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The document is an editorial conclusion for a special issue on "New Theory and Applications of Nonlinear Analysis, Fractional Calculus, and Optimization." It highlights the widespread and significant applications of nonlinear analysis in various fields of mathematics and science. The special issue includes 10 research papers that cover topics such as optimality conditions, fixed point results, determinantal expressions, pricing of credit risk derivatives, pseudo-asymptotically periodic solutions, common fixed points, local unique solvability, finite-time stability, summation and integral representations, and the existence of solutions. The authors express their appreciation to the contributors and reviewers and hope that the papers inspire future research in these areas. [Extracted from the article]

The transition from the Uniform Building Code (UBC-97) to the International Building Code (IBC-21) marked a major shift in the definition of seismic hazard. The term "seismic hazard" in the form of peak ground acceleration (PGA) is replaced by spectral acceleration. This paper investigates the effect of using new seismic hazards on the structural performance of reinforced concrete (RC) buildings. It also looks into the financial impact on the capital costs of new buildings. Useful insights are made to understand the structural performance and financial impact of adopting IBC 21 for structural design in contrast to UBC 97. This study was carried out from the perspective of a developing country, Pakistan. Reinforced concrete moment resisting and dual frames are used as the main structural system of a typical 7-story residential building to investigate the aforementioned effect. The frames are assumed to be located in two locations with high and low seismic hazards. The effect on structural performance is investigated via nonlinear pushover analysis. Financial impact is judged mainly through cost estimation for steel and concrete. A detailed discussion is also presented on the seismic design guidelines in both codes. [ABSTRACT FROM AUTHOR]

With the advancement of technology, social media has become an integral part of people's daily lives. This has resulted in the emergence of a new group of individuals known as "professional operation people". These individuals actively engage with social media platforms, taking on roles as content creators, influencers, or professionals utilizing social media for marketing and networking purposes. Therefore, in this article, we designed a six-dimensional fractional-order social media addiction model (FOSMA) in the sense of Caputo, which took into account the professional operations population. Initially, we established the positivity and boundedness of the FOSMA model. After that, the basic regeneration number and the equilibrium points (no addiction equilibrium point and addiction equilibrium point) were computed. Then, the local asymptotic stability of the equilibrium points were proved. In order to investigate the bifurcation behavior of the model when R 0 = 1 , we extended the Sotomayor theorem from integer-order to fractional-order systems. Next, by the frequency analysis method, we converted the fractional order model into an equivalent partial differential system. The tanh function was introduced into the scheme of sliding mode surface. The elimination of addiction was achieved by the action of the fractional order sliding mode control law. Finally, simulation results showed that fractional order values, nonlinear transmission rates, and specialized operating populations had a significant impact on predicting and controlling addiction. The fractional-order sliding mode control we designed played an important role in eliminating chatter, controlling addiction, and ensuring long-term effectiveness. The results of this paper have far-reaching implications for future work on modeling and control of fractional-order systems in different scenarios, such as epidemic spread, ecosystem stabilization, and game addiction. With the advancement of technology, social media has become an integral part of people's daily lives. This has resulted in the emergence of a new group of individuals known as "professional operation people". These individuals actively engage with social media platforms, taking on roles as content creators, influencers, or professionals utilizing social media for marketing and networking purposes. Therefore, in this article, we designed a six-dimensional fractional-order social media addiction model (FOSMA) in the sense of Caputo, which took into account the professional operations population. Initially, we established the positivity and boundedness of the FOSMA model. After that, the basic regeneration number and the equilibrium points (no addiction equilibrium point and addiction equilibrium point) were computed. Then, the local asymptotic stability of the equilibrium points were proved. In order to investigate the bifurcation behavior of the model when we extended the Sotomayor theorem from integer-order to fractional-order systems. Next, by the frequency analysis method, we converted the fractional order model into an equivalent partial differential system. The tanh function was introduced into the scheme of sliding mode surface. The elimination of addiction was achieved by the action of the fractional order sliding mode control law. Finally, simulation results showed that fractional order values, nonlinear transmission rates, and specialized operating populations had a significant impact on predicting and controlling addiction. The fractional-order sliding mode control we designed played an important role in eliminating chatter, controlling addiction, and ensuring long-term effectiveness. The results of this paper have far-reaching implications for future work on modeling and control of fractional-order systems in different scenarios, such as epidemic spread, ecosystem stabilization, and game addiction. [ABSTRACT FROM AUTHOR]

In this two-paper series, we prove the invariance of the Gibbs measure for a threedimensional wave equation with a Hartree nonlinearity. The novelty lies in the singularity of the Gibbs measure with respect to the Gaussian free field. In this paper, we focus on the dynamical aspects of our main result. The local theory is based on a paracontrolled approach, which combines ingredients from dispersive equations, harmonic analysis, and random matrix theory. The main contribution, however, lies in the global theory. We develop a new globalization argument, which addresses the singularity of the Gibbs measure and its consequences. [ABSTRACT FROM AUTHOR]

This is the second paper in a series of papers addressing the characteristic gluing problem for the Einstein vacuum equations. We solve the codimension-10 characteristic gluing problem for characteristic data which are close to the Minkowski data. We derive an infinite-dimensional space of gauge-dependent charges and a 10-dimensional space of gauge-invariant charges that are conserved by the linearized null constraint equations and act as obstructions to the gluing problem. The gauge-dependent charges can be matched by applying angular and transversal gauge transformations of the characteristic data. By making use of a special hierarchy of radial weights of the null constraint equations, we construct the null lapse function and the conformal geometry of the characteristic hypersurface, and we show that the aforementioned charges are in fact the only obstructions to the gluing problem. Modulo the gauge-invariant charges, the resulting solution of the null constraint equations is C m + 2 for any specified integer m ≥ 0 in the tangential directions and C 2 in the transversal directions to the characteristic hypersurface. We also show that higher-order (in all directions) gluing is possible along bifurcated characteristic hypersurfaces (modulo the gauge-invariant charges). [ABSTRACT FROM AUTHOR]

