R1ρ relaxation functions for weak, intermediate and strong collision models, revisited for frequency swept RF pulses.

Bounded-acceleration impact time control guidance based on look-angle shaping.

A hybrid approach using logistic sigmoid, radial basis, and hyperbolic tangent neural networks to model M-pox disease dynamics

Each curve for which Grothendieck’s section conjecture has been proved has no rational points, and additionally it has index different from 1 . We provide many new examples of curves satisfying the conjecture; in particular, we prove that examples of index 1 are very common. Given an odd prime p , we prove that every hyperbolic curve with a faithful action of a non-cyclic p -group has a twisted form of index 1 which satisfies Grothendieck’s section conjecture. Furthermore, we prove that for every hyperbolic curve S over a field k finitely generated over ℚ there exists a finite extension K / k and a finite étale cover C → S K such that C satisfies the conjecture.

Images obtained from imaging instruments can endure issues such as high degradation, color distortion, and weak brightness. Effective systems for enhancing these images are critically required. To improve the image quality, herein, we propose two filters based on simple functions, including cosine, sine, hyperbolic secant, and the inverse of hyperbolic cosecant. These filters are used for enhancing the images obtained from a fluorescence imaging system, a near-infrared camera, and low-light condition. The contrast is increased while the image quality is improved. They perform better than a matched filter. Moreover, the combination of our filters with the filter based on the watershed algorithm or the matched filter can be used to extract the marginal features from images generated under water environment. Furthermore, their application in image fusion is explored. Our designed filters may be potentially used for future applications on target identification and tracking.

This paper investigates the stochastic Davey-Stewartson equation, which represents the evolution of weakly nonlinear wave packets under the effect of randomness. This equation is developed within a stochastic framework that incorporates multiplicative Brownian motion perturbations to reflect the impact of environmental fluctuations and noise-induced phenomena present in genuine physical systems. We apply the Riccati–Bernoulli sub-ordinary differential equation method, a unified and systematic approach that converts the stochastic Davey-Stewartson equation into solvable deterministic sub-ordinary differential equation, to obtain accurate stochastic solutions. The proposed method enables the production of a wide range of innovative stochastic wave solutions, such as solitons, breather-type structures, rational solutions, and periodic wave patterns, all characterised in terms of hyperbolic, trigonometric, or rational functions. The resulting solutions reveal intricate dynamical characteristics and demonstrate how random perturbations influence phase modulation, and stability features. The scientific significance of the resulting stochastic solutions is thoroughly examined, with a focus on applications in nonlinear optics, plasma physics, fluid dynamics, Bose-Einstein condensates, and ocean wave propagation, where random disturbances play an important role. Finally, the proposed technique is a robust and adaptable analytical tool for analysing stochastic nonlinear evolution equations, providing novel insights into noise-driven wave events in complex media.

Aiming at solving the problems of severe chattering, irreconcilable convergence speed, and steady-state accuracy in traditional sliding-mode control (SMC) for the speed regulation system of permanent magnet synchronous motors (PMSMs) in rail transit traction, as well as its poor adaptability to complex disturbances such as frequent acceleration/deceleration and sudden load changes under traction conditions, a sliding-mode control strategy integrating improved piecewise terminal integral sliding-mode control (IPTISMC) with an adaptive smooth exponential reaching law (ASERL) is proposed. Taking the surface-mounted PMSM for rail transit traction as the research object, the d-q axis mathematical model is established, and a terminal integral sliding surface with a piecewise nonlinear function is designed, which resolves the problems of complex solutions and steady-state errors of the traditional sliding surface through a piecewise cooperative mechanism for large and small error stages. The designed ASERL realizes adaptive gain adjustment based on the state variables of the sliding surface and replaces the sign function with the hyperbolic tangent function, thus alleviating the inherent contradiction between convergence and chattering in the fixed-gain reaching law. The global stability and finite-time convergence of the system are rigorously proved based on Lyapunov stability theory. Furthermore, comparative experiments involving no-load operation, acceleration and deceleration, sudden load application and removal, and parameter perturbation are carried out on a DSP experimental platform for SMC-ERL, ISMC-ERL, IPTISMC-ERL and the proposed IPTISMC-ASERL. Experimental results show that the proposed IPTISMC-ASERL strategy can significantly improve the dynamic response and steady-state control accuracy of the PMSM speed regulation system for rail transit traction, effectively suppress chattering to enhance riding comfort, and simultaneously strengthen the system’s anti-disturbance capability and parametric robustness. It can fully meet the engineering control requirements for high precision and high stability of PMSMs in rail transit traction applications.

