We investigate Ricci-Yamabe solitons (RYSs) and gradient Ricci-Yamabe solitons (GRYSs) on four-dimensional Lorentzian manifolds (M⁴,g) admitting a unit timelike torse-forming vector field. We show that when V = ζ and ρ , 0, the soliton equation is compatible with a perfect fluid spacetime structure. For the case of a constant scalar curvature, it is shown that if (M⁴,g) admits an RYS or a GRYS, then (M⁴,g) is an Einstein spacetime, the associated soliton vector field is Killing, and consequently, the RYS or GRYS is trivial. In the non-constant scalar curvature case, the scalar curvature is shown to satisfy a screened wave (Klein-Gordon-type) equation in the RYS setting, whereas the potential function of a GRYS satisfies a second-order differential equation governing its convexity and concavity along the integral curves of the unit timelike vector field. Finally, a specific constant-curvature example is presented in which the GRYS becomes trivial under the corresponding parameter relations.

This work investigated normalized solutions for the Choquard equation with external potential and mixed local-nonlocal nonlinearities

where $N \geq 3, \gamma, \mu>0, \lambda \in \mathbb{R}, p \in\left(2+\frac{4}{N}, 2^{*}\right), 2^{*}=\frac{2 N}{N-2}$, and Iα stood for the Riesz potential when α ∈ (0,N). Under finite potential conditions, normalized ground states were verified. For trapping potentials, normalized ground states paired with bound states were obtained.

This study investigates a biologically constrained computational model of the hippocampal- cortical circuit incorporating magnetic-flow feedback to elucidate the nonlinear dynamical mechanisms through which magnetic stimulation modulates network states and drives transitions among memory- related neural rhythms. Bifurcation analysis characterizes the response of the hippocampal CA3 excitatory population to variations in the magnetic-flow feedback coefficients. One-parameter bifurcation analysis identifies critical bifurcations governing rhythm initiation, stability, and complexity, whereas two-parameter bifurcation diagrams show that cortical feedback expands the oscillatory regime more strongly than hippocampal feedback. Combined feedback produces the largest expansion and generates closed torus-bifurcation curves, indicating quasi-periodic dynamics. An automated sharp wave ripple (SWR) detection algorithm quantifies the incidence of model- derived SWR-related events across feedback conditions, thereby relating changes in the magnetic-flow feedback coefficients to changes in simulated SWR-related rhythmic activity. We further examine how SWR counts depend on two key CX1 microcircuit parameters: excitatory self-connection strength and local connectivity probability. Comparative analysis of SWR distributions illustrates how the network transitions from baseline quiescence or irregular firing to coherent, feedback- driven rhythmic discharge. SWR-count heatmaps further map the modulation of SWR-related activity across the parameter space. Collectively, these results establish a theoretical framework for understanding how magnetic-flow feedback modulates hippocampal-cortical dynamics and SWR- related activity, providing a basis for investigating targeted magnetic neuromodulation in memory- related neural processes.

In this paper, we extend semi-infinite variational programming problems to a class of fractional variational control problems using Caputo-Fabrizio fractional derivatives. In this context, by using integration by parts, the necessary optimality conditions for these problems are obtained, incorporating complete Karush-Kuhn-Tucker (KKT) criteria which include both state and control stationarity conditions. Then, we build a Lagrange functional, where duality properties are derived under suitable assumptions of the involved functions. Furthermore, saddle point criteria connected to the considered Lagrange functional are developed. The main contribution of the study is the extension of semi-infinite fractional variational programming to a controlled setting, leading to a unified framework that combines state and control stationarity conditions, Lagrange duality, and saddle-point characterization. An illustrative numerical example is also provided to demonstrate the applicability of the developed framework to a specific state-control pair.