Purpose: The alteration of tooth surface microtopography has an influence on the dynamic behavior of gear transmission. In order to obtain accurate dynamic analysis results, a dynamic model of gear transmission with tooth surface roughness characteristics is required. Methods: A dynamic model of gear transmission with tooth surface roughness characteristics is established by employing fractal theory. Moreover, gears with varied roughness are measured and the corresponding transmission errors are obtained via simulation computation based on the collected data. Results: The numerical simulations demonstrate that the dynamic properties of the gear transmission gradually degenerate with the enhancement of the roughness. Moreover, the initial gear backlash has a little effect on the dynamic behavior of the gear, but has an effect on the impact strength when it meshes in and out. Compared with the traditional dynamic model, the model established in this paper has a better predictive capability. The experimental outcomes demonstrate that the dynamic behavior of the gears attenuates with the increment of the tooth surface roughness. Comparison with existing experimental data reveals that the simulation outcomes agree with the experimental findings in the frequency range from 0.2 to 0.6 as well as from 1.2 to 1.4. In the interval from 0.6 to 1.2, the simulation results follow the experimental data to a certain extent, with a generally consistent trend. Conclusions: This paper theoretically substantiates the correlation between tooth surface roughness and the dynamic behavior of gear transmission, establishing a foundational theoretical base for the design of gear surface. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to select the optimal section of different cross-sectional multi-cell hexagonal tubes under axial dynamic loads in three categories of internal edge thicknesses. The explicit non-linear FE code LS-DYNA is employed for numerical simulation. The results of crashworthiness performance criteria are obtained for various alternatives of configurations. TOPSIS method introduces the rank of different sections. The most effective section in the three categories is selected. In the continuation of the research, the straight inner sides of small hexagons were replaced with semi-elliptic and semicircle, but with respect to the symmetry of the larger hexagon diameter and equal perimeter size in order to evaluate the crashworthiness criteria in the selected section. [ABSTRACT FROM AUTHOR]

This paper is focused on the diagnostics of multicopter UAV propulsion system, in which the temporary transient states occur during operation in faulty conditions (eg. not all motor phases working properly). As a diagnostic sensor, the piezo strip has been used, which is very sensitive to any vibrations of the multi-rotor frame. The paper concerns the precise location of the sensor for more effective monitoring of the propulsion system state. For this purpose, a nonlinear analysis of the vibration times series was carefully presented. The obtained non-linear time series were studied with the recurrence analysis in short time windows, which were sensitive to changes in Unmanned Aerial Vehicle motor speeds. The tests were carried out with different percentage of the pulse width modulation signal used for the operation of the brushless motor and for different locations of the piezosensor (side and top planes of the multicopter arm). In the article, it was shown that the side location of the piezosensor is more sensitive to changes in the Unmanned Aerial Vehicle propulsion system, which was studied with the Principal Component Analysis method applied for four main recurrence quantifications. The research presented proves the possibility of using nonlinear recurrence analysis for propulsion system diagnostics and helps to determine the optimal sensor location for more effective health monitoring of multicopter motor. [ABSTRACT FROM AUTHOR]

This paper is devoted to the local null-controllability of the nonlinear KdV equation equipped the Dirichlet boundary conditions using the Neumann boundary control on the right. Rosier proved that this KdV system is small-time locally controllable for all noncritical lengths and that the uncontrollable space of the linearized system is of finite dimension when the length is critical. Concerning critical lengths, Coron and Crépeau showed that the same result holds when the uncontrollable space of the linearized system is of dimension 1; later Cerpa, and then Cerpa and Crépeau, established that the local controllability holds at a finite time for all other critical lengths. In this paper, we prove that, for a class of critical lengths, the nonlinear KdV system is not small-time locally controllable. [ABSTRACT FROM AUTHOR]

In this paper, the modified matrix exponential (MME) method under zero-order hold (ZOH) assumption, is applied to solve systems of stiff ordinary differential equations. Some examples are given to illustrate the accuracy and effectiveness of the method. We compare our results with results obtained by matrix exponential (ME) method and by the Matlab ode23 solver. [ABSTRACT FROM AUTHOR]

Maximising the power production of large wind farms is key to the transition towards net zero. The overarching goal of this paper is to propose a computational method to maximise the power production of wind farms with two practical design strategies. First, we propose a gradient-free method to optimise the wind farm power production with high-fidelity surrogate models based on large-eddy simulations and a Bayesian framework. Second, we apply the proposed method to maximise wind farm power production by both micro-siting (layout optimisation) and wake steering (yaw angle optimisation). Third, we compare the optimisation results with the optimisation achieved with low-fidelity wake models. Finally, we propose a simple multi-fidelity strategy by combining the inexpensive wake models with the high-fidelity framework. The proposed gradient-free method can effectively maximise wind farm power production. Performance improvements relative to wake-model optimisation strategies can be attained, particularly in scenarios of increased flow complexity, such as in the wake steering problem, in which some of the assumptions in the simplified flow models become less accurate. The optimisation with high-fidelity methods takes into account nonlinear and unsteady fluid mechanical phenomena, which are leveraged by the proposed framework to increase the farm output. This paper opens up opportunities for wind farm optimisation with high-fidelity methods and without adjoint solvers. [ABSTRACT FROM AUTHOR]

This paper explores two sample-based methods for analysing multistable systems: basin stability and basin entropy. Both methods rely on many numerical integration trials conducted with diverse initial conditions. The collected data is categorised and used to compute metrics that characterise solution stability, phase space structure, and system dynamics predictability. Basin stability assesses the overall likelihood of reaching specific solutions, while the basin entropy measure aims to capture the structure of attraction basins and the complexity of their boundaries. Although these two metrics complement each other effectively, their original procedures for computation differ significantly. This paper introduces a universal approach and algorithm for calculating basin stability and entropy measures. The suitability of these procedures is demonstrated through the analysis of two non-linear systems. [ABSTRACT FROM AUTHOR]

