Abstract This study examines the well-posedness and asymptotic behavior of a nonlinear suspension bridge with a deck modeled according to the Bresse vibration theory. We establish the existence and uniqueness of global solutions by means of semigroup theory of linear operators, which gives rise to a dynamical system of solutions. From the perspective of quasi-stability properties, we prove the existence of a global and exponential attractor for the dynamical system and the finiteness of the fractal dimension and the regularity of the attractor. Finally, we establish conditions for a finite set of bounded linear functionals defined on phase space to be a set of determining functionals for the dynamical system.

The sustainable transformation of electronics supply chains (ESCs) increasingly relies on effective green supply chain planning under carbon pricing and demand uncertainty. However, prior studies often lack an integrated framework that jointly considers carbon taxation, green technology investment, and profitability—environment trade-offs in forward and reverse supply chains. To address this gap, this study proposes a fuzzy multi-goal optimization model using linear goal programming under progressive carbon taxation. The model incorporates fuzzy demand (triangular fuzzy numbers), carbon emissions, carbon taxes, and green investment costs and is converted into a solvable linear form via a defuzzification-based procedure to simultaneously achieve multiple aspiration levels for economic and environmental objectives. A real-world ESC case validates the model. The results show that carbon taxation and green investments can reduce emissions while maintaining profitability, with total cost and emission sensitivity of ±10–20% across different policies and demand uncertainty settings. The findings support adaptive, policy-aware planning by guiding green investment intensity and forward–reverse logistics decisions to balance cost efficiency and emissions reduction and provide actionable insights for managers facing progressive carbon pricing regulations.

Polynomial exact solutions of the Navier–Stokes equations for describing micropolar incompressible fluid flows with energy dissipation are reported. The transformation of mechanical energy into thermal energy is taken into account. The heat equation for the Rayleigh function contains the sum of the squares of the components of the Cauchy velocity tensor (the main component for the dissipative function). Unidirectional homogeneous and non-homogeneous fluid flows with moment stresses are considered. The solvability of overdetermined systems for studying homogeneous and non-homogeneous shear flows is studied. The paper pays attention to the exact integration of equations for three-dimensional flows. The construction of classes of exact solutions is carried out first using the Lin–Sidorov–Aristov solution family. In other words, the velocity field depends linearly on part of the coordinates. The coefficients of the linear forms of the velocity field depend on the third coordinate and time. The pressure field and the temperature field are quadratic forms with similar functional arbitrariness. In addition, exact solutions for the velocity field with a nonlinear dependence on part of the coordinates are considered.

Rings for which general linear forms are exact zero divisors

Abstract To compare lipid-rich food waste conversion through thermophilic anaerobic digestion, a nonlinear model was developed by combining ADM1 and some of the regulatory features of ADM2. The model integrates the suppression of LCFA and a fixed and pH-dependent suppression and calculates the finer details of this action using sigmoid and Hill equations. The coupled equations representing substrate degradation, microbes growth, and LCFA accumulation and methane generation were assessed with the help of a MATLAB program with the help of an ode15s routine. A study was performed on nine simulated conditions with a concentration of LCFA between 0.2 and 0.6 g/L and pH of 6.0–7.0. It was found out that the success of the process was most affected by pH. At pH of 6.0, production was 0.02 gCOD and production of methane at pH of 7.0 was 1.93 gCOD under high concentrations of LCFA. Besides, AUC analysis also showed that, during wastewater treatment process, when pH changed between 6.0 and 7.0, the AUC changed to 55.5 gCOD (day) to 0.7 gCOD (day). The model is able to present key behaviors associated with the co-digestion of lipid-rich substrates like washout of microbes and the degradation of inhibitions. The study establishes that maintenance of pH balance and the maintenance of the quantity of fatty acids or LCFAs produced in linear form improve biogas in high-fat wastes treatment systems.