Relapsing–remitting multiple sclerosis (RRMS) is characterized by recurrent immune activation, lesion development, and marked variability in disease activity. To investigate how lesion- associated activity may feed back on immune regulation, we extend an established effector T cell– regulatory T cell (Teff–Treg) model by introducing a normalized lesion-activity variable and a feedback factor that amplifies antigen-presentation-related immune activation. The resulting closed-loop system links autoreactive effector T-cell activity, lesion-associated activity, and subsequent immune reactivation through lesion–immune feedback. Positivity, global existence, and uniform boundedness hold in the feasible region. Positive equilibria satisfy α = Φ_κ(S ), with S the combined regulatory strength. The feedback-free branch is monotone, and $\mathcal{F}$ > 1 gives backward bending and at least two positive equilibria for α_{S N} < α < α_c, though their exact number and stability remain analytically undetermined. For the working parameters, branch reconstruction and full-Jacobian spectral checks reveal a nondegenerate fold and coexisting stable tolerant and active equilibria separated by a saddle; time integration shows initial-condition dependence, and a schematic branch-following construction illustrates hysteresis-like switching. Routh–Hurwitz conditions, together with conditional saddle- node and Hopf criteria, are derived. Numerical verification identifies a transverse imaginary-pair crossing and a negative first Lyapunov coefficient, consistent with a supercritical Hopf bifurcation, with simulations showing sustained coupled oscillations. The computed two-parameter boundaries concern equilibrium existence and local stability in the scanned regime, not a global classification of attractors or calibrated clinical relapse intervals.

The nonlinear eigenvalue problem

for fixed p > q > 1, was studied under some conditions on the positive potential ω. We used various Prüfer angle methods to characterize the eigenvalue properties for problems on the half-line and finite intervals.

In this paper, the global dynamics and optimal control strategies in a brucellosis transmission model with distribution incubation delays were investigated. The basic reproduction number of the model was first calculated, and then the threshold criteria for the global asymptotic stability of disease-free and endemic equilibria were established. Furthermore, the several effective measures for controlling the spread of diseases are introduced, and then an optimal control model that incorporates these measures was proposed. By providing a reasonable objective function, some optimal control strategies were established. Through numerical simulation of these optimal control strategies, reasonable prevention, control, and treatment measures for brucellosis were proposed.

To address the vulnerability of output-layer gradient leakage during the distributed training of hot-rolled steel strip-crown prediction across multiple steel mills, this paper proposes a privacy-preserving split-layer federated learning scheme based on multi-client functional encryption. The proposed scheme keeps the input layer parameters at local clients, where they are updated using local data but are neither uploaded nor aggregated. Only the output layer gradients are encrypted and aggregated to update the shared output layer parameters. Leveraging the inner-product property of multiclient functional encryption alongside a capacity-aware, fixed client partitioning strategy, the secure aggregation of output layer gradients is achieved entirely within the ciphertext domain. Theoretical analysis derives a conditional stationarity bound for the shared output layer optimization phase under fixed local input layer parameters and quantization error. Furthermore, a reduction-based security analysis establishes single-round and multi-round ciphertext indistinguishability under the condition that all authorized fixed-subset outputs are identical between the compared inputs in every communication round. Under the honest-but-curious aggregation server and external eavesdropper threat models, this result provides confidentiality beyond the information revealed by these authorized outputs. Experimental results demonstrate that the proposed secure aggregation framework based on multi-client functional encryption achieves a root mean square error of 3.6290 µm for strip-crown prediction. This result confirms the feasibility of applying privacy-preserving gradient aggregation to this industrial prediction task.

Nonlinear partial differential equations are of particular interest to mathematicians and physicists because of their ability to model a wide range of complex nonlinear phenomena. Consequently, obtaining their exact analytical solutions is of considerable importance. In this study, we invoked the Lie symmetry method to construct new exact explicit solutions to a generalized 2D B-type Kadomtsev-Petviashvili (2D-gnBKP) equation. The Lie symmetry method provides a systematic framework for identifying continuous symmetries admitted by a differential equation and, subsequently, reducing its order and complexity. First, the infinitesimal generators were derived and using these, a one-dimensional optimal system of subalgebras was constructed. The optimal system enables the classification of inequivalent symmetry reductions and avoids redundant solution representations. Thereafter, symmetry reductions were performed that reduce the 2D-gnBKP equation to multiple ordinary differential equations. These reduced equations were then analyzed using a variety of analytical techniques. In particular, exact solutions were obtained through direct integration, the simplest equation, (G^′/G)-expansion, and Kudryashov’s techniques. Finally, for the first time in the literature, we constructed conserved vectors for the equation using the multiplier approach and Ibragimov’s method. The resulting conserved quantities include physically meaningful conservation laws related to momentum and energy, thereby highlighting important structural and physical properties of the model.