The heating of a thin metal film subjected to the ultra-short laser pulse is presented. Mathematical description of this process is based on the system of equations describing the electron and lattice temperatures and dependences between intensity of heat fluxes and temperature gradients supplemented by appropriate boundary and initial conditions. In this approach, a system of four equations needs to be solved. In this paper, another method of solution of the above formulated problem is proposed. Using appropriate mathematical manipulations, instead of four equations, two equations describing the lattice and electron temperature distributions are obtained. This system of two equations is solved using an implicit scheme of the finite difference method. The results obtained using both approaches were compared. They were almost identical, which confirms the correctness of the proposed method. [ABSTRACT FROM AUTHOR]

The paper contains a parametric dynamic analysis of cable-strut domes. The special structures named tensegrity are considered. Two qualitative different tensegrity domes, i.e., the Geiger dome and the Levy dome are taken into account. The aim of the study is to compare the dynamic behaviour of such structures. The first stage of analysis involves the identification of initial prestress forces (system of internal forces, which holds structural components in stable equilibrium) and infinitesimal mechanisms. The second stage focuses on calculating natural frequencies, while in the last, the impact of time-independent external loads on vibrations is studied. The influence of initial prestress and external load on the dynamic response of the structures is considered. A geometrically non-linear model is used to analysis. Presented considerations are crucial for the next step in the analysis, i.e., dynamic stability analysis of the behaviour of tensegrity structures under periodic loads. [ABSTRACT FROM AUTHOR]

This paper presents an innovative approach for improving the seismic protection of existing structures by introducing an additional dissipative structure (ADS). The seismic energy impacting the building can be dissipated through the contribution provided by the ADS, thereby reducing the need for the existing building to ensure its seismic capacity. This retrofitting technique is well-suited for structures facing architectural restrictions or challenging-to-update elements. It can help to address foundational issues by applying loads to new external components. This paper describes the design of the ADS and proposes a displacement-based design procedure. The design process involves a nonlinear static analysis and a simple procedure that must be iteratively repeated until the retrofitting target is achieved. This approach is simple and computationally efficient and can also be used for complex and irregular structures. Such structures are frequently encountered, and existing structures often exhibit unusual geometries and materials requiring extensive numerical modeling. The efficacy of this technique was evaluated using the case study of a school building located in central Italy. The results of numerical analyses indicated that owing to the ADS's contribution, the seismic capacity of both buildings was enhanced, addressing the challenges associated with complex foundational interventions. [ABSTRACT FROM AUTHOR]

This paper introduced a parametric workflow for the design of tensile structures, encompassing form-finding, patterning, flattening, and geometrically nonlinear structural analysis of cables and membranes, and how these design steps can be sequenced and iterated. The concepts of parametric design and visual programming languages were outlined, with a particular focus on structural design. The implementation of these concepts was straightforward, and the paper explained their application into a new Grasshopper plug-in, called BATS - basic analysis of tensile structures, capable of performing the full design cycle of this type of structures. [ABSTRACT FROM AUTHOR]

Neural network models are often used to analyse non-linear systems; here, in cases of small datasets, we review our complementary approach to deep learning with the purpose of highlighting the importance and roles (linear, non-linear or threshold) of certain variables (assumed as causal) in determining the behaviour of a target variable; this also allows us to make predictions for future scenarios of these causal variables. We present a neural tool endowed with an ensemble strategy and its applications to influence analyses in terms of pruning, attribution and future predictions (free code issued). We describe some case studies on climatic applications which show reliable results and the potentialities of our method for medical studies. The discovery of the importance and role (linear, non-linear or threshold) of causal variables and the possibility of applying the relationships found to future scenarios could lead to very interesting applications in medical research and the study and treatment of cancer, which are proposed in this paper. [ABSTRACT FROM AUTHOR]

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This paper shows an extensive study on the Typical Connections used in Double-Layer Space Truss. For this structural system, the ends of the bars are flattened to connect the bars. However, the flattening process results in a highly plastic stamping zone susceptible to warping with the appearance of two eccentricities, one of which causes rotation of the connection, with the presence of a bending moment with local rupture resulting in progressive collapse of the entire coverage system, as already evidenced in several countries. Therefore, eccentricity in this paper is studied and an analytical solution to the problem is presented through the use of a new device called a spacer. Furthermore, a preliminary study with complex numerical simulation was carried out with nonlinear analysis in ABAQUS were evaluated. For this study, nine space trusses were experimentally tested with reinforcement spacer in reduced trusses. After confirming the efficiency of the spacer proposal, another six space trusses were tested in the laboratory, this time, on a full-scale. In this study, two types of spacers were evaluated, one made of USI SAC 350 steel and another cheaper one made from recycled tires from heavy vehicles with multiple filaments of steel and nylon wires in the rubber layers. The two devices presented very close resistance capacity values, with a resistance gain of approximately 30% in relation to connections without reinforcement, with structural failure characterized by buckling of the bars. Finally, a numerical study of space trusses with spacers was developed. In practical design terms, from these FE simulations it was possible to determine the normal stresses for different spacers applied in the different modeled spans. [ABSTRACT FROM AUTHOR]

This paper delves into the asymptotic and oscillatory behavior of all classes of solutions of fourth-order nonlinear neutral delay differential equations in the noncanonical form with damping terms. This research aims to improve the relationships between the solutions of these equations and their corresponding functions and derivatives. By refining these relationships, we unveil new insights into the asymptotic properties governing these solutions. These insights lead to the establishment of improved conditions that ensure the nonexistence of any positive solutions to the studied equation, thus obtaining improved oscillation criteria. In light of the broader context, our findings extend and build upon the existing literature in the field of neutral differential equations. To emphasize the importance of the results and their applicability, this paper concludes with some examples. [ABSTRACT FROM AUTHOR]

