Search Results (164)

Urban green space (UGS) is crucial for enhancing ecosystem services (ESs), offering both ecological and social benefits. The multifunctional and synergistic development of UGS is essential for addressing ecological security challenges and meeting the demand for high-quality urban living. In densely urbanized areas, optimizing green space scale is essential for maximizing its multifunctionality. This study focuses on the Taihu Lake region in China, assessing six ESs. A self-organizing map (SOM) was employed to identify five distinct ecosystem service bundles (ESBs), while redundancy analysis (RDA) explored how green space scale characteristics influence ESs within each bundle. The results indicate that ESs exhibit significant spatial heterogeneity, with the ESBs showing two typical patterns in terms of synergistic-tradeoff relationships. The green ratio (GR) is the primary driver, with largest patch index (LPI) acting as the secondary factor, while other indicators’ effects vary across ESBs. This study systematically examines the pathways through which UGS scale characteristics influence ESs under multiple scenarios, adopting the ESB perspective. It proposes a tiered UGS scale regulation framework aimed at achieving synergistic, multi-value outcomes. Such a framework has strong potential to enhance both the ecological performance and spatial efficiency of UGS allocation. The findings contribute a novel approach to resolving multifunctional integration challenges in high-density urban settings and providing valuable insights for landscape planning and management. Full article

This study aims to demonstrate how mathematics, especially calculus concepts, can be expanded to include semi-entities and how these can be applied to sampling activities. Here, the multivalued logic uses pseudo-complemented lattices, instead of Boolean algebras. Truth values can express the intensity of a property: for example, the property of being heavy intensifies as weight increases. They can also express the state-of-the-art knowledge of an individual about a certain thing. To express that a number $x$ approaches $a$ is to say that the statement “$x=b$” is not fully true but approaches the full-true value as $b-a$ approaches zero. This approach generalizes the concept of a limit and the concepts derived from it, such as differentiation and integration. A Monte Carlo algorithm replaces one function with another with finite domain, preferably its finite part, by sampling the domain and calculating its map. The discussion extends to integration over an unbounded interval, integral transforms, and differential equations. This study then covers strategies for producing Monte Carlo estimates of respective problems and determining their crucial truth values. In the discussion, a topic related to axiomatizing set theory is also suggested. Full article

In the present paper, the concept of the related orbital completeness of two metric spaces for multivalued mappings is introduced. A new related fixed point theorem for multivalued mappings is proven, and some important results are obtained as corollaries of the main theorem. A single-valued version of the main theorem is also derived as a simple corollary, and two illustrative examples are provided. Full article

This paper is concerned with the investigation of a nonlocal sequential multistrip boundary-value problem for fractional differential inclusions, involving $(k_1,{\psi }_1)$-Hilfer and $(k_2,{\psi }_2)$-Caputo fractional derivative operators, and $(k_2,{\psi }_2)$- Riemann–Liouville fractional integral operators. The problem considered in the present study is of a more general nature as the $(k_1,{\psi }_1)$-Hilfer fractional derivative operator specializes to several other fractional derivative operators by fixing the values of the function ${\psi }_1$ and the parameter $\beta$. Also the $(k_2,{\psi }_2)$-Riemann–Liouville fractional integral operator appearing in the multistrip boundary conditions is a generalized form of the ${\psi }_2$-Riemann–Liouville, $k_2$-Riemann–Liouville, and the usual Riemann–Liouville fractional integral operators (see the details in the paragraph after the formulation of the problem. Our study includes both convex and non-convex valued maps. In the upper semicontinuous case, we prove four existence results with the aid of the Leray–Schauder nonlinear alternative for multivalued maps, Mertelli’s fixed-point theorem, the nonlinear alternative for contractive maps, and Krasnoselskii’s multivalued fixed-point theorem when the multivalued map is convex-valued and $L^1$-Carathéodory. The lower semicontinuous case is discussed by making use of the nonlinear alternative of the Leray–Schauder type for single-valued maps together with Bressan and Colombo’s selection theorem for lower semicontinuous maps with decomposable values. Our final result for the Lipschitz case relies on the Covitz–Nadler fixed-point theorem for contractive multivalued maps. Examples are offered for illustrating the results presented in this study. Full article