This paper proposes a complex fast recursive least-squares (FRLS) channel-estimation algorithm for single-carrier electromagnetic (EM) communications across the seawater–air interface, where severe attenuation and multipath cause strong SNR fluctuations. By redesigning the input-data structure and using forward–backward joint estimation, FRLS reduces the per-iteration complexity from the quadratic cost of classical RLS to a linear form (14L + 20 operations per iteration, where L is the channel length). Simulations under representative one- to three-path channels show that FRLS achieves the lowest steady-state mean-square deviation (MSD) at low SNR, outperforming LMS, IPNLMS, RLS, and PRLS. Offshore experiments further validate the practicality: after MMSE equalization, FRLS yields higher OSNR and improves the BER distribution, demonstrating an effective accuracy–complexity trade-off for hardware-constrained cross-medium EM links.

When adopting a viscous friction model in a piecewise nonlinear rotor–stator rubbing system, it becomes a Filippov system with smoothness of degree one. The nonautonomous system exhibits an interesting nonsmooth induced bifurcation phenomenon, that is, as the rotating speed increases, a quasi-periodic response emerges just after a periodic orbit of the linear sub-system touches the switching manifold, while the nonlinear sub-system possesses no regular periodic solution nearby. To investigate the mechanism of the nonsmooth induced bifurcation, the system is first transformed to the rotating coordinate system to get an equivalent autonomous system. Then, further transformations are performed to transform the system to an equivalent linear normal form in the neighborhood of the boundary equilibrium of the linear sub-system on the straightened switching manifold. After that, the Poincaré return map is constructed, and through numerical and analytical methods, it is shown that the tangency points of the two subsystems are mostly visible–invisible folds and invisible–invisible folds, and the system generates a limit cycle crossing the switching manifold. Through this analysis, the mechanism of the nonsmooth bifurcation in the original nonautonomous rotor–stator rubbing system is clarified. Moreover, the approximate model not only can accurately predict the maximum amplitude of quasi-periodic responses, but also reveal the coexistence of quasi-periodic and periodic motions. This highlights the usefulness of the proposed analytical approach for handling nonsmooth systems with engineering relevance.

Abstract The Subspace Theorem due to Schmidt (1972) is a broad generalisation of Roth’s Theorem in Diophantine Approximation (1955) which, in the same way as the latter, suffers a notorious lack of effectivity. This problem is tackled from a probabilistic standpoint by determining the proportion of algebraic linear forms of bounded heights and degrees for which there exists a solution to the Subspace Inequality lying in a subspace of large height. The estimates are established for a class of height functions emerging from an analytic parametrisation of the projective space. They are pertinent in the regime where the heights of the algebraic quantities are larger than those of the rational solutions to the inequality under consideration, and are valid for approximation functions more general than the power functions intervening in the original Subspace Theorem. These estimates are further refined in the case of Roth’s Theorem so as to yield a Khintchin–type density version of the so–called Waldschmidt conjecture (which is known to fail pointwise). This answers a question raised by Beresnevich, Bernik and Dodson (2009).

Peptide cyclization is a strategy to improve biological stability and functional activity, but direct comparison between linear and cyclic peptides with the same sequence is still limited. In this study, linear (L-CR5) and cyclic (C-CR5) forms were synthesized, and biological functions such as antioxidant, whitening, and anti-wrinkle activity were compared and evaluated. C-CR5 showed about 22.3 times of DPPH radical scavenging activity, which was significantly stronger than L-CR5, and tyrosinase inhibition increased rapidly in C-CR5 to reach inhibition of 95% or more, whereas L-CR5 showed only moderate activity in the same range (about 6.5 times). MMP-1 expression in the evaluation of anti-wrinkle activity did not show a decreasing trend in L-CR5 at all, while C-CR5 showed an anti-wrinkle effect, which was reduced by about 92.8% at 400 μg/mL. As a result of molecular docking analysis, C-CR5 exhibited lower MolDock scores than L-CR5 toward both tyrosinase and MMP-1, indicating a potentially higher binding affinity and improved binding stability. This is expected to be due to reduced structural flexibility and optimized residue directions (especially Tyr and Arg). These results indicate that peptide cyclization is an example of enhanced functional bioactivity of CYGSR and provides a positive case for the structure–activity relationship.