The paper is a continuation and completion of the paper Bruno, A.D.; Azimov, A.A. Parametric Expansions of an Algebraic Variety Near Its Singularities. Axioms 2023, 5, 469, where we calculated parametric expansions of the three-dimensional algebraic manifold Ω , which appeared in theoretical physics, near its 3 singular points and near its one line of singular points. For that we used algorithms of Nonlinear Analysis: extraction of truncated polynomials, using the Newton polyhedron, their power transformations and Formal Generalized Implicit Function Theorem. Here we calculate parametric expansions of the manifold Ω near its one more singular point, near two curves of singular points and near infinity. Here we use 3 new things: (1) computation in algebraic extension of the field of rational numbers, (2) expansions near a curve of singular points and (3) calculation of branches near infinity. [ABSTRACT FROM AUTHOR]

In order to meet the needs of military, road construction, multimedia industry and other aspects, UAVs are gradually given more functions. As the basic function of UAV applications, the fixed-point delivery problem model has higher and higher accuracy requirements. However, in the actual scene, the UAV delivery problem is affected by the interaction of various factors such as flight height, air resistance, and dive angle, which makes it difficult to achieve high stability and high hit accuracy. This paper will analyze the complex motion model based on the fixed-point delivery of explosives by UAV, study the relationship between the stability of UAV delivery and the hit accuracy, and analyze the influence of relevant parameters on the problem by using modeling. In this paper, a multivariate nonlinear continuous time change model is proposed, and a continuous time slice discretization idea operation model is introduced to approximate the time slice splitting inside the UAV launch motion. Secondly, the design quantified evaluation index reaction the initial velocity of the explosive, the launch Angle, the height off the ground and other parameters to analyze the model. Finally, the best scheduling strategy is obtained and verified by using the idea of variable traversal and trial- and-error simulation. The experimental results show that the variation of UAV flying height, speed, depression and other interference factors is consistent with the prediction of score and hit accuracy, according to the environment setting of this model, when the UAV is 300 meters above the ground and 290 meters away from the target horizontal position, the delivery speed is 250m/s, and the pitch angle is about 27°, the fixed-point delivery of explosives is the best strategy. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear dynamic model of a parallel shaft gear system consisting of two involute spur gears is developed to investigate the coupling effect between the gradual surface wear of gear teeth over time and nonlinear dynamic characteristics. A uniform wear model that accounts for how the volumetric wear of the gear teeth affect their meshing position, backlash, and stiffness is proposed. Additionally, a nonlinear dynamic model with six degrees of freedom is described that considers friction, time-varying gear backlash, and time-varying meshing stiffness. The proposed model significantly changes the mesh stiffness, not only in terms of value but also in terms of contact ratio. Furthermore, the nonlinear dynamic characteristics of the gear system vary significantly. It is found that the gradual wear of gear teeth affects the meshing position and further has a significant impact on the nonlinear dynamic characteristics of the spur gear system. This paper provides a basis for studying the nonlinear dynamic characteristics of the spur gear system as it experiences the gradual wear of teeth over time. [ABSTRACT FROM AUTHOR]

Hangers or suspenders in cable-supported bridges are key load transfer components. These members are vulnerable to sudden fracture due to accidental damage, corrosion, fatigue, or during extreme events. Examples of collapse or damage in cable-supported bridges that are initiated by the sudden loss of hangers have been observed recently. However, specific design provisions that address sudden hanger loss for tied-arch bridges are largely absent. This paper focuses on the sudden loss of hangers in tied-arch bridges, a topic on which there are very limited studies. In this paper, the behavior of a tied-arch bridge that is subjected to single and multiple hanger losses was investigated computationally through a high-fidelity finite-element model (FEM) of a bridge. The simulation results showed that the network tied-arch bridge exhibited robustness against the failure of a single hanger. With the sequential loss of multiple hangers, the loss of hangers that slanted backward had a much larger effect than that of hangers that slanted forward. Inelastic arch buckling precipitated a full system collapse after the loss of nine hangers. [ABSTRACT FROM AUTHOR]

This paper aims to demonstrate nonlinear risk factor interactions based on a data-driven approach using a Bayesian network model, providing a road safety use case. Road safety is a critical issue worldwide, with approximately 1.3 million road traffic deaths each year (WHO). Traditional road safety risk assessment methods often analyze individual factors separately; however, these assessments fail to capture the complex dynamics of real-world analysis, in which multiple factors interact through nonlinear relationships. In this study, a novel road safety risk assessment approach that uses a Bayesian network model to explore the nonlinear relationships among road safety risk factors is developed. Through the analysis of extensive crash reports from the state of Maryland, the complex interdependencies among various risk factors and their cumulative impact on road safety are investigated. Our findings show that two combined risk factors have different effects on risk level when considered individually. Two case studies related to human state risk factors and environmental risk factors, such as driving under the influence and snowy roads, as well as fatigue and snowy roads, have an amplified effect on the risk level. The findings highlight the importance of considering nonlinear interactions among risk factors when developing effective and targeted strategies for accident prevention and road safety improvement. This research contributes to the field of road safety by presenting a new methodology for understanding and mitigating road safety hazards. [ABSTRACT FROM AUTHOR]

It is widely recognized that certain structures, when subjected to static compression, may exhibit a bifurcation point, leading to the potential occurrence of a secondary equilibrium path. Also, there is a tendency of deflection increment without a bifurcation point to occur for imperfect structures. In this paper, some relatively unknown phenomena are investigated. First, it is demonstrated that in some conditions, the linear buckling mode shape may differ from the result of geometrically nonlinear analysis. Second, a mode jumping phenomenon is described as a transition from a secondary equilibrium path to an obscure one as a tertiary equilibrium path or a second bifurcation point. In this regard, some non-square plates with unsymmetric layer arrangements (in the presence of extension–bending coupling) are subjected to a uniaxial in-plane compression. By considering the geometrically linear and nonlinear problems, the bucking modes and post-buckling behaviors, e.g., the out-of-plane displacement of the plate versus the load, are obtained by ANSYS 2023 R1 software. Through a parametric analysis, the possibility of these phenomena is investigated in detail. [ABSTRACT FROM AUTHOR]