Pine wilt disease represents a devastating forest pest with severe ecological risks. Biological control based on the natural enemy Dastarcus helophoroides has become a core management strategy. Most existing dynamical models mainly focus on a single time delay or the effects of natural enemies, and studies comprehensively incorporating the coupled interplay of temperature, interspecific relationships, and time delay are still limited. Motivated by this situation, we establish a three-dimensional model of delayed differential equations, which captures the tripartite interaction among pine wood nematodes,Monochamus alternatus, and Dastarcus helophoroides. The model combines logistic population growth, Holling type II functional response, and the Briére type II nonlinear temperature-dependent developmental function, and introduces parasitic time delay to reflect temperature-driven regulation of development and reproduction across all three species. Analytically, we prove the existence of positive equilibria and derive criteria for the local asymptotic stability of the model. Taking the parasitic time delay as the bifurcation parameter, we obtain the critical time delay threshold and the transversality condition for Hopf bifurcation. The multiple time scales method is applied to derive the normal form of Hopf bifurcation, which further determines the stability and bifurcation direction of the periodic orbits. Numerically, we perform systematic simulations to examine how key parameters shape the model’s dynamical behavior. Simulation results indicate that as the time delay increases, attracting periodic solutions emerge under the tested parameter values and initial histories. The ecological insights and biological control implications derived from this work are model-based hypotheses that may serve as a reference for further studies on pine wilt disease.

By combining analytic number theory methods with Williams’s classical work, this paper investigated the computational problem of a class of power means involving Dedekind sums, and established a novel explicit conversion identity. Furthermore, we obtained exact formulas for even power means of Kloosterman sums via properties of character sums.

Up to now, linear operators with uncomplemented null-space have been playing only a minor role in regularization theory for ill-posed inverse problems in Banach spaces. We show that ill-posedness due to an uncomplemented null-space and ill-posedness due to a non-closed range can be regarded as dual concepts, and we may switch between both views at will by restricting or extending the ill-posed operator under consideration in a suitable well-defined way. We apply the duality result to Mazur-type operators, which represent a class of bounded linear operators with uncomplemented null- space. Mazur-type operators in their natural form are not accessible to Tikhonov-type regularization, but after transferring ill-posedness to the range, Tikhonov regularization can be applied. On the other hand, the null-space view of ill-posedness may open up an alternative path for developing new regularization methods for operators ill-posed in the classical sense, that is, for operators ill-posed due to a non-closed range.

We study state-dependent delay differential equations whose delays are generated by variable-exponent modular functionals. Because translations are not, in general, bounded on $L^{p(\cdot)}\left(-h_{0}, 0 ; \mathbb{R}^{n}\right)$, the classical delay shift semigroup cannot be constructed directly on the variable- exponent space. We therefore combine the Ito-Kappel semigroup framework with the modular structure of $L^{p(\cdot)}$. We establish an equivalent abstract semilinear formulation, prove local well- posedness, and obtain well-posedness on finite intervals under stronger Lipschitz and growth assumptions. For modular state-dependent delays, we verify the required local Lipschitz properties and derive sufficient conditions for decay relative to the zero equilibrium and for conditional incremental contraction. Numerical experiments illustrate the role of the variable exponent through the modular delay and the distinction between these two sufficient estimates.

This paper investigates spatial properties of transient heat equations on two special cylinders under non-homogeneous boundary conditions. By introducing a key cross-sectional parameter, the author reveals how the cylinder’s geometry affects the asymptotic behavior of solutions. Furthermore, spatial growth and decay rates are derived for different parameter ranges.

