Search

The increase in crop yield can be primarily attributed to the combined effect of genetic advancements, as well as increased contributions from nitrogen (N) and water. The accumulation of dry matter plays a crucial role in determining grain yield in winter wheat. The current study aimed to better understand the source‐sink dynamics, analyse the dry matter transport (DMT) before and after anthesis and calculate its ratio to grain yield. In this experiment, eight main cultivars of winter wheat that have been widely cultivated in Shaanxi Province since the 1940s were selected as planting material. Field examinations were conducted using three levels of both irrigation and N. The yield‐related parameters, dry matter accumulation, dry matter distribution, DMT and DMT efficiency were measured. The results showed that irrigation prolonged the time of dry matter accumulation, and the application of N fertiliser increased the rate of dry matter accumulation. The analysis of the dynamic characteristic parameters of dry matter in winter wheat showed that irrigation and N had a significant impact on rate of dry matter accumulation. The proportion of stems, leaves and spikes of new varieties increased significantly (p < 0.05), which increased by 56.67%–69.7%, 13.26%–18.07% and 15.78%–28.26%, respectively, with the varietal improvement. The DMT efficiency increased with varietal improvement and also with increased irrigation and N application. The response of irrigation treatment to DMT and dry matter was more significant. In addition, the irrigation treatment had a higher effect on the DMT efficiency of vegetative organs after anthesis. The logistic equation analysis revealed that water stress accelerated the fulfilment of maximum daily temperature (Tmax), while both the maximum growth rate (Gmax) and dry matter weight (Wmax) decreased as water stress increased. There was a positive linear relationship between dry matter accumulation after anthesis and grain yield. The structural equation model showed that varieties, N application and irrigation had significant positive effects on DMT, post‐anthesis dry matter and grain yield, while irrigation had significant negative effects on DMT efficiency. The accumulation of dry matter in winter wheat after anthesis showed a significant increase with the succession of varieties. The combination of moderate deficit irrigation and fertilisation improved transportation and dry matter accumulation after anthesis in winter wheat, thereby enhancing its production capacity. [ABSTRACT FROM AUTHOR]

Phosphorus (P) deficiency is one of the main reasons limiting plant production of Brassica napus L. Exploring the dynamics of leaf intracellular substances and the correlations with photosynthesis and growth helps to understand the response mechanisms of B. napus L. to P deficiency. This study conducted experiments on B. napus L. plants by measuring the leaf electrophysiological parameters, leaf structure, elastic modulus (Em), photosynthesis, and growth indices under different P treatment conditions. The dynamics of leaf intracellular water and nutrients of B. napus L. were calculated and analyzed by using the electrophysiological parameters, and the plant tolerance threshold to low-P stress was discovered. The results indicated that the status of the leaf intracellular water and nutrients remained stable when the P concentration was not lower than 0.250 mmol·L−1, but maximized the photosynthesis and growth at a P level of 0.250 mmol·L−1. The 0.125 mmol·L−1 P concentration significantly decreased the mesophyll cell volume, and the palisade–sponge ratio and tightness degree of leaf tissue structure were remarkably increased. This led to an increase in cell elastic modulus, and significantly improved the water retention capacity of leaf cells. At the same time, the intracellular water use efficiency and total nutrient transport capacity of leaves remained stable. As a result, the photosynthesis and growth of plants were maintained at the same level as that of the control group. However, photosynthesis and growth were clearly inhibited with a further decrease in P concentration. Therefore, 0.125 mmol·L−1 was the tolerance threshold of B. napus L. to low P. With the help of electrophysiological information, the effects of the dynamics of intracellular substances on photosynthesis and growth of B. napus L. under low-P stress can be investigated, and the plant's adaptive response can be revealed. However, the findings of the current hydroponic study are not directly applicable to field conditions with naturally P-deficient soils. [ABSTRACT FROM AUTHOR]