In this work, we use two unique methodologies, the homotopy perturbation transform method and Yang transform decomposition method, to solve the fractional nonlinear seventh-order Kaup–Kupershmidt (KK) problem. The physical phenomena that arise in chemistry, physics, and engineering are mathematically explained in this equation, in particular, nonlinear optics, quantum mechanics, plasma physics, fluid dynamics, and so on. The provided methods are used to solve the fractional nonlinear seventh-order KK problem along with the Yang transform and fractional Caputo derivative. The results are significant and necessary for exploring a range of physical processes. This paper uses modern approaches and the fractional operator to develop satisfactory approximations to the offered problem. To solve the fractional KK equation, we first use the Yang transform and fractional Caputo derivative. He's and Adomian polynomials are useful to manage nonlinear terms. It is shown that the suggested approximate solution converges to the exact one. In these approaches, the results are calculated as convergent series. The key advantage of the recommended approaches is that they provide highly precise results with little computational work. The suggested approach results are compared to the precise solution. By comparing the outcomes with the precise solution using graphs and tables we can verify the efficacy of the offered strategies. Also, the outcomes of the suggested methods at various fractional orders are examined, demonstrating that the findings get more accurate as the value moves from fractional order to integer order. Moreover, the offered methods are innovative, simple, and quite accurate, demonstrating that they are effective for resolving differential equations. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying a class of fuzzy fractional switched implicit differential equations (FFSIDEs) with non-instantaneous impulses that there are few papers considering this issue. Considering switching law and the memory property of fractional calculus, we first present a formula of solution for FFSIDEs with non-instantaneous impulses. Subsequently, based on a sequence of Picard functions, we explore the existence of solutions for the addressed equations by successive approximation. Furthermore, Ulam–Hyers (U–H) stability for this considered equations is derived. The main results are obtained using fuzzy-valued fractional calculus and nonlinear analysis. Finally, two numerical examples illustrating the theoretical result are given. [ABSTRACT FROM AUTHOR]

The 2020 Zagreb earthquake caused extensive damage to historically significant buildings, including the Cathedral of the Assumption of Mary, a key monument of Croatian cultural heritage. The earthquake rendered the cathedral unsafe due to significant damage to its towers and numerous cracks in its vaults and walls. Urgent measures were necessary to ensure safety and facilitate planned reconstruction and strengthening efforts. A specialised scaffolding design was developed to support inaccessible and unstable areas, involving over 1000 tonnes of steel. This paper details the structural concepts and specific scaffolding design implemented for the urgent restoration and seismic retrofitting of Zagreb Cathedral, ensuring it meets high earthquake resistance requirements. [ABSTRACT FROM AUTHOR]

The paper deals with frame steel structures required to ensure sufficient resistance, appropriate ductility and safety against brittle failure. This special aim cannot be reached by utilizing standard procedures and standard beam elements. Therefore, the present study proposes an innovative design strategy devoted to plane steel frames constituted by I-shaped cross-section beam elements and subjected to simultaneous combinations of serviceability limit state conditions and ultimate limit state conditions. Special factory-made I-shaped uniform piecewise steel profiles are utilised to provide the optimal behaviour of the frame. The proposed design strategy consists of two subsequent steps: at first a classical sizing of the frame is performed by utilising standard steel profiles, then a specific optimal design problem is performed to define the optimal geometry of the I-shaped steel profiles that fulfils all the constraints related to the required resistance and the limited deformability as well as special introduced constraints related to the protection against the brittle failure. The reliability of the procedure and the expected optimal behaviour of the frame are checked by performing nonlinear static analyses employing a recently proposed Fibre Smart Displacement-Based (FSDB) beam element model. The proposed beam element is defined by adopting displacement shape functions capable of embedding the cross-section discontinuities by means of the use of generalised functions. Furthermore, the proposed shape functions are addressed to as "smart" since capable of update in accordance with the development of plastic deformations detected by means of fibre discretisation of the cross-section. The results related to a simple steel portal confirmed the expected optimal behaviour of the structure. [ABSTRACT FROM AUTHOR]

Due to factors such as climate change, natural disasters, and deforestation, most measurement processes and initial data may have errors. Therefore, models with imprecise parameters are more realistic. This paper constructed a new predator-prey model with an interval biological coefficient by using the interval number as the model parameter. First, the stability of the solution of the fractional order model without a diffusion term and the Hopf bifurcation of the fractional order α were analyzed theoretically. Then, taking the diffusion coefficient of prey as the key parameter, the Turing stability at the equilibrium point was discussed. The amplitude equation near the threshold of the Turing instability was given by using the weak nonlinear analysis method, and different mode selections were classified by using the amplitude equation. Finally, we numerically proved that the dispersal rate of the prey population suppressed the spatiotemporal chaos of the model. [ABSTRACT FROM AUTHOR]

This paper provides new and useful insights into the performance and efficiency of geotechnical seismic isolation (GSI) systems with gravel-rubber mixtures containing 10%, 25% and 40% volumetric rubber content (VRC). Finite element numerical models were developed in OpenSees and subjected to sinusoidal ground motions with varying input base acceleration and frequency. The best seismic performance was attained for VRC = 40% at a frequency of 8 Hz. Using a newly developed GSI efficiency index, the energy dissipation efficiency of VRC = 40% was found to vary between good to excellent, while that of VRC = 10% and 25% is poor. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of solutions and analyze the large-time behavior for Gurtin–Maccamy population model involving conformable fractional derivatives. As a preliminary step, we construct a generic structure of the solution associated with our proposed model by utilizing some basic properties and tools of conformable fractional calculus. We establish the existence of a unique solution of the given model with the given initial conditions. At last, by using the upper and lower solutions for the characteristic equation, we define the upper and lower boundaries for the obtained solution and describe the large-time behavior of the total population. [ABSTRACT FROM AUTHOR]