In this article, we will introduce a new generalized proximal $\theta$-contraction for multivalued and single-valued mappings named ${(\mathcal{f}-{\theta }_{\kappa })}_{C_P}$-proximal contraction and ${(\mathcal{f}-{\theta }_{\kappa })}_{B_P}$-proximal contraction. Using these newly constructed proximal contractions, we will establish new results for the coincidence best proximity point, best proximity point, and fixed point for multivalued mappings in the context of rectangular metric space. Also, we will reduce these contractions for single-valued mappings, named ${\left({\theta }_{\kappa }\right)}_{C_P}$-proximal contraction and ${\left({\theta }_{\kappa }\right)}_{B_P}$-proximal contraction, to establish results for the coincidence proximity point, best proximity point, and fixed point results. We will give some illustrated examples for our newly generated results with graphical representations. In the last section, we will also find the solution to the equation of motion by using our defined results. Full article

Base excitation sources significantly impact vehicle-body vibrations in maglev systems, with the dynamic performance of the suspension system playing a crucial role in mitigating these effects. The second-series suspension system of a maglev vehicle typically employs an air spring, which has a great impact on the stability of maglev vehicle operation. Considering that the suspension system has certain dynamic characteristics under the foundation excitation, the present study proposes the fractional-order nonlinear Nishimura model to describe the memory-restoring force characteristics of the air spring. The fractional-order derivative term is made equivalent to a term in the form of trigonometric function, the steady-state response of the system is solved by the harmonic balance method, and the results are compared with a variety of other methods. The influence of the foundation excitation source on the dynamic behavior of the vibration isolation system is discussed significantly. The variation law of the jump phenomenon and the diversity of periodic motion of the multi-value amplitude curve are summarized. The numerical simulation also revealed the presence of multi-periodic motion in the system when variations occurred in the gap of the suspension system. Combined with the cell mapping algorithm, the distribution law of different attractors on the attraction domain of periodic motion is discussed, and the rule of the transition of periodic motion stability with different fundamental excitation amplitudes is summarized with the Lyapunov exponent. Full article

This study investigates fuzzy fixed points and fuzzy best proximity points for fuzzy mappings within the newly introduced framework $\theta$-fuzzy metric spaces that extends various existing fuzzy metric spaces. We establish novel fixed-point and best proximity-point theorems for both single-valued and multivalued mappings, thereby broadening the scope of fuzzy analysis. Furthermerefore, we have for aore, we apply one of our key results to derive conditions, ensuring the existence and uniqueness of a solution to Hadamard $\Psi$-Caputo tempered fuzzy fractional differential equations, particularly in the context of the SIR dynamics model. These theoretical advancements are expected to open new avenues for research in fuzzy fixed-point theory and its applications to hybrid models within $\theta$-fuzzy metric spaces. Full article

We introduce a new and a faster iterative method for the approximation of the fixed point of multivalued nonexpansive mappings in the setting of uniformly convex Banach spaces. We prove some stability and data-dependence results for this novel iterative scheme. A series of numerical illustrations and examples was constructed to validate our results. As an application, we propose a novel method for solving a certain fractional differential equation using our newly developed iterative scheme. Our results extend, unify, and improve several of the known results in the literature. Full article

We test here the prediction capabilities of the new generation of deep learning predictors in the more challenging situation of multistate multidomain proteins by using as a case study a coiled-coil family of Nucleotide-binding Oligomerization Domain-like (NOD-like) receptors from A. thaliana and a few extra examples for reference. Results reveal a truly remarkable ability of these platforms to correctly predict the 3D structure of modules that fold in well-established topologies. A lower performance is noticed in modeling morphing regions of these proteins, such as the coiled coils. Predictors also display a good sensitivity to local sequence drifts upon the modeling solution of the overall modular configuration. In multivalued 1D to 3D mappings, the platforms display a marked tendency to model proteins in the most compact configuration and must be retrained by information filtering to drive modeling toward the sparser ones. Bias toward order and compactness is seen at the secondary structure level as well. All in all, using AI predictors for modeling multidomain multistate proteins when global templates are at hand is fruitful, but the above challenges have to be taken into account. In the absence of global templates, a piecewise modeling approach with experimentally constrained reconstruction of the global architecture might give more realistic results. Full article