ABSTRACT This paper takes the integrable Kuralay equations as the research object, aiming to derive various types of soliton solutions and explore the integrable motion of space curves induced by the equations, so as to support the research on nonlinear spin dynamics in the field of magnetic materials. In this paper, the unified ‐expansion method is used to systematically derive soliton solutions expressed by Jacobian elliptic functions. Through parameter degeneration (degenerating into hyperbolic function solutions when the modulus and trigonometric function solutions when ), the evolutionary relationship among different solutions is revealed. Eight types of soliton solutions are obtained in this paper, including periodic trigonometric function solutions, parabolic function solutions, singular solutions, and M‐shaped/W‐shaped solitons (corresponding to Figures 1–8). The parameter configurations and 2D/3D graphical characteristics of each solution are clarified (e.g., kink waves show unidirectional step‐like transitions, and M‐shaped bright waves possess symmetric double peaks). All solitons have clear boundaries without diffusion. For numerical verification, the fourth‐order Runge‐Kutta method combined with Richardson extrapolation is adopted, reducing the calculation error from to . In addition, phase portrait, bifurcation, and initial condition sensitivity analyses are supplemented, and the stability of equilibrium points is classified by the eigenvalues of the Jacobian matrix. In terms of physical implications, the soliton solutions are deeply associated with magnetic spin systems. For instance, kink waves correspond to the migration of spin domain walls, supporting the reading and writing operations of magnetic storage; M‐shaped/W‐shaped solitons contribute to the realization of multistate and high‐density storage. The quantitative influences of parameters on the low‐power consumption and high‐capacity performance of devices are clarified, providing theoretical support and practical guidance for the research on nonlinear spin dynamics and the design of magnetic storage and magneto‐optical modulation devices.

Let K ( r ) and arctanh ⁡ r be the complete elliptic integral of the first kind and inverse hyperbolic tangent function, respectively. In 2004, Alzer and Qiu conjectured that r ↦ G ( r ) = ln ⁡ ( 2 / π ) + ln ⁡ K ( r ) ln ⁡ arctanh ⁡ r − ln ⁡ r is strictly increasing and convex from ( 0 , 1 ) onto ( 3 / 4 , 1 ) . In this paper, we prove the stronger results than Alzer–Qiu's conjecture, that is, the functions − ( 1 / G ( x ) ) ′ , ( ln ⁡ G ( x ) ) ′ and G p ( x ) for all p>0 are all absolutely monotonic on ( 0 , 1 ) . This leads to a series of new sharp bounds for K ( r ) , which greatly improve and extend existing results. The significance of our findings lies not only in solving the Alzer–Qiu's conjecture and further establishing several related absolutely monotonic functions, but more importantly, in providing a new and effective approach to deal with the absolute monotonicity of fractional functions.

Abstract. This paper introduces an improved adaptive fuzzy sliding-mode control approach for semi-active seat suspension utilizing magnetorheological fluid (MRF) dampers. Firstly, the damping characteristic of the MRF damper was tested, and the dynamics model of MRF damper was established. Secondly, the 5-degree-of-freedom “human-seat” suspension system model was built and adaptively simplified, and a suitable adaptive control law was designed to estimate the perturbations generated during the simplification process of the human-seat model online. Based on the simplified model, a fuzzy algorithm was adopted to optimize the approach rate parameters in the sliding-mode control so as to improve the robustness of the system while guaranteeing the approach rate, and hyperbolic tangent function was employed to replace the sign function in the switching term to make the system more continuous during the switching process, which effectively reduces the “chatter” problem in the sliding-mode control. Thirdly, the dynamics model of the MRF damper is added into the sliding-mode control model to ensure the effectiveness of the MRF damper output control force. Finally, the effectiveness of the improved adaptive fuzzy sliding-mode control method was confirmed through simulation, demonstrating its capability to significantly reduce seat acceleration and suspension dynamic deflection under different working conditions compared with passive damping, skyhook control, and sliding-mode control.

Abstract We present a novel approach for constructing quasi-isospectral higher-order Hamiltonians from time-independent Lax pairs by reversing the conventional interpretation of the Lax pair operators. Instead of treating the typically second-order $L$-operator as the Hamiltonian, we take the higher-order $M$-operator as the starting point and construct a sequence of quasi-isospectral operators via intertwining techniques. This procedure yields a variety of new higher-order Hamiltonians that are isospectral to each other, except for at least one state. We illustrate the approach with explicit examples derived from the KdV equation and its extensions, discussing the properties of the resulting operators based on rational, hyperbolic, and elliptic function solutions. In some cases, we present infinite sequences of quasi-isospectral Hamiltonians, which we generalise to shape-invariant differential operators capable of generating such sequences. Our framework provides a systematic mechanism for generating new candidate integrable structures/integrable operator families associated with known Lax pairs.