Predictive, field-relevant descriptions of cadmium attenuation remain essential for safeguarding freshwater systems. This study evaluates a magnetically retrievable covalent organic framework (COF@Fe3O4) sorbent for Cd2+ removal from lake water, integrating characterization, equilibrium modelling, and kinetics. The composite was characterized by FT-IR, XRD, and SEM, and its pHpzc was determined. Batch tests were conducted over a pH range of 5.0-9.0, varying contact times, and initial Cd2+ concentrations of 20-100 mg L-1. High percent removals were achieved under mildly alkaline conditions, with residual Cd close to the detection limit at pH 9.0 and about 98% removal at the operative dose using simple magnetic handling. Equilibrium behavior was analyzed with parallel nonlinear and linear treatments using consistent error functions. Langmuir provided the best description, yielding qmax = 86.99 mg g-1 with KL = 0.0318L mg-1 in nonlinear fitting and qmax = 93.67 mg g-1 with KL = 0.0281L mg-1 from the linear form, indicating monolayer uptake on a finite set of sites. Toth also fit well and reflected mild site-energy heterogeneity. Time-dependent uptake for 100 mg L- 1 Cd2+ was the most consistent with a pseudo-second-order model, and intraparticle diffusion analysis gave a positive intercept, indicating a diffusion contribution that is not the sole rate-limiting step. Reusability and structural stability of the material was verified by magnetic recovery with water-only rinsing, maintaining performance across cycles. Overall, the combined characterization, isotherm, and kinetic evidence together with high removals supported COF@Fe3O4 as a practical, magnetically separable platform for Cd2+ treatment in lake water.

This paper explores the nonconvex input-constrained consensus problem of multi-agent systems under sampled-data settings, switching graphs and communication delays. A sampled-data based consensus control algorithm is developed for systems with nonconvex input-constrained second-order dynamic. To address the nonlinearities arising from the coupling of nonconvex input constraints and sampled-data setting, the scaling factors are applied to convert the nonconvex input-constrained system into a time-varying linear form. Then, an inductive approach utilising the lower bounds of these scaling factors is developed to analyse the system's convexity. It is verified that the nonconvex input constrained consensus under sampled-data settings, switching graphs, and communication delays can be achieved. Finally, the theoretical conclusions are verified through numerical examples.

The phenomenon of stretching sheets is vital in various industrial and engineering applications, significantly affecting the efficiency and quality of processes such as the manufacturing of electronic components, aerodynamic designs, among many others. This study explores the interaction between magnetohydrodynamics and a reactive viscous Casson-Jeffery nanofluid. The physical system is transformed into a mathematical framework by applying conservation laws and translating observable phenomena into precise, quantifiable equations. Non-similar analysis is used to transform the system into a dimensionless form. The system of differential equations is simplified into a linear form through the local linearization technique, after which a bivariate spectral-based method is implemented to approximate the solutions of the differential equations. The convergence analysis of the method confirms the reliability of the spectral-based technique. It was found that the Casson fluid has greater thermal sensitivity and higher fluid flow than the Jeffrey fluid. However, when the fluid parameters are varied, the Jeffrey fluid exhibits higher concentration peaks under identical conditions than the Casson fluid. The Jeffery fluid has higher species sensitivity than the Casson fluid. The findings of this study contribute to the understanding of complex fluid dynamics, which can be used to validate or refine theoretical models and simulations.

Let N be the maximal unipotent subgroup in the simple algebraic group of type Φ. It naturally acts on the space dual to the Lie algebra n of N, and this action is called coadjoint. Such orbits play the key role in the orbit method of A.A. Kirillov. In this work, we classify the orbits of this action in the case of Φ = F_4 in terms of supports of canonical forms. This means that we will present a set S of linear forms such that for any coadjoint orbit there exists a unique form from S belonging to that orbit. The set of canonical forms will be explicitly described in terms of supports.