In this research, we investigated the well-posedness of the Lord–Shulman model of generalized thermoelasticity for inhomogeneous anisotropic materials with variable coefficients. The presence of the differential thermoelastic coupling operator (1 + τ₀∂_t) prevents the use of the standard energy method due to the lack of cancellation of the coupling terms in the weak formulation. To overcome this difficulty, we introduced a suitable transformation that absorbs the time derivative in the coupling term into new variables, which is an algebraic device to facilitate cancellation in energy estimates. The transformed problem was analyzed using the Faedo–Galerkin method and energy estimates, leading to the existence and uniqueness of weak solutions. The solution of the original system was then recovered through the inverse transformation.

We study the synchronization of piecewise-constant-order Caputo systems whose lower terminal is reset at prescribed times. Under linear feedback, a computable dissipativity margin yields an error bound consisting of one Mittag-Leffler factor per completed reset interval. The argument combines standard local Caputo inequalities with continuous endpoint matching; periodic schedules give an explicit cycle factor and a physical-time decay envelope. We also quantify the difference between resetting and retaining memory: A total-variation estimate controls the integrated omitted history and the resulting trajectory discrepancy. An exact scalar example shows that refining the reset mesh need not approximate a fixed-origin equation. A conditional bounded-region Lorenz result gives explicit sufficient gains. Matched-grid computations with identical gains and order schedules compare reset and fixed-origin models and include step refinement and discarded-history diagnostics. In the alternating 0.94/0.86 benchmark with unit dwell, the reset model reaches a 10⁻⁵ error near t = 2.04, whereas the fixed-origin error is approximately 2.15 × 10⁻³ at t = 8. The reset master approaches an equilibrium over this horizon. These results concern synchronization under prescribed memory reinitialization; they establish neither chaotic dynamics nor a general performance advantage for a fixed-memory plant.

This work investigated the exponential synchronization (ES) of reaction-diffusion neural networks (RDNNs) via a novel aperiodic intermittent event-triggered control strategy. The proposed scheme enables each network node to independently configure its event-triggered threshold, control interval, and rest interval, thereby reducing unnecessary response-state sampling/transmission and controller updates under the assumption that the drive state is locally available. By constructing a piecewise Lyapunov functional and adopting Dini derivative analysis and graph-theory techniques, sufficient conditions for exponential synchronization were established. Furthermore, the exclusion of Zeno behavior was strictly proven to guarantee the feasibility of the designed event-triggered mechanism. Numerical simulations on a 10-node directed RDNN with fully heterogeneous node-wise configurations and 200 Monte Carlo runs validated the effectiveness and advantage of the proposed algorithm in reducing response-state sampling and transmission as well as controller updates compared with event-triggered synchronous schemes.

Using a fixed point theorem due to Krasnosel’skii, we showed that the first-order nonlinear conformable impulsive dynamic equations on time scales (3.1) has a solution. Using the idea of contraction, we demonstrated that the solution is unique under a somewhat stricter inequality.

Finite-time surrounding control possesses superior performance in terms of tracking accuracy and rapidity. Nevertheless, most existing finite-time surrounding algorithms are only applicable to integrator systems, restricted to single-target scenarios, and fail to maintain rapid dynamic responses throughout the entire convergence process. To address these limitations, this paper extends the framework to multiple moving targets and generalizes integrators to nonlinear systems with unknown control coefficients. Meanwhile, an accelerated distributed control scheme is developed to improve the convergence performance of each agent throughout the entire process. Specifically, dynamic high-gain distributed observers are constructed for each follower, which achieve target state estimation merely using local relative information. Combined with adaptive techniques, a novel accelerated distributed surrounding protocol based on high-gain is proposed, which realizes finite- time multi-target encirclement and significantly improves global convergence rapidity compared with existing finite-time strategies. The embedded dynamic high-gain mechanism effectively compensates the unknown control coefficients while strictly preserving the fully distributed feature of the protocol, which guarantees strong operational robustness. Numerical simulations further verify the feasibility and effectiveness of the developed control scheme, demonstrating its promising application potential in practical multi-agent cooperative surrounding missions.