The dimensions and arrangement of columns have a significant impact on the seismic behavior of a structure. The objective of this paper is to ascertain the appropriate dimensions and configuration of columns for a building utilizing a frame system and framed tube system. Various column sizes and configurations were utilized to model four different types of buildings. The pushover analysis method was employed to determine the deformation capacity. The results obtained from the pushover analysis, indicate that the drift ratio for each building model remains below the prescribed 2% drift limit. The fourth building model, known as the framed tube system, exhibits the lowest drift ratio among the models, measuring at 0.81%. Upon reviewing the budget plan, it is evident that the second model building exhibits the lowest cost, displaying a notable disparity of 20.98% in comparison to the fourth model building, which boasts the highest cost. After considering both structural performance and budgeted cost, it is determined that the framed tube structural system is the optimal configuration. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the use of Lambert W functions in the analysis of nonlinear dynamics and bifurcations of a new two-dimensional γ -Ricker population model. Through the use of such transcendental functions, it is possible to study the fixed points and the respective eigenvalues of this exponential diffeomorphism as analytical expressions. Consequently, the maximum number of fixed points is proved, depending on whether the Allee effect parameter γ is even or odd. In addition, the analysis of the bifurcation structure of this γ -Ricker diffeomorphism, also taking into account the parity of the Allee effect parameter, demonstrates the results established using the Lambert W functions. Numerical studies are included to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Ferrite-loaded gyromagnetic nonlinear transmission line (GNLTL) provides a possible option to compress an input pulse to a narrower width for its remarkable sharpening effect. However, it is difficult to accurately predict the output of the GNLTL due to the complex interaction between the magnetic moment of ferrite and the bias magnetic field. In this paper, a finite element model of the GNLTL is established based on the Landau–Lifshitz–Gilbert equation to investigate the performance of the GNLTL. To validate this model, a prototype is used for experimental comparison. The result demonstrates good agreement between experiment and simulation. This paper further explores the influence of the bias magnetic field and the length of the GNLTL on the output pulse. Moreover, a method to sharpen the falling edge is proposed based on the reflection and superposition of the GNLTL output. Simulation and experimental results show its effectiveness and feasibility. [ABSTRACT FROM AUTHOR]

Summary: This paper studies the finite‐time tracking problem for nonlinear impulsive differential inclusion systems with randomly varying trial lengths. First, we convert the set‐valued mapping in the differential inclusion systems to single‐valued mapping by a Steiner‐type selector. For the tracking problem of random discontinuous output trajectories, this paper defines a piecewise continuous variable by zero‐order holder to correct the tracking error of segmented continuity. Then, we introduce the average operator with forgetting factor to design three novel learning schemes, and establish convergence results by using the mathematical analysis tools such as impulsive Gronwall inequality and λ$$ \lambda $$‐norm. Finally, a numerical example verifies the validity of the theoretical results, and we compare the tracking performance of the output trajectories for different forgetting factors. [ABSTRACT FROM AUTHOR]

This study presents the problem of spreading non fatal disease in a population by using the Morgan-Voyce collocation method. The main aim of this paper is to find the exact solutions of the SIR model with vaccination. The problem may be modelled mathematically with a nonlinear system of ordinary differential equations. The presented method reduces the problem into a nonlinear algebraic system of equations by using unknown coefficient Morgan-Voyce polynomials and expanding approximate solutions. Morgan-Voyce polynomials are used. These unknown coefficients are calculated via the collocation method and matrix operation derivations. Two examples are given to show the feasibility of the method. To calculate the solutions, MATLAB R2021a is used. Additionally, comparing our method to the Homotopy perturbation method (HPM) and the Laplace Adomian decomposition method (LADM) proves the accuracy of the solution. The method studied can be seen as effective from these comparisons. So, it is essential to find solutions for the governing model. The study will contribute to literature since we also discuss the vaccination situation. The results of this study are valuable for controlling an epidemic. [ABSTRACT FROM AUTHOR]

With continuous improvement of lifting height and operation range for all-terrain crane in engineering construction, the buckling failure analysis of slender boom composite structure has become a hot research direction in order to ensure the safety and efficiency. In this paper, eigenvalue buckling analysis and nonlinear buckling analysis under multiple loads are carried out on the boom system of telescopic boom and truss auxiliary boom. The results show that the instability will occur in the amplitude plane for slender structure with super-lift system. Meanwhile, as the increase in the elevation angle for boom structure, the buckling load value increases and the stability is enhanced. Compared with geometric nonlinear and eigenvalue buckling load, when the elevation angle of the boom is 70°, the difference can reach 72.53%. Moreover, geometric initial defects are introduced. Compared displacement–load curves and buckling load values with and without geometric initial defects, the influence on slender composite structure is smaller. The results show that in order to prevent the buckling failure of structure, the hoisting load should not exceed rated load when the elevation angle is small, which provides a basis for engineering design. [ABSTRACT FROM AUTHOR]