Cardiovascular diseases (CVD) cause many deaths in the world. Heart disease is one important type of CVD. Classical tools such as the Framingham Risk Score use only a few variables and a simple linear form, so they cannot show complicated links between many risk factors. Electronic medical records are now very common, and machine-learning methods give another way to build risk prediction models from this data. This study uses the UCI Heart Disease (Cleveland) dataset to build a heart disease risk prediction method that puts feature engineering together with a stacking ensemble. It start from 14 clinical variables and design five enhanced features and three new composite features from blood pressure, cholesterol, ST depression, chest pain type, and exercise-induced angina. Logistic regression (LG), random forest (RF), XGBoost, support vector machine (SVM), and k-nearest neighbours (KNN) are used as base models in a two-layer stacking structure. It judges model performance with AUC, accuracy, precision, recall, and F1-score. The results show that the engineered features give small but clear improvements for most base models, and the stacking model has the best performance with a test AUC of 0.8771. Under a small sample size, the method keeps good accuracy and stability, and may be a useful tool for early screening of high-risk groups.

The present work aimed to synthesize pillared clays with titanium (Ti-PILC) and aluminum (Al-PILC) from montmorillonite (LG-PILC) and to verify their efficiency in removing the anionic diazo dye Congo red via adsorption. The clays were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), Fourier transform infrared (FTIR) spectroscopy, zeta potential, Brunauer-Emmett-Teller (BET) surface area, and energy-dispersive X-ray spectroscopy (EDS). In the adsorption tests, the kinetics of equilibrium, adsorption dosage, and adsorption isotherms were studied, as well as the recovery and reutilization of the adsorbents. The results of the adsorption tests indicated that the process reached equilibrium after 90min; the amount of dye removed per gram of adsorbent (qe, mg.g-1) was 23.01, 34.92, and 25.45 for the clays LG-PILC, Ti-PILC, and Al-PILC, respectively. In the kinetic studies of adsorption, all samples followed the pseudo-second-order model. The optimal adsorbent dosage for removing Congo red across all samples was 0.5g.L-1. Among the adsorption isotherm models tested, the isotherms found in LG-PILC and Al-PILC samples were closest to the Henry isotherm (R2 = 0.94 and 0.84 for LG-PILC and Al-PILC, respectively). In contrast, the isotherm found in Ti-PILC clay was closest to the Langmuir model in linear form (R2 = 0.98). XRD results showed that the clay composition is mainly montmorillonite, and all other characterization results indicated that the pillars formed within the clay. In the recovery and reuse of clays (with post-treatment), it was observed that the clays maintained the ability to remove Congo red at each reuse stage. Still, they decrease after each cycle (reaching stability as the cycles go by). The clays studied in this research demonstrated high potential for removing Congo red, with the most promising being titanium pillared clay (Ti-PILC). The Ti-PILC clay showed superior adsorption properties to other adsorbents reported in the current literature.

A bstract This paper develops a framework for the Hamiltonian quantization of complex Chern-Simons theory with gauge group $$\text{SL}(2,{\mathbb{C}})$$ at an even level $$k\in {\mathbb{Z}}_{+}$$ . Our approach follows the procedure of combinatorial quantization to construct the operator algebras of quantum holonomies on 2-surfaces and develop the representation theory. The *-representation of the operator algebra is carried by the infinite dimensional Hilbert space $${\mathcal{H}}_{\overrightarrow{\lambda }}$$ and closely connects to the infinite-dimensional *-representation of the quantum deformed Lorentz group $${\mathcal{U}}_{\text{q}}\left(s{l}_{2}\right)\otimes {\mathcal{U}}_{\widetilde{\text{q}}}\left(s{l}_{2}\right)$$ . The quantum group $${\mathcal{U}}_{\text{q}}\left(s{l}_{2}\right)\otimes {\mathcal{U}}_{\widetilde{\text{q}}}\left(s{l}_{2}\right)$$ also emerges from the quantum gauge transformations of the complex Chern-Simons theory. Focusing on a m -holed sphere Σ 0, m , the physical Hilbert space $${\mathcal{H}}_{\text{phys}}$$ is identified by imposing the gauge invariance and the flatness constraint. The states in $${\mathcal{H}}_{\text{phys}}$$ are the $${\mathcal{U}}_{\text{q}}\left(s{l}_{2}\right)\otimes {\mathcal{U}}_{\widetilde{\text{q}}}\left(s{l}_{2}\right)$$ -invariant linear functionals on a dense domain in $${\mathcal{H}}_{\overrightarrow{\lambda }}$$ . Finally, we demonstrate that the physical Hilbert space carries a Fenchel-Nielsen representation, where a set of Wilson loop operators associated with a pants decomposition of Σ 0, m are diagonalized.