Finite-time control theory has been widely used as a mathematical tool to design robust controllers. By manipulating the finite-time convergence proof of this theory, we developed a new control design appropriately tuned for the finite-time control of the chaotic logistics system. In this experimental setup, the logistic equation is programmed into a PIC microcontroller, and a part of the controller was conceived using analog electronics. Because the system to be controlled is in the discrete-time domain, and the finite-time stability proof is stated in the continuous-time representation, our finite-time control approach is a good example for designing control algorithms in both time domain schemes. Hence, our experimental results support our main contribution. Pulse width modulation (PWM) is the format used to translate digital signals into the continuous-time field. Therefore, the main contribution of this article is the theoretical foundations for creating a recent controller that satisfies the convergence criterion in finite time and its construction using an 8-bit microcontroller. All this contributes to the chaotic logistical map. [ABSTRACT FROM AUTHOR]

This paper propose two new generalizations of the logistic function, each drawing on non-extensive thermodynamics, the q-logistic equation and the logistic equation of arbitrary order respectively. It demonstrate the impact of chaos theory by integrating it with logistics equations and reveal how minor parameter variations will change system behavior from deterministic to non-deterministic behavior. As well, this work presents BifDraw – a Python program for making bifurcation diagrams using classical logistic function and its generalizations illustrating the diversity of the system's response to the changes in the conditions. The research gives a pivotal role to the logistic equation's place in chaos theory by looking at its complicated dynamics and offering new generalizations that may be new in terms of thermodynamic basic states and entropy. Also, the paper investigates dynamics nature of the equations and bifurcation diagrams in it which present complexity and the surprising dynamic systems features. The development of the BifDraw tool exemplifies the practical application of theoretical concepts, facilitating further exploration and understanding of logistic equations within chaos theory. This study not only deepens our comprehension of logistic equations and chaos theory but also introduces practical tools for visualizing and analyzing their behaviors.

This paper proposed two new generalizations of the logistic function, each drawing on non-extensive thermodynamics, the q-logistic Equation and the logistic Equation of arbitrary order, respectively. It demonstrated the impact of chaos theory by integrating it with logistics Equations and revealed how minor parameter variations will change system behavior from deterministic to non-deterministic behavior. Moreover, this work presented BifDraw – a Python program for drawing bifurcation diagrams using classical logistic function and its generalizations illustrating the diversity of the system’s response to the changes in the conditions. The research gave a pivotal role to the place of the logistic Equation in chaos theory by looking at its complicated dynamics and offering new generalizations that may be new in terms of thermodynamic basic states and entropy. Also, the paper investigated dynamics nature of the Equations and bifurcation diagrams in it which present complexity and the surprising dynamic systems features. The development of the BifDraw tool exemplifies the practical application of theoretical concepts, facilitating further exploration and understanding of logistic Equations within chaos theory. This study not only deepens the comprehension of logistic Equations and chaos theory, but also introduces practical tools for visualizing and analyzing their behaviors. [ABSTRACT FROM AUTHOR]

Abstract Apparent thermal conductivity of soil (λ) as a function of soil water content (θ), i.e., λ(θ) is needed to determine the heat flow in soil. The function of λ(θ) can be used in heat and water flow models for simplicity. The objective of this study was to develop a sigmoidal model based on logistic equation for entire range of soil water contents and a wide range of soil textures that can be used in simulation of heat and water flow in respected modes. Further, performance of the developed sigmoidal model along with two other models in literature was evaluated. In the proposed sigmoidal model, the constants of this model are estimated based on empirical multivariate equations by using soil sand content and bulk density. The sigmoidal model was validated with good accuracy for a wide range of soil textures, as the relationship between the measured and predicted λ showed slope and intercept values of nearly 1.0 and 0.0, respectively. Comparison of the results obtained by sigmoidal model with those obtained from Johansen and Lu et al. models indicated that, the sigmoidal model was superior to the other two models in prediction of λ for a wide range of soil textures and soil water contents. Furthermore, comparison with a recently proposed model by Xiong et al. indicated that our sigmoidal model is superior. Therefore, our developed sigmoidal model can be used in heat and water flow models to predict the soil temperature and heat flow.