In this research, a [Formula: see text]-model approximation method is employed to investigate the localized wave solutions for the Lakshmanan-Porsezian-Daniel equation with beta-derivative. This equation integrates the fundamental phenomena such as Space-Time Dispersion (STD), Group Velocity Dispersion (GVD) and parabolic-law-governed by nonlinear behavior. A variety of optical soliton waves are obtained by applying the [Formula: see text]-model expansion approach. These waves are expressed as Jacobi elliptic functions [Formula: see text] that based on the particular values of the parameter A, that can be converted into solutions of trigonometric or hyperbolic functions. This technique provides variety of solutions, including dark soliton solutions, hyperbolic solutions, periodic waves solutions, bright solitons, singular soliton solution and singular periodic waves solutions. To further explore the system's behavior, bifurcation analysis is done. For this analysis planar dynamical system is obtained by using Galilean transformation. This analysis offers deep understanding of the phase portraits, time series, chaotic behavior and sensitivity analysis of the equation to external perturbations. The sensitivity and dynamics of optical solitons are thoroughly investigated that offers significant insights into their behavior within fractional models.

This work extends the analytical understanding of the M-fractional double-chain model of DNA and analyzes its behavior using the modified Sardar sub-equation method (mSSEM). The proposed method is an analytical approach to establish connections between mathematical variables and the physical quantities associated with DNA. The double-chain model of DNA plays an important role in the protection and transmission of genetic data. The model is constructedof two long, elastic, and homogeneous strands that represent two polynucleotide chains of DNA molecules, connected by an elastic membrane that represents the hydrogen bonds between the base pairs of the two chains. We utilize the truncated M-fractional derivative definition, allowing for a more detailed analysis of the double-chain model of DNA's behavior. The hyperbolic, trigonometric, and exponential function solutions are found by using the mSSEM. In addition, we also give the physical representation of some presented solutions under the appropriate parameter values with 3D, 2D plots, and classify optical solitons (bright, dark, singular, bright-dark, bright-singular, periodic function, mixed trigonometric, combo, combo bright-singular). This study offers a valuable analytical tool for researchers and scientists working in nonlinear dynamics such as molecular biology, biophysics, and bioinformatics.

Abstract We introduce the notion of cover time to dynamical systems. This quantifies the rate at which orbits become dense in the state space and can be viewed as a global, rather than the more standard local, notion of recurrence for a system. Using transfer operator tools for systems with holes and inducing techniques, we obtain an asymptotic formula for the expected cover time in terms of the decay rate of the measure of the ball of minimum measure. We apply this to a wide class of uniformly hyperbolic and non-uniformly hyperbolic interval maps, including the Gauss map and Manneville–Pomeau maps.

ABSTRACT Robust Integral of the Sign of the Error (RISE) control is a class of continuous robust controllers that addresses the limitations of discontinuous sliding mode (SM) controllers all while utilizing its robustness to deal with uncertain terms that are bounded by constants. However, RISE controllers require the dynamic model and the control input to be continuously differentiable. As a result, the use of the RISE control approach is not possible for nonsmooth or switched systems. Motivated by the robustness of RISE controllers, an auxiliary RISE (ARISE) control architecture is developed to extend the benefits of RISE control to discontinuous/switched systems. To enhance the applicability of the ARISE control approach, a saturated hyperbolic tangent function is incorporated into the control input to account for the limitations of physical actuators during real‐world applications. A nonsmooth Lyapunov‐like stability analysis is performed for the proposed saturated ARISE control system to prove that the closed‐loop error system is uniformly ultimately bounded for a switched dynamic model. A series of numerical simulations were performed to compare the performance of the saturated ARISE controller with standard saturated SM and integral SM controllers.

The discrete ordinates method has served as a cornerstone of numerical radiative transfer since A. Schuster introduced its foundation in 1905. G.C. Wick and S. Chandrasekhar significantly advanced the method in the mid-20th century to study planetary atmospheres. In 1963, B.G. Carlson formally applied the method to neutron transport, initiating its widespread use thereafter. Since then, the discrete ordinates method has grown from simple linear interpolation to sophisticated multidimensional algorithms applied to reactor analysis and weapons design. In this work, we consider a 1D, monoenergetic response matrix discrete ordinates method to solve the even-parity, second-order form analytically with hyperbolic matrix functions. Our focus then turns to incorporating a nascent delta function source (DFS) through faux interpolation of discrete angular fluxes. Finally, we benchmark the DFS approach against the conventional first collision source (FCS) to demonstrate agreement to eight or nine significant digits.

