Search Results (279)

This paper proposes a fast midcourse trajectory optimization method by using the Bézier curve as a transcription scheme to represent the interceptor trajectories. First, the trajectory optimization problem is established with the constraints during midcourse guidance and the performance index of the terminal velocity. Then, the interceptor position coordinates are represented using Bézier functions, which directly satisfy the boundary constraints. Other state and control variables are also expressed as Bézier functions. Finally, the original trajectory optimization problem is transformed into optimizing the Bézier parameters, which can be obtained by sequential quadratic programming. Numerical examples verify the rapidity of the proposed method when compared with various traditional numerical optimization methods. In addition, the result of the proposed method can be used as a fast solution satisfying all the boundary and path constraints, and it can also be used as an initial guess for further optimizations. Full article

We present a novel and completely deterministic method to model chaotic orbits in nonlinear discrete dynamics, taking the quadratic map as an example. This method is based on the resurgent analysis developed by Écalle to perform the resummation of divergent power series given by asymptotic expansions in linear differential equations with variable coefficients. To determine the long-term behavior of the dynamics, we calculate the zeros of a function representing the unstable manifold of the system using Newton’s method. The asymptotic expansion of the function is expressed as a kind of negative power series, which enables the computation with high accuracy. By use of the obtained zeros, we visualize the set of homoclinic points. This set corresponds to the Julia set in one-dimensional complex dynamical systems. The presented method is easily extendable to two-dimensional nonlinear dynamical systems such as Hénon maps. Full article

Evolutionary processes involving sustainability are here expressed in units of classical mechanics, where newly evolved traits are distance, segments of evolutionary trees are time, and species as entire character sets are mass. Data arranged on a morphological evolutionary tree (caulogram) allow precise calculations of evolutionary velocity, acceleration, momentum and force, with force interpretable as resistance to environmental change. Stem-taxon trees of species of the moss family Streptotrichaceae and Pottiaceae tribe Pleuroweisieae were developed as sets of minimally monophyletic genera, and annotated with numbers of newly evolved traits per species. Calculations provided evidence that precise and comparative measures of the results of sustainable evolutionary processes may be calculated, and, as directly derived from expressed traits, are also accurate and informative about processes leading to resilience across multiple extinction events. The two groups evidenced similar, gradual evolutionary rates, implying that similar evolutionary processes occur across 110 my for Streptotrichaceae and 66 my for Pleuroweisieae, although habitats differ. Extension of sets of new traits per species into the past imply origination of the oldest extinct recognizable progenitors near the Permian–Triassic extinction event, when a cut-off in all data imply a complete over-haul of the character set for both groups, i.e., a major change in evolutionary mass. Speciation occurs in bursts. Extinction is gradual, the negative of acceleration. The rates of origination of genera over time for both groups are nearly the same as those previously proposed for genera of extinct horses. Plateaus in graphs of species per genus imply ancient quadratic patterns of speciation. The combination of process-governed stability through stasis of morphological traits, and of resilience as the ability to survive multiple extinction events has apparently little changed, and both contribute to sustainability over geologic time. Full article