Apparent thermal conductivity of soil (λ) as a function of soil water content (θ), i.e., λ(θ) is needed to determine the heat flow in soil. The function of λ(θ) can be used in heat and water flow models for simplicity. The objective of this study was to develop a sigmoidal model based on logistic equation for entire range of soil water contents and a wide range of soil textures that can be used in simulation of heat and water flow in respected modes. Further, performance of the developed sigmoidal model along with two other models in literature was evaluated. In the proposed sigmoidal model, the constants of this model are estimated based on empirical multivariate equations by using soil sand content and bulk density. The sigmoidal model was validated with good accuracy for a wide range of soil textures, as the relationship between the measured and predicted λ showed slope and intercept values of nearly 1.0 and 0.0, respectively. Comparison of the results obtained by sigmoidal model with those obtained from Johansen and Lu et al. models indicated that, the sigmoidal model was superior to the other two models in prediction of λ for a wide range of soil textures and soil water contents. Furthermore, comparison with a recently proposed model by Xiong et al. indicated that our sigmoidal model is superior. Therefore, our developed sigmoidal model can be used in heat and water flow models to predict the soil temperature and heat flow. [ABSTRACT FROM AUTHOR]

To explore the effect of the photoperiod on the accumulation and distribution of dry matter in potato, a pot experiment was carried out in 2021 and 2022 with two varieties (Atlantic and Hezuo 88). The varieties were used as the main plot, and light treatments (short-day and long-day) were used as the subplot. The results showed that extended hours of light delayed tuber formation in Hezuo 88, however, the effect was not obvious for the Atlantic. Comprehensive analyses were carried out using the potato developmental process, dynamic equation fitting of the tuber and whole-plant dry matter accumulation, and the dry matter accumulation and distribution rate of each organ of the two varieties under two photoperiods. The two photoperiods had different effects on the parameters of rapid tuber and whole-plant dry matter accumulation: the starting point of the period of the rapid dry matter accumulation (t1), the duration period of the rapid dry matter accumulation (Δt), and the average growth rate of the period of the rapid dry matter accumulation (Vmean). According to comprehensive analysis, tuber dry matter accumulation in Atlantic was the highest under the short-day condition, while Hezuo 88 showed the lowest tuber dry matter accumulation under the long-day condition and was the latest to enter the rapid tuber dry matter accumulation period. The whole-plant dry matter accumulation in Atlantic was the highest under the long-day condition and lowest in Hezuo 88; meanwhile, Hezuo 88 was the latest to enter the rapid whole-plant dry matter accumulation period. In terms of the dry matter accumulation and dry matter partitioning ratio of various organs, Hezuo 88 had the lowest mean tuber dry matter accumulation and partitioning ratio under the long-day condition but the highest mean stem, leaf, root, underground stem, and stolon dry matter partitioning ratio. On the contrary, Atlantic had the highest mean tuber dry matter accumulation and portioning ratio under the short-day condition but the lowest mean stem, leaf, root, underground stem, and stolon dry matter partitioning ratio. It was concluded that different varieties of potato respond differently to the photoperiod. In the case of Hezuo 88, prolonging the photoperiod affected the dynamics and distribution of dry matter accumulation; increased the stem, leaf, root, and underground stem dry matter partitioning ratio; and decreased the tuber dry matter partitioning ratio, which resulted in a decrease in tuber dry matter accumulation and consequently delayed the emergence of the equilibrium period between the aboveground and underground dry matter. [ABSTRACT FROM AUTHOR]

The logistic equation with delay and diffusion and with nonclassical boundary conditions is studied. The stability of a nontrivial equilibrium state is investigated, and the resulting bifurcations are studied numerically. [ABSTRACT FROM AUTHOR]