The Tribonacci-Lucas sequence {𝑆 𝑛 } ≥0 is defined by the linear recurrence relation 𝑆 𝑛+3 = 𝑆 𝑛+2 + 𝑆 𝑛+1 + 𝑆 𝑛 , for 𝑛 ≥ 0, with the initial conditions 𝑆 0 = 𝑆 2 = 3 and 𝑆 1 = 1. A palindromic number is a number that remains the same when its digits are reversed. This paper uses Baker’s theory for nozero lower bounds for linear forms in logarithms of algebraic numbers, and reduction methods involving the theory of continued fraction to determine all Tribonacci-Lucas numbers that are palindromic concatenations of two distinct repdigits.

Abstract We develop a novel topological framework that yields results constraining the distribution of zeros of certain zero mean real-valued maps, namely those obtained from composing a fixed equivariant map with linear functionals. We use this framework to establish upper bounds for the topology of set systems in the domain where (multivariate) trigonometric polynomials do not change their sign, generalizing and, in certain regimes, strengthening results in the literature. Our results more generally contain restrictions on the distribution of zeros of Chebyshev spaces as special cases. Lastly, we apply this framework to derive existence results for efficient cubature rules for compositions of affine functionals and equivariant maps.

Suppose that the sequences {Pi}i≥0 , {Ri}i≥0 , and {Ji}i≥0 correspond to the Padovan numbers, Perrin numbers, and Jacobsthal numbers, respectively. In this paper, we determine all Padovan and Perrin numbers that can be written as the sum of two Jacobsthal numbers by applying Baker’s method for linear forms in logarithms, combined with the reduction technique of Dujella and Peth˝o.

Photo-induced bond linkage isomerization (BLI) in metal–nitrosyl compounds provides a molecular mechanism for controlling light-induced changes in refractive index and phase modulation. In this study, the ground and metastable states of a series of Ru–NO complexes and their Au20, Ag20, and mixed Au10Ag10 nanocluster hybrids were investigated by DFT and TDDFT calculations. The photochemical rearrangement between the linear, side-on, and O-bound forms of Ru–NO was examined together with their electronic transitions, oscillator strengths, and characteristic vibrational shifts. From these data, parameters describing radiative efficiency, non-radiative coupling, and metastable-state stability were derived to identify compounds with favorable properties for holography and photonic applications. Particular attention was given to the [(Salen)Ru(NO)(HS)@Au20] complex, which shows a strong red-to-NIR response and balanced stability among its linkage isomers. Frequency-dependent polarizabilities α(ω) were calculated for its ground and metastable states and compared with those of the classical holographic material [Fe(CN)5NO]2− (nitroprusside). The refractive-index changes derived from α(ω) reveal that the Au20–salen hybrid produces a much larger and more strongly wavelength-dependent Δn(λ) than nitroprusside. At 635 nm, the modulation reaches approximately 0.06 for the hybrid, compared with 0.02 for nitroprusside. This enhancement reflects the cooperative effect of the Ru–NO chromophore and the Au20 nanocluster, which amplifies both polarizability and optical dispersion. The results demonstrate that coupling molecular photo-linkage isomerism with nanoplasmonic environments can significantly improve the performance of molecular systems for holography and optical-phase applications.