The objective of this study was to investigate the impact of exogenous catalase (CAT) on antioxidant properties, as well as on hepatic and intestinal health, in piglets exposed to Fusarium graminearum mycotoxins (FGM). Forty female weaned piglets were divided into five groups (eight replicates per group). The pre-feeding period was 3 days, followed by a 28-day experimental period. The piglets in the control (CON) group were fed a diet without FGM contamination, while those in the FGM-exposed (TOX) group were fed a diet with FGM contamination. The LCAT, MCAT, and HCAT groups received an FGM-contaminated diet supplemented with 100, 200, and 400 U/kg of CAT, respectively. The results indicated that 400 U/kg CAT supplementation inhibited (p < 0.05, linear p < 0.05, quadratic p < 0.05) the decreases in average daily gain and average daily feed intake of piglets exposed to FGM. Moreover, all doses of supplemental CAT suppressed (p < 0.05) the increases in diarrhea rate and diarrhea index of FGM-exposed piglets. Additionally, supplemental CAT reversed (p < 0.05, linear and quadratic p < 0.05 in ileal tissue, quadratic p < 0.05 in ileal chyme) the decrease in ileal tissue and increase in ileal chyme of reactive oxygen species of piglets exposed to FGM. Supplemental CAT also enhanced the activities of ileal CAT (p < 0.05, quadratic p < 0.05) coupled with hepatic superoxide dismutase and CAT (p < 0.05, linear p < 0.05, quadratic p < 0.05) and elevated (p < 0.05) the expression of ileal and hepatic antioxidation-related genes of FGM-exposed piglets. Furthermore, the CAT supplementation increased (p < 0.05) the expression of Occludin and Claudin-1 in the ileum and colon of piglets exposed to FGM. The FGM-induced increase in the genus Staphylococcus and decrease in the genus Lactobacillus in the ileum of piglets were inhibited (p < 0.05) by supplemental 400 U/kg CAT, which also modulated the metabolite profiles involved in the glycerophospholipid metabolism pathway in hepatic portal vein blood. Exogenous CAT mitigates oxidative stress induced by FGM, along with improving intestinal and hepatic health of piglets, which can be associated with its ability to enhance intestinal microbiota and regulate hepatic glycerophospholipid metabolism, aside from its direct ability to scavenge oxygen radicals. The appropriate amount of supplemental CAT was 400 U/kg. Full article

Economic dispatch using wind power plants plays a role in reducing the price of electricity production by dispatching power among different generating units for thermal and wind power plants, and supplying load demand while meeting the power system equality and inequality constraints. Adding wind power plants to the economic dispatch model can significantly reduce electricity production costs and reduce carbon dioxide emissions. In this paper, fuel cost and emission minimization are considered as the objective function of the economic dispatch problem, taking into account transmission loss using the B matrix. The quadratic model of the fuel cost and emission criterion functions is modeled without considering a valve-point loading effect. The real power generation limits for both wind and conventional generating units are considered. In addition, a closed-form expression based on the incomplete gamma function is provided to define the impact of wind power, which includes the cost of wind energy, including overestimation and underestimation of available wind power using a Weibull-based probability density function. In this research work, Lagrange’s algorithm is proposed to solve the Wind–Thermal Economic Emission Dispatch (WTEED) problem. The developed Lagrange classical optimization algorithm for the WTEED problem is validated using the IEEE test systems with 6-, 10-, and 40-generation unit systems. The proposed Lagrange optimization method for WTEED problem solutions demonstrates a notable improvement in both economic and environmental performance compared to other heuristic optimization methods reported in the literature. Specifically, the fuel cost was reduced by an average of 4.27% in the IEEE 6-unit system, indicating more economical power dispatch. Additionally, the emission cost was lowered by an average 22% in the IEEE 40-unit system, reflecting better environmental compliance and sustainability. These results highlight the effectiveness of the proposed approach in achieving a balanced trade-off between cost minimization and emission reduction, outperforming several existing heuristic techniques such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Differential Evolution (DE) under similar test conditions. The research findings report that the proposed Lagrange classical method is efficient and accurate for the convex wind–thermal economic emission dispatch problem. Full article

Glutamine (Gln) supplementation during the weaning period can alleviate stress in piglets. However, free Gln has poor stability and low absorption in the small intestine. Glycyl-glutamine (Gly-Gln), a stable dipeptide form of Gln, has been evaluated as a potential alternative in pig nutrition. This study investigated the effects of Gly-Gln at 0, 0.125%, 0.25%, 0.375%, and 0.50%, as well as a Gly + Gln positive control, on growth performance, intestinal morphology, immunity, antioxidant status, and nutrient apparent digestibility in weaned piglets. The results showed that dietary supplementation with 0.25%, 0.375%, or 0.50% Gly-Gln significantly increased average daily gain, average daily feed intake, and final weight (p < 0.05). Linear and quadratic effects (p < 0.05) were observed for growth performance indicators, suggesting that moderate supplementation levels yielded optimal benefits. Dietary Gly-Gln supplementation with 0.25%, 0.375%, or 0.50% Gly-Gln significantly increased serum immunoglobulin (IgG, IgA, and IgM), insulin, insulin growth factor 1, growth hormone, and T4 and T3 contents, and decreased IFN-γ and IL-1β contents (p < 0.05). Diets supplemented with 0.25, 0.375, or 0.50% Gly-Gln increased total antioxidant capacity and superoxide dismutase content in serum and liver, and decreased MDA content (p < 0.05). Compared with the negative control group, dietary supplementation of 0.25%, 0.375%, or 0.50% Gly-Gln significantly increased the mRNA expression of ZO-1, Occludin, and Claudin-1 in the jejunum (p < 0.05). Furthermore, crude protein digestibility was significantly improved in piglets receiving 0.375% and 0.5% Gly-Gln (p < 0.05), with a significant linear relationship between Gly-Gln level and digestibility. In conclusion, 0.25% is the minimum effective dose of Gly-Gln for improving weaning outcomes. Gly-Gln is more effective than equivalent doses of free glycine and glutamine in enhancing growth performance, gut barrier integrity, and nutrient utilization in weaned piglets. Full article

