the attention of many researchers, the corresponding fractional obstacle problems have been widely applied in mathematical finance, particle systems, and elastic theory. Furthermore, the monoton...

We introduce an iterative algorithm which converges strongly to a common element of fixed point sets of nonexpansive mappings and sets of zeros of maximal monotone mappings. Our iterative method is quite general and includes a large number of iterati...

Iterative methods for solving constraint nonlinear monotone equations have been developed and improved by many researchers. The aim of this research is to present a modified three-term conjugate descent (TTCD) derivative-free method for constrained n...

We unify a known technique used for fixed points and coupled, tripled and N-tupled fixed points for weak monotone maps, i.e., maps that exhibit monotone properties for each of their variables. We weaken the classical contractive condition in partiall...

The reflected–forward–backward splitting (RFBS) method is well-established for solving monotone inclusion problems involving Lipschitz continuous operators in Hilbert spaces, where it converges weakly under mild assumptions. Extending thi...

Tautenhahn (2002) studied the Lavrentiev regularization method (LRM) to approximate a stable solution for the ill-posed nonlinear equation $\kappa \left(u\right)=v$, where $\kappa :D\left(\kappa \right)\subseteq X⟶X$ is a nonlinear monotone operator and X is a Hilbert spac...