This paper investigates the spectral recoverability of a final-time inverse load problem for a Caputo fractionally damped Euler–Bernoulli beam. The unknown source is assumed to be separable in space and time, and the aim is to recover the spatial load profile from terminal displacement data. For a simply supported beam with constant coefficients, the terminal input-output map is diagonalized by the beam eigenfunctions, leading to a modal relation between the unknown load and the observation. The associated singular values are determined by the terminal responses of fractional-order modal equations and depend explicitly on the damping order. A truncated spectral reconstruction method with Tikhonov filtering is used for stable recovery from noisy data. Several effective indicators, including the minimum retained singular value, the effective condition number, and the maximum regularized amplification factor, are introduced to assess reconstruction stability. Numerical experiments show that the fractional damping order can reshape the effective terminal spectrum and influence the stability of the inverse problem. In suitable parameter regimes, fractional memory damping improves recoverable modal responses and reduces noise amplification compared with the classical integer-order damping model.

To investigate how a finite-duration protective intervention interacts with hypovirus-mediated biological control, we formulate a chestnut blight-inspired host–pathogen–hyperparasite model containing susceptible, temporarily protected, pathogen-infected, and hyperparasite-associated host classes. Although no broadly effective and scalable chemical treatment is currently available for chestnut blight, several experimental studies have reported temporary reductions in canker expansion or disease incidence following chemical treatment under specimen-tree, orchard, nursery, or otherwise managed conditions. Motivated by these limited observations, the class M is interpreted as a temporarily protected class rather than as an immunologically immune class. Susceptible hosts enter this class at rate δ and return to the susceptible class after protection is lost at rate ρ. Basic reproduction numbers R_0IS and R_0HS are derived, and the existence and stability of the boundary, disease-free, and positive equilibria are analyzed. We further introduce the composite protection index Θ(δ, ρ) = 1 + δ/(ρ+d), which quantifies the combined influence of entry into and loss from the temporarily protected class. Increasing δ decreases the effective reproduction numbers and raises the pathogen-invasion thresholds, whereas increasing ρ has the opposite effect. The parameters δ and ρ also shift the transcritical-bifurcation thresholds associated with hyperparasite invasion and alter the equilibrium distribution among the pathogen-only and hyperparasite-associated classes. Numerical simulations illustrate these threshold shifts and the nonmonotone interaction between temporary protection and hypovirus transmission. The chemical component of the model therefore represents a finite-duration protective effect under idealized conditions, rather than a chemical cure or chemically induced immunity. The results should be interpreted as a theoretical investigation of how temporary protection may affect chestnut blight transmission dynamics, not as a directly validated management prescription for chestnut blight.

The low structural damping characteristics of a large slender tower crane leads to challenges with respect to vibrations and structural failure risk due to external load excitation. The finite element method is often used for dynamic analysis of tower crane jib, while a model‑order reduction technique with advantages is rarely studied and applied to this engineering field. With the reduced-order model, the essential cause of system dynamic characteristics and the physical meaning of key control parameters can be revealed in an intuitive way. Therefore, a novel and competitive reduced-order model of large slender tower crane jib was introduced and was well-suited for the complex truss structure with multiple flexible beams in this study. In this work, we were concerned with the equivalent continuum modeling procedure for the large slender tower crane jib with asymmetric configuration and analysis of coupling vibration characteristics, aiming to focus more on potential studies of nonlinear vibration and vibration control. First, the equivalent anisotropic continuum beam model for tower crane jib with oblique triangular prism configuration was established by means of energy equivalence formulation. Subsequently, an equivalent 6-DOFs coupled beam model, including multiple and complex coupling terms, was solved by the finite element method, leading to reduced- order representation. In the numerical studies, a cantilevered truss structure of a large slender tower crane jib was simulated by commercial finite element software ANSYS to check the accuracy and validity of the proposed reduced-order model. The results, including the natural characteristic and dynamic response of the proposed reduced-order model, were presented by comparison with those of the finite element model for the original tower crane jib, indicating that the established reduced-order model is valid. Moreover, the coupled vibration characteristics were studied between the reduced-order model and original tower crane jib, indicating that the coupled vibration strength is weak.