Aiming at the characteristics of limited actuation capability of the semi-active control system and strong nonlinearity of the hydro-pneumatic suspension, a constrained nonlinear control strategy of a semi-active hydro-pneumatic suspension system is proposed. According to the mathematical model of nonlinear hydro-pneumatic suspension, the static stiffness and linear damping coefficient based on the equivalent energy are calculated, and then the control-oriented dynamic equation whose expression minimizes the nonlinear term is constructed. Combined with actuation capacity constraints, an optimization model with constraints is established to minimize the deviation between the actual overall control force and the expected optimal control force, and the optimal approximation from nonlinear control to linear quadratic optimal control is realized. The control simulation results of various methods show that the nonlinear control with constraints of the semi-active hydro-pneumatic suspension system, which effectively combines the actuation capacity constraints and nonlinear characteristics of the system, achieves a good comprehensive control effect for the nonlinear suspension control with constraints. Full article

Accurate trajectory control during atmospheric entry is critical for the success of Mars landing missions, where strong non-linearities and uncertain dynamics pose significant challenges to conventional control strategies. This study develops a computational framework that integrates fuzzy parameter-varying models with Lyapunov-based analysis to achieve robust trajectory stabilization of Mars entry vehicles. The non-linear longitudinal dynamics are reformulated via sector-bounded approximation into a Takagi–Sugeno fuzzy parameter-varying model, enabling systematic gain-scheduled controller synthesis. To reduce the conservatism typically associated with quadratic Lyapunov functions, a fuzzy Lyapunov function approach is adopted, in conjunction with the Full-Block S-procedure, to derive less restrictive stability conditions expressed as linear matrix inequalities. Based on this formulation, several controllers are designed to accommodate the variations in atmospheric density and flight conditions. The proposed methodology is validated through numerical simulations, including Monte Carlo dispersion and parametric sensitivity analyses. The results demonstrate improved stability, faster convergence, and enhanced robustness compared to existing fuzzy control schemes. Overall, this work contributes a systematic and less conservative control design methodology for aerospace applications operating under severe non-linearities and uncertainties. Full article

Carnosic acid (CA), a natural phenolic terpenoid compound, is widely distributed in plants such as sage and rosemary, and exhibits a strong antioxidant capacity. The aim of this study was to investigate the effects of different levels of CA on growth performance, antioxidant capacity, and intestinal health of yellow-feathered broilers, and then to determine the optimal dose of CA to promote sustainable broiler production. A total of 384 1-day-old yellow-feathered broilers were randomly allocated into six treatment groups with eight replicates per group and eight birds per replicate pen. The control group (CON) was fed a basal diet and the CA treated groups (CA5, CA10, CA20, CA40, and CA80) were fed diets given different doses of CA (5, 10, 20, 40, and 80 mg/kg), respectively, for 53 days (1~21 d and 22~53 d). The results showed that, in the later stages of the experiment, supplementation with 10, 20, and 40 mg/kg of CA increased (p < 0.05) the final body weight and average daily gain. Morphometric analyses of the jejunum showed that supplementation of CA increased (p < 0.05) the ratio of villus height to crypt depth (V/C). Antioxidant indices revealed that CA significantly reduced MDA levels in plasma, liver, and jejunum, while enhancing activities of GSH-Px, T-SOD, and T-AOC (p < 0.05). Moreover, CA upregulated hepatic Nrf2, HO-1, GSH-Px, and GSR expression via downregulated Keap1. The analysis of intestinal microbiota showed that CA increased (p < 0.05) microbial α diversity (Ace, Chao, and Sobs indices) and increased (p < 0.05) beneficial bacteria, such as Streptococcus, Enterococcus, and Phascolarctobacterium. In conclusion, CA improves growth performance, antioxidant capacity, intestinal health, and gut microbial diversity in broilers. Under the conditions of this experiment, quadratic regressions for different variables showed that the optimal range for supplemental CA in chicken’s diet was 19.11~76.85 mg/kg. Combined with experimental observation and regression analysis, the optimal level of supplementation was 40 mg/kg. Full article