Sepia esculenta as an important cephalopod resource in China, has high economic and nutritional value. This paper was based on a trawl survey of Sepia esculenta samples collected in the central part of the East China Sea （123. 0°E-127. 5°E, 27. 5°N-31. 5°N） from September of the same year to March of the following year from 2017 to 2021, and analyzed their mantle length and body mass composition, gonadal development, and the first sexual maturity mantle length L50. The results showed that the dominant mantle length groups of both female and male individuals in the Sepia esculenta are 81-120 mm and 81-140 mm, respectively; the dominant body mass groups are 41-280 g and 41-200 g, respectively. Individuals with low gonadal development in the Sepia esculenta grow faster than individuals with high gonadal development; and females grow faster than males. During the investigation period, the gonads developed over time; no I stage individuals were found in the group with a mantle length of over 161 mm. The results using the logistic equation and polynomial mantle length and body mass model to estimate L50 are: 124. 30 mm and 127. 98 mm for females, 129. 18 mm and 142. 44 mm for males, respectively. The L50 estimated based on the polynomial mantle length and body mass equation has a better fitting effect. The Sepia esculenta has obvious seasonal reproductive characteristics, with a breeding period of 1-3 months during the sampling period; during maturity, females transit more energy from body growth to gonadal development, and their change in growth mode is significantly earlier than males; to facilitate fishing by fishermen and ensure that all individuals have reached maturity, it is recommended that the minimum opening length of the Sepia esculenta in the central waters of the East China Sea should be greater than 142 mm. [ABSTRACT FROM AUTHOR]

The gelation kinetics of agar aqueous solutions were studied by means of the viscosity flow curves using a coaxial Couette cylinder viscometer. The viscosity curves show an unusual sigmoidal trend or an exponential decay to a viscous steady state. An original theory of gelation kinetics was developed considering the coarsening of increasingly larger and more stable clusters due to Ostwald ripening and the breakup of clusters that were too large due to the instability of rotating large particles induced by the shear rate. The developed Bounded Ripening Growth model takes into account the trend of the viscosity curves by means of an autocatalytic process with negative feedback on aggregation according to the logistic kinetic equation, in which the constants  k 1 (γ)  and  k − (ν)  are governed by the surface tension and shear rate, respectively. A dimensionless equation based on the difference between the Weber number and the ratio of the inverse kinetic constant to forward constant, accounts for the behavior of the dispersed phase in equilibrium conditions or far from the hydrostatic equilibrium. [ABSTRACT FROM AUTHOR]

We study the local dynamics of the delay logistic equation with an additional feedback containing a large delay. Critical cases in the problem of stability of the zero equilibrium state are identified, and it is shown that they are infinite-dimensional. The well-known methods for studying local dynamics based on the theory of invariant integral manifolds and normal forms do not apply here. The methods of infinite-dimensional normalization proposed by the author are used and developed. As the main results, special nonlinear boundary value problems of parabolic type are constructed, which play the role of normal forms. They determine the leading terms of the asymptotic expansions of solutions of the original equation and are called quasinormal forms. [ABSTRACT FROM AUTHOR]

Finite-time control theory has been widely used as a mathematical tool to design robust controllers. By manipulating the finite-time convergence proof of this theory, we developed a new control design appropriately tuned for the finite-time control of the chaotic logistics system. In this experimental setup, the logistic equation is programmed into a PIC microcontroller, and a part of the controller was conceived using analog electronics. Because the system to be controlled is in the discrete-time domain, and the finite-time stability proof is stated in the continuous-time representation, our finite-time control approach is a good example for designing control algorithms in both time domain schemes. Hence, our experimental results support our main contribution. Pulse width modulation (PWM) is the format used to translate digital signals into the continuous-time field. Therefore, the main contribution of this article is the theoretical foundations for creating a recent controller that satisfies the convergence criterion in finite time and its construction using an 8-bit microcontroller. All this contributes to the chaotic logistical map.