To predict renewable energy sources such as solar power in microgrids more accurately, a hybrid power prediction method is presented in this paper. First, the self-attention mechanism is introduced based on a bidirectional gated recurrent neural network (BiGRU) to explore the time-series characteristics of solar power output and consider the influence of different time nodes on the prediction results. Subsequently, an improved quantum particle swarm optimization (QPSO) algorithm is proposed to optimize the hyperparameters of the combined prediction model. The final proposed LQPSO-BiGRU-self-attention hybrid model can predict solar power more effectively. In addition, considering the coordinated utilization of various energy sources such as electricity, hydrogen, and renewable energy, a multi-objective optimization model that considers both economic and environmental costs was constructed. A two-stage adaptive multiobjective quantum particle swarm optimization algorithm aided by a Lévy flight, named MO-LQPSO, was proposed for the comprehensive optimal scheduling of a multi-energy microgrid system. This algorithm effectively balances the global and local search capabilities and enhances the solution of complex nonlinear problems. The effectiveness and superiority of the proposed scheme are verified through comparative simulations. [ABSTRACT FROM AUTHOR]

The implementation of fluid viscous dampers has been proven as a feasible method to improve the seismic performance of buildings. However, the different variables involved in the damper's design affect the structural response, especially in terms of seismic demand on non-structural elements. This paper presents a parametric study on the floor acceleration response of three case study buildings equipped with fluid viscous dampers through nonlinear time-history analysis. The results show that the different design parameters of fluid viscous dampers significantly modify the floor acceleration response, with some damper configurations yielding floor accelerations larger than those of the buildings without dampers. [ABSTRACT FROM AUTHOR]

At present, there are few studies considering both nonlinear and fractional characteristics of suspension in vehicle systems. In this paper, a fractional nonlinear model of a quarter vehicle with two-degree-of-freedom (2-DOF) is innovatively proposed to describe the suspension system containing the viscoelastic material metal rubber. Given the lack of a general calculation scheme for the multi-degree-of-freedom fractional-order incremental harmonic balance method (IHBM), a general calculation scheme for the 2-DOF incremental harmonic balance method for nonlinear systems with fractional order is derived. The nonlinear dynamical properties of the presented model are acquired using this method. The accuracy of the proposed method is verified through a comparison with the power series expansion method. Afterward, the effects of the various parameters on the dynamic performance are analyzed. The vibration peak value of the fractional-order model is significantly higher than that of the integer-order model (IOM). Therefore, the suspension parameters should be designed with a margin when using IOM. [ABSTRACT FROM AUTHOR]

Steel-concrete composite construction picked up its utility because of efficient combination of steel and concrete offering high ductility, strength and stiffness to the structure. Loading action is one of the key parameters to understand the behaviour of a structural element. An attempt has been made in this paper to review the structural performance of steel-concrete composite beams under different loading actions. In addition, the results of nonlinear analysis of steel-concrete composite beams subjected to static loading, using commercial finite element software ANSYS, have been included. Numerical investigations have been performed to understand the behaviour of steel-concrete composite beams under static loading criteria. Numerical models of beams have been created and two-point loading was applied. Load versus mid-span deflection has been plotted. Earlier, validation has been done by comparing the analysis results by authors with the experimental results obtained by previous authors available in literature. The results obtained have shown that dimensions of shear connectors used are having influence on ultimate load capacity of steel-concrete composite beams subjected to static loading. [ABSTRACT FROM AUTHOR]

Since the COVID-19 pandemic was first reported in 2019, it has rapidly spread around the world. Many countries implemented several measures to try to control the virus spreading. The healthcare system and consequently the general quality of life population in the cities have all been significantly impacted by the Coronavirus pandemic. The different waves of contagious were responsible for the increase in the number of cases that, unfortunately, many times lead to death. In this paper, we aim to characterize the dynamics of the six waves of cases and deaths caused by COVID-19 in Rio de Janeiro city using techniques such as the Poincare plot, approximate entropy, second-order difference plot, and central tendency measures. Our results reveal that by examining the structure and patterns of the time series, using a set of non-linear techniques we can gain a better understanding of the role of multiple waves of COVID-19, also, we can identify underlying dynamics of disease spreading and extract meaningful information about the dynamical behavior of epidemiological time series. Such findings can help to closely approximate the dynamics of virus spread and obtain a correlation between the different stages of the disease, allowing us to identify and categorize the stages due to different virus variants that are reflected in the time series. [ABSTRACT FROM AUTHOR]

This paper investigates the lateral-torsional instability of soft-core sandwich beams. This physical phenomenon, which has received limited attention in the framework of sandwich structures, is investigated here in the context of fully nonlinear analysis for the first time. The research addresses, quantifies, and explores the lateral-torsional instability with emphasis on the unique features of the sandwich structure and its geometrically nonlinear response. The research questions relate to the nature of the instability and to the role of the deformability of the core layer in the unique mechanism. The results of the investigation include a new, high-order, nonlinear model for the analysis of the torsional-lateral response as well as new insight into the evolution of the phenomenon in sandwich beams. [ABSTRACT FROM AUTHOR]

This paper discusses the time-fractional nonlinear Schrödinger model with optical soliton solutions. We employ the f + ( G ′ G) -expansion method to attain the optical solution solutions. An important tool for explaining the particular explosion of brief pulses in optical fibers is the nonlinear Schrödinger model. It can also be utilized in a telecommunications system. The suggested method yields trigonometric solutions such as dark, bright, kink, and anti-kink-type optical soliton solutions. Mathematica 11 software creates 2D and 3D graphs for many physically important parameters. The computational method is effective and generally appropriate for solving analytical problems related to complicated nonlinear issues that have emerged in the recent history of nonlinear optics and mathematical physics. Furthermore, we venture into uncharted territory by subjecting our model to chaotic and sensitivity analysis, shedding light on its robustness and responsiveness to perturbations. The proposed technique is being applied to this model for the first time. [ABSTRACT FROM AUTHOR]