This narrative review examines the genomic-adjusted radiation dose (GARD), a biologically informed framework developed to personalize radiotherapy by integrating tumor-specific genomic data. GARD combines the radiosensitivity index (RSI), based on gene expression, with the linear quadratic model to estimate patient-specific radiation effect. Since its introduction in 2017, GARD has demonstrated prognostic value across multiple cancer types in retrospective studies. This review summarizes key studies evaluating GARD across various tumor types and clinical contexts. Emerging trials, including a Phase II trial in HPV-positive oropharyngeal cancer, aim to validate GARD-guided dosing in precision radiotherapy. Future efforts may focus on refining RSI, addressing tumor heterogeneity, and validating GARD-guided dosing in prospective settings. Full article

This study explores how to support Turkish–American secondary school students to co-develop covariational reasoning (CR) and representational fluency (RF) in solving contextually based quadratic function tasks in an after-school community center learning setting. We conducted a teaching experiment (n = 8) at a community center. Ongoing and retrospective analyses of classroom interaction and video transcripts revealed a culturally inclusive mathematics learning environment framework with several intertwined components: co-developing CR and RF and community-based practices. This study provides evidence that students coordinate symbolic, tabular, and graphical representations, which not only deepen their understanding of how quantities change in relation to one another but also enable them to interpret and construct representations in increasingly flexible ways. This reciprocal process of co-developing CR and RF allowed students to recognize and express quantitative relationships as meaningful functional relationships, demonstrating a dynamic interplay between reasoning about change and fluency across representations. This study situates learning within culturally inclusive learning environments and acknowledges the reflexive positionality of the teacher–researcher in relation to students. We highlight how shared community-based practices can enhance mathematics teaching and learning. Full article

The optimal design of electromagnetic interference (EMI) filters relies on accurate characterization of noise source impedance. The conventional insertion loss method involves integrating two distinct passive two-port networks between the linear impedance stabilization network (LISN) and the equipment under test (EUT). The utilization of the insertion loss to formulate a system of binary quadratic equations concerning the real and imaginary components of the impedance of the noise source enables the precise extraction of the magnitude and phase of the noise source impedance in theory. However, inherent inaccuracies in the insertion loss method during extraction can compromise impedance accuracy or even cause extraction failure. This work employs a series inductance method to overcome these limitations. Exact analytical expressions are derived for the magnitude and phase of the noise source impedance. Subsequently, the application scope of the series insertion loss method is analyzed, and the impact of insertion loss measurement error on noise source impedance extraction accuracy is quantified. Requirements for improving extraction accuracy are discussed, and method optimization strategies are proposed. The permissible range of insertion loss error ensuring a solution exists is deduced. Finally, simulation and experimental results validate the proposed approach in a buck converter. Full article