In this article, the embeddings of Banach space valued (briefly by B-valued) Lorentz-Karamata martingale spaces are established. Different from the previous approach, we employ the technique of martingale transforms defined by some operator sequences, which can often supply a clear and succinct method in the research of martingale theory and Harmonic analysis. It’s worth mentioning that the results obtained here are connected closely with the geometrical properties of the Banach spaces in which the martingales take values, such as p-uniform smoothness and q-uniform convexity.

The wedge-flow configuration has particular significance in engineering applications because it provides a fundamental model for boundary-layer flow over inclined or tapered surfaces, where the imposed pressure gradient strongly influences boundary-layer development, wall shear stress, and heat transfer. Understanding and controlling these characteristics is crucial in many practical engineering applications. Existing studies, however, have mainly considered the effects of individual physical parameters, while the systematic identification of the dominant parameters governing skin-friction behavior and their subsequent use for flow prediction remains limited. Motivated by this gap, the present study aimed to analyze the flow of a non-Newtonian Eyring–Powell fluid over a wedge in the presence of magnetohydrodynamics, thermal radiation, and chemical reaction phenomena, with particular emphasis on sensitivity analysis of the flow parameters using analysis of variance to identify the dominant factors and an ANN model for rapid prediction of the flow behavior. The proposed methodology integrates numerical simulation, response surface methodology, analysis of variance-based sensitivity analysis, and a feedforward artificial neural network trained using the Levenberg–Marquardt algorithm. The magnetic field parameter was found to be the most influential factor affecting the skin friction coefficient, followed by the Eyring–Powell parameter and the wedge parameter, according to the sensitivity analysis. The skin friction coefficient was found to range from 0.9094 to 1.1642. The ANOVA model achieved R² =100% , adjusted -R² =100% , and predicted R² =99% , with an overall p <0.005 . Moreover, the Levenberg–Marquardt artificial neural network yielded regression values ranging from 0.999 to 0.9999 and MSE values on the order of 10^-9 for the Eyring–Powell parameters, indicating highly accurate predictions of the numerical results. The research provides useful insights into the behavior of non-Newtonian flows over wedge surfaces, as well as a practical framework for thermal-fluid analysis in high-performance aerospace, industrial, and thermal-management applications.

In this paper, we studied the relationship between several partial orders on multipartitions, including dominance order, θ-dominance order, weak θ-dominance order, a-function order, Webster’s ordering, and Lusztig’s a_σ-ordering.

The problems we investigated are whether two types of economic information can improve the selection of forecasting models, and whether any resulting gains persist in portfolio construction. The first is the timing of scheduled macroeconomic announcements. The second is how closely the current market resembles past (calm, stressed, or recovery) periods. We proposed an event-conditional mixture-of-experts model (Event-MoE). The model combines a long short-term memory (LSTM) network, a gated recurrent unit (GRU), and a transformer encoder. An event-conditional gate sets the mixture from a calendar of Federal Open Market Committee (FOMC), Consumer Price Index (CPI), and nonfarm-payroll (NFP) releases. A regime layer trains one such mixture per historical regime and blends them by how closely the present resembles each. Since per-stock data are limited, the experts are pooled across all stocks. An augmented variant adds a linear expert, a load-balanced gate, and one-step GARCH and HAR-RV volatility forecasts. The models were evaluated both statistically and through long-only portfolio performance, net transaction costs, and an equal-weight benchmark. Statistical significance was assessed using the Diebold–Mariano and Jobson–Korkie/Memmel tests, and robustness was verified through a walk-forward check. The central finding was that forecast accuracy and portfolio value are distinct objectives. So a more-accurate forecast does not automatically translate into a better portfolio.