This paper introduces a novel closed-form coordinate-free expression for the higher-order Cayley transform, a concept that has not been explored in depth before. The transform is defined by the Lie algebra of three-dimensional vectors into the Lie group of proper orthogonal Euclidean tensors. The approach uses only elementary algebraic calculations with Euclidean vectors and tensors. The analytical expressions are given by rational functions by the Euclidean norm of vector parameterization. The inverse of the higher-order Cayley map is a multi-valued function that recovers the higher-order Rodrigues vectors (the principal parameterization and their shadows). Using vector parameterizations of the Euler and higher-order Rodrigues vectors, we determine the instantaneous angular velocity (in space and body frame), kinematics equations, and tangent operator. The analytical expressions of the parameterized quantities are identical for both the principal vector and shadows parameterization, showcasing the novelty and potential of our research. Full article

Magnetic shape memory alloy-based actuators (MSMA-BAs) have extensive applications in the field of micro-nano positioning technology. However, complex hysteresis seriously affects its performance. To describe the hysteresis of MSMA-BA, this study proposes integrating a hysteresis operator and the rate-of-change function of the input signal into the least squares support vector machine (LS-SVM) framework to construct a rate-dependent dynamic hysteresis model for MSMA-BAs. The hysteresis operator converts the multi-valued mapping of hysteresis into a one-to-one mapping, while the rate-of-change function of the input signal captures the rate dependence of the hysteresis, thereby enhancing the model’s ability to describe complex hysteresis. In addition, with the powerful nonlinear fitting capability and good generalization of LS-SVM, the dynamic performance of the proposed model is effectively improved. Experimental results show that the proposed model accurately describes the hysteresis of MSMA-BA. Full article

The objective of this research article is to introduce Kikkawa and Suzuki-type contractions in the setting of topological vector space-valued cone metric space with a solid cone and establish some new fixed point results for multi-valued mappings. The problem of finding fixed points for multi-valued mappings satisfying locally contractive conditions on a closed ball is also addressed. Our findings generalize a number of well-established results in the literature. To highlight the uniqueness of our key finding, we present an example. As a demonstration of the applicability of our principal theorem, we prove a result in homotopy theory. Full article

In this paper, we delve into the ideas of Geraghty-type proximal contractions and their relation to multivalued, single-valued, and self mappings. We begin by introducing the notions of ${\left(\psi \omega \right)}_{MCP}$-proximal Geraghty contraction and rational ${\left(\psi \omega \right)}_{RMCP}$-proximal Geraghty contraction for multivalued mappings, aimed at establishing coincidence point results. To enhance our understanding and illustrate the concepts, practical examples are provided with each definition. This study extends these contractions to single-valued mappings with the introduction of ${\left(\psi \omega \right)}_{SCP}$-proximal Geraghty contraction and rational ${\left(\psi \omega \right)}_{RSCP}$-proximal Geraghty contraction, supported by relevant examples to reinforce the main results. Then, we explore ${\left(\psi \omega \right)}_{SFP}$ Geraghty contraction and rational ${\left(\psi \omega \right)}_{RSFP}$ contraction for self-mappings, obtaining fixed point theorems and clearly illustrating them through examples. Finally, we apply the theoretical framework developed to investigate the existence and uniqueness of solutions to certain two-dimensional Volterra integral equations. Specifically, we consider the transformation of first-kind Volterra integral equations, which play crucial roles in modeling memory in diverse scientific fields like biology, physics, and engineering. This approach provides a powerful tool for solving difficult integral equations and furthering applied mathematics research. Full article

In this manuscript, for the purpose of investigating the coincidence best proximity point, best proximity point, and fixed point results via alternating distance $\varphi$, we discuss some multivalued ${(\varphi -{\mathcal{F}}_{\tau })}_{C_P}$ and ${(\varphi -{\mathcal{F}}_{\tau })}_{B_P}-$proximal contractions in the context of rectangular metric spaces. To ascertain the coincidence best proximity point, best proximity point, and the fixed point for single-valued mappings, we reduce these findings using ${({\mathcal{F}}_{\tau })}_{C_P}$ and ${({\mathcal{F}}_{\tau })}_{B_P}-$proximal contractions. To make our work more understandable, examples of both single- and multivalued mappings are provided. These examples support our core findings, which rely on coincidence points, as well as the corollaries that address fixed point conclusions. In the final phase of our study, we use the obtained results to verify that a solution to a Fredholm integral equation exists. This application highlights the theoretical framework we built throughout our study. Full article