Abstract Objective functions play a pivotal role in signal recovery and necessitate optimized selection in practical applications. In this paper, we propose a novel notion termed p-concavity with p∈(0,1], and the induced functions encompass representative objective functions in the literature, including the ℓ_p (quasi-)norm function, logarithmic function, exponential function and hyperbolic tangent function. Based on the classical restricted isometry property (RIP) framework, sharp and uniform conditions in terms of tk-order RIP constants δ_{tk} are derived ensuring stable recovery of sparse signals. Furthermore, for t∈(0,2], the tk-order conditions are proved to be tight. Two DC(difference of convex functions)-programming-based algorithms are established to solve the unconstrained minimization problem of p-concave functions. A series of numerical experiments and analyses are presented on both random k-sparse signals and greyscale images to demonstrate the recovery capabilities of the proposed p-concave functions.

The objective of this paper is to examine new soliton solutions for the [Formula: see text]-dimensional extended Jimbo–Miwa model with nonlinear properties. The model represents a wide range of scientific processes in domains such as mathematical biology, nonlinear optics, and quantum field theory, which include complex wave interactions. To begin, we employ the homogeneous balance method to create the original Auto-Bäcklund and Cole–Hopf transformations for the given model, leading to the derivation of various soliton-like solutions that exhibit hyperbolic, trigonometric, and exponential wave functions. After that, a Bäcklund transformation is generated, which has an equal number of arbitrary parameters and bilinear equations. Then, this formation is used to generate two categories of exponential and rational traveling wave solutions with arbitrary wave numbers, resulting in numerous soliton-like solutions. This study also constructs new complexiton solutions using the extended transform rational function method combined with the Hirota bilinear form. To provide further insight into the physical aspects of these solutions, we depict them through a range of visual methods, including 3D, 2D, and density plots. The results of this research are innovative and contribute significantly to the ongoing investigation of the equation, providing useful guidance for researchers in future studies. Also, the obtained exact solutions and their physical interpretations are expected to attract considerable interest in the study of nonlinear evolution equations, integrable models, and soliton theory within theoretical physics.

Flow around a circular cylinder is a canonical bluff-body problem for tubular and offshore structures, where separation and vortex shedding govern unsteady loads. Here, experimental particle image velocimetry data at Reynolds number Re = 8 × 103 were used to train an artificial neural network (ANN) surrogate for the wake of a vortex-generators (VGs)-equipped circular cylinder. The surrogate learned a pointwise mapping from the VGs angles and spatial coordinates (α, β, x, y) to five flow statistics: mean velocities (⟨u⟩, ⟨v⟩), velocity fluctuations (urms′, vrms′), and Reynolds shear stress ⟨u′v′⟩. A comprehensive search of 1736 ANN candidates identified the best architecture as a multilayer perceptron with a 4-neuron linear projection layer followed by two 65-neuron hidden layers with hyperbolic tangent activation, trained with a mini-batch size of 2; near-unity accuracy was achieved across all five quantities (R2 ≈ 0.98–0.99) with low errors. SHapley Additive exPlanations (SHAP) and Sobol analyses showed that α is the primary control parameter: mean |SHAP| for α was 0.004 29 m/s for J(urms′), 0.007 88 m/s for J(vrms′), and 3.298 × 10−4 m2/s2 for J(⟨u′v′⟩), exceeding β by factors of 3.1, 2.9, and 2.6. The ANN was then coupled with Particle Swarm Optimization and Musk Ox Optimization, and both converged to the same optima for each target, yielding distinct (α, β) pairs for J(urms′), J(vrms′), and thereby demonstrating clear trade-offs among turbulence metrics.

The nano-ionic current along microtubules equation allows microtubules to act as nonlinear electrical transmission lines and allows ions to flow through the cylindrical shapes of the microtubules. The paper derives new solitary-wave solutions of the dynamical equations of ionic currents along microtubules with the aid of an new extended direct algebraic method (NEDAM) which is much relevant to nanotechnology. The NEDAM is a strong analytical tool that allows us to derive solutions, such as bright, dark, combined dark–bright solitons, the w-shaped soliton, kink, anti-kink, and singular solitons, based on various mathematical functions, including polynomial, rational, exponential, hyperbolic, and trigonometric functions. We produce 2D, 3D, density, and contour graphs to illustrate the soliton’s propagation under particular conditions, demonstrating an accurate representation of real instances. Furthermore, we examine the microtubule equation for modulation instability in the nano-ionic currents. We discovered that the suggested approach provides precise and analytical answers and is accurate and efficient. Mathematica is used to verify all results, guaranteeing their precision and stability.