This study aimed to investigate the effects of dietary supplementation with different levels of ursolic acid (UA) on the growth performance, immune function, intestinal antioxidant capacity, and anti-inflammatory responses of weaned rabbits. A total of 160 Hyla meat rabbits aged 35 days were randomly assigned to four groups. Each treatment group consisted of 8 replicates, with 5 rabbits per replicate. The rabbits were fed a basal diet (control group, CON) or experimental diets supplemented with 50, 100, or 200 mg/kg UA for 28 days. Dietary supplementation with 50 mg/kg UA significantly increased (p < 0.05) the average daily gain and average daily feed intake. The villus height, crypt depth, and villus height to crypt depth ratio exhibited quadratic responses (p < 0.05) to increasing dietary UA levels, with rabbits fed 50 mg/kg UA showing optimal ileal morphology. Compared with the CON group, dietary supplementation with 50 mg/kg UA significantly enhanced (p < 0.05) cecal catalase activity, secretory immunoglobulin A, and interleukin-10 (IL-10) levels, while the addition of 200 mg/kg UA increased (p < 0.05) serum catalase activity. The concentrations of serum tumor necrosis factor-α (TNF-α) and cecal IL-10 responded quadratically (p < 0.01 and p = 0.01, respectively) as the dietary UA level increased. With increasing UA supplementation, cecal Kelch-like ECH-associated protein 1 and IL-10 mRNA expression showed linear upregulation (p < 0.05), whereas nuclear factor erythroid 2-related factor 2 (Nrf2), superoxide dismutase 1 (SOD1), quinone oxidoreductase 1 (NQO1), TNF-α, interleukin-6, and interleukin-8 displayed quadratic responses (p < 0.05). Dietary UA at 50 mg/kg significantly downregulated cecal TNF-α and interleukin-1β mRNA expression while upregulating Nrf2, NQO1, and SOD1 mRNA levels (p < 0.05). In conclusion, dietary supplementation with 50 mg/kg UA significantly improved the growth performance of weaned rabbits by improving intestinal morphology, immune function, and antioxidant and anti-inflammatory capacities, demonstrating its efficacy as a natural phytogenic feed additive. Full article

Hilbert proved in 1888 that a positive semi-definite (PSD) homogeneous quartic polynomial of three variables always can be expressed as the sum of squares (SOS) of three quadratic polynomials, and a psd homogeneous quartic polynomial of four variables may not be sos. Only after 87 years, in 1975, Choi gave the explicit expression of such a psd-not-sos (PNS) homogeneous quartic polynomial of four variables. An $m\times n$ biquadratic polynomial is a homogeneous quartic polynomial of $m+n$ variables. In this paper, we show that an $m\times n$ biquadratic polynomial can be expressed as a tripartite homogeneous quartic polynomial of $m+n-1$ variables. Therefore, by Hilbert’s theorem, a $2\times 2$ PSD biquadratic polynomial can be expressed as the sum of squares of three quadratic polynomials. This improves the result of Calderón in 1973, who proved that a $2\times 2$ biquadratic polynomial can be expressed as the sum of squares of nine quadratic polynomials. Furthermore, we present a necessary and sufficient condition for an $m\times n$ psd biquadratic polynomial to be sos, and show that if such a polynomial is sos, then its sos rank is at most $mn$. Then we give a constructive proof of the sos form of a $2\times 2$ psd biquadratic polynomial in three cases. Full article

Kolmogorov–Arnold networks (KANs) represent a promising modeling framework for applications requiring interpretability. In this study, we investigate the use of KANs to analyze time series of water quality parameters obtained from a publicly available dataset related to an aquaponic environment. Two water quality indices (WQIs) were computed—a linear case based on the weighted average WQI, and a non-linear case using the weighted quadratic mean (WQM) WQI, both derived from three water parameters: pH, total dissolved solids (TDS), and temperature. For each case, KAN models were trained to predict the respective WQI, yielding explicit algebraic expressions with low prediction errors and clear input–output mathematical relationships. Model performance was evaluated using standard regression metrics, with $R^2$ values exceeding 0.96 on the hold-out test set across all cases. Specifically for the non-linear WQM case, we trained 15 classical regressors using the LazyPredict Python library. The top three models were selected based on validation performance. They were then compared against the KAN model and its symbolic expressions using a 5-fold cross-validation protocol on a temporally shifted test set (approximately one month after the training period), without retraining. Results show that KAN slightly outperforms the best tested baseline regressor (multilayer perceptron, MLP), with average $R^2$ scores of $0.998\pm 0.001$ and $0.996\pm 0.001$, respectively. These findings highlight the potential of KAN in terms of predictive performance, comparable to well-established algorithms. Moreover, the ability of KAN to extract data-driven, interpretable, and lightweight symbolic models makes it a valuable tool for applications where accuracy, transparency, and model simplification are critical. Full article