Most engineering structures serve in complex and harsh dynamic environments and suffer from nonlinear vibrations generated by random excitations such as strong winds and waves, which need to be mitigated. To this end, a novel viscoelastic nonlinear energy sink (VNES) device is proposed for the vibration control of structures, whereby the random vibration of a nonlinear oscillator with a VNES device is analyzed in this paper. Specifically, the mathematical model of the structure-VNES is formulated. An approximate technique for the treatment of viscoelastic damping element modeled by the fractional derivative is developed, whereby an equivalent nonlinear system without fractional derivative is derived. The averaged Itô equations associated with the amplitude envelopes are then obtained by resorting to the stochastic averaging method. The closed-form solution of the stationary response is solved from the Fokker–Planck–Kolmogorov (FPK) equation and verified by the Monte Carlo simulation (MCS) data simultaneously. The effects of system parameters and noise intensity on the stationary response are sequentially examined. By comparing the VNES system to the case without attachment and one equipped with the commonly used tuned mass damper (TMD) device, the performance and robustness of the VNES are highlighted. The conclusions of this work may contribute to the efficacy of the application of the VNES in practice. [ABSTRACT FROM AUTHOR]

Purpose: The primary objective of the paper is to examine the asymmetric Cointegration and asymmetric causality between financial development and poverty alleviation on annual data in Indian context over the period from 1980 to 2019. Design/methodology/approach: First nonlinearity test by Brooks et al. (1999) is applied to ascertain the nonlinear behavior of the variables used. Once the nonlinear behavior of variables is confirmed, asymmetric and nonlinear unit root tests by Kapetanios and Shin (2008) are applied to check for the order of integration of selected variables. Next, nonlinear autoregressive distributed lag model (NARDL) is employed to analyze the asymmetric Cointegration. Finally, Hatemi-j- asymmetric causality tests is applied to work out the direction of asymmetric causality. Findings: The empirical findings document the existence of asymmetries in the short-run as well as long-run between poverty and financial development. The asymmetry reveals that negative financial development shocks leave a more profound impact on poverty alleviation than their positive equivalents. The findings of Wald's test also confirm the presence of asymmetric Cointegration. The asymmetric cumulative dynamic multipliers used to examine the behavior of asymmetries and adjustments with respect to time lend credence to the results calculated using NARDL estimator. This result exhibits the robustness of the model. Furthermore, the result emanating from recently introduced asymmetric causality test reveals a unidirectional asymmetric causality between negative shocks in financial development and poverty. The findings of the present study necessitate the need for investigating asymmetric and nonlinear effects in finance–poverty nexus, which existent literature has completely neglected, in order to have relevant policy conclusions. Research limitations/implications: The study used "Per capita consumption expenditure" as a measure for poverty due to lack of continuous time series data on headcount ratio. In future, researchers can extend this study by incorporating headcount ratio as a measure of poverty in their respective works. There is further scope of research on this issue by finding out the impact of formal and informal sources of credit on poverty separately. A panel data study for developing countries over a period of time could further confirm/negate the findings of the present study. Originality/value: To the best of the authors' knowledge none of the studies in Indian context has scrutinized asymmetric and nonlinear impact of financial development on poverty. To dredge up asymmetric structures at work, the authors have used the highly celebrated NARDL estimator. To enrich the existent body of knowledge along the lines of asymmetric (nonlinear) linkages, the authors have also used recently introduced asymmetric causality test by Hatemi-j-(2012) to find out the direction asymmetric causality. [ABSTRACT FROM AUTHOR]

In the existing building stock, typically characterised by a high degree of irregularity, the effects of earthquakes are strongly dependent on the epicentre–structure direction and the angle of incidence of the seismic motion. However, the scientific community has not yet reached a unanimous consensus on the evaluation of the effects of seismic incidence angles. Therefore, this paper conducts an extensive investigation of the international literature on current methods to consider seismic directionality, systematically reviewing more than 80 publications on this topic. Following a brief overview of the problem and an analysis of the initial developments of the multidirectionality concept of seismic input, a state-of-the-art review is presented based on the considered analysis methods, specifically response spectrum analysis, nonlinear static analysis, and nonlinear response history analysis. Moreover, the adoption of multidirectional seismic input in popular codes and standards is presented and discussed. This study provides the first comprehensive synthesis of research on the seismic incidence angles across diverse building typologies, offering crucial insights for future code revisions and highlighting significant gaps in current analytical methods and standards, thereby setting a new direction for subsequent empirical investigations. Specifically, the extensive state-of-the-art review revealed that, until now, the evaluation of the angle of incidence was primarily conducted on existing reinforced concrete buildings with a limited number of storeys, analysed with nonlinear response history analysis. This underscores the need for future research to extensively investigate the impact of the angle of incidence on other types of construction typologies. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to apply and verify Fourier series analysis in combination with non-linear regression as a tool of forecasting and planning of inputs in the logistics process of a retail chain store. Design/methodology/approach: For many popular products, a significant effect of seasonality of sales is expected; therefore, the method of Fourier series was chosen as one of the main forecast calculation techniques. However, the use of this method directly for forecasting sales has a limitation in the form of a complete reconstruction of the shape of the curve from of the given monitored time. Thus, the forecast is based only on the significant harmonic components from the Fourier series analysis that will participate in forecast forming. In addition, to respect the trend of series, the results of Fourier series analysis are combined with the non-linear regression. Findings: The results showed that the number of significant harmonic components from the Fourier series analysis is suitable to reflect the future behaviour of the sale in standard market conditions. Forecasting of the sale and accurate purchase planning of goods has a positive effect on reducing the waste of unsold products after their shelf and on increasing of a customer satisfaction. Research limitations/implications: This study has an application in a certain period of time (relatively calm behaviour of the food market) and only for a certain region. Therefore, it is not possible to generalize these results as the behaviour of consumers, e.g. within the state. It will also be interesting to monitor and forecast sales of other food items. Practical implications: This provides a practical and relatively simple tool for implementing or improving the process of forecasting seasonally dependent products in the food industry. Originality/value: This study shows the possibility of forecast that is based on adding the significant harmonic components from the Fourier series analysis to form forecast with the non-linear regression. [ABSTRACT FROM AUTHOR]