Phosphorus (P) deficiency is one of the main reasons limiting plant production of Brassica napus L. Exploring the dynamics of leaf intracellular substances and the correlations with photosynthesis and growth helps to understand the response mechanisms of B. napus L. to P deficiency. This study conducted experiments on B. napus L. plants by measuring the leaf electrophysiological parameters, leaf structure, elastic modulus (Em), photosynthesis, and growth indices under different P treatment conditions. The dynamics of leaf intracellular water and nutrients of B. napus L. were calculated and analyzed by using the electrophysiological parameters, and the plant tolerance threshold to low-P stress was discovered. The results indicated that the status of the leaf intracellular water and nutrients remained stable when the P concentration was not lower than 0.250 mmol·L−1, but maximized the photosynthesis and growth at a P level of 0.250 mmol·L−1. The 0.125 mmol·L−1 P concentration significantly decreased the mesophyll cell volume, and the palisade–sponge ratio and tightness degree of leaf tissue structure were remarkably increased. This led to an increase in cell elastic modulus, and significantly improved the water retention capacity of leaf cells. At the same time, the intracellular water use efficiency and total nutrient transport capacity of leaves remained stable. As a result, the photosynthesis and growth of plants were maintained at the same level as that of the control group. However, photosynthesis and growth were clearly inhibited with a further decrease in P concentration. Therefore, 0.125 mmol·L−1 was the tolerance threshold of B. napus L. to low P. With the help of electrophysiological information, the effects of the dynamics of intracellular substances on photosynthesis and growth of B. napus L. under low-P stress can be investigated, and the plant’s adaptive response can be revealed. However, the findings of the current hydroponic study are not directly applicable to field conditions with naturally P-deficient soils.

In this work, we study a multi-patch model, where the patches are coupled by asymmetrical migration terms, and each patch follows a logistic law under the assumption that some growth rates are much larger than the other. First, for Two-patch model where one growth rate is much larger than the second one, the total equilibrium population is greater or smaller than the sum of two carrying capacities for all migration rates. Second, we consider Three-patch model in the two cases: (i) where two growth rates are much larger than the third one, and (ii) where one growth rate is much larger than the other two. For both cases, we give a complete classification of all possible situations under which the fragmentation can lead to a total equilibrium population greater or smaller than the sum of the three carrying capacities. Finally, in the general case, we consider the model of n patches with the assumption that: (i) all growth rates but one are much larger than the n th growth rate, (ii) two blocks where the growth rates of the first block are much larger than that of the second one. For the first case, we give a complete classification of all possible situations under which the fragmentation can lead to a total equilibrium population greater or smaller than the sum of the n carrying capacities, and in the second case, we construct a reduced model and we prove its global stability. [ABSTRACT FROM AUTHOR]

【Objective】 The purpose of this paper is to investigate the effect of drip irrigation amount on dry matter accumulation and distribution, as well as the yield formation of the grain machine harvest maize. 【Method】 The study was based on the drip irrigation experiment established in 2018 in the Experimental Field of Inner Mongolia Academy of Agricultural and Animal Husbandry Sciences. The experiment consisted of five irrigation treatments by irrigating 415 m3/hm2 (W1), 645 m3/hm2 (W2), 945 m3/hm2 (W3), 1 275 m3/hm2 (W4) and 1 605 m3/hm2 (W5), respectively. A rain-fed plot was taken as the control (CK). In each treatment, we measured the accumulation and distribution of above-ground dry matter in 2020 and 2021. Logistic model was used to describe the temporal change in dry matter accumulation, from which we further analyze the characteristics of dry matter accumulation and distribution, as well as the relationship of drip irrigation amount and yield under different treatments. 【Result】 Irrigation significantly increased the dry matter accumulation in the upper part of the plant; temporal change in the dry matter accumulation is well described by the logistic model, with R2>0.888. In 2020 and 2021, the maximum growth rate of the dry matter accumulation increased as the irrigation amount increased, with the increase in the CK being the least and the increase in W5 being the highest. The biological yield in W5 was the highest in both 2020 and 2021; the harvest index in W4 and W3 was the highest, being 0.51 and 0.50 respectively. Compared with CK, irrigation reduced dry matter distribution in the vegetative organs at maturity stage but increased dry matter accumulation in the grains. With the increase in irrigation amount, the economic yield in 2020 first increased, followed by a decline, maximizing in W4, reaching 14 282.42 kg/hm2 in 2021. The yield in W4 (15 480.33 kg/hm2) and W5 (15 892.52 kg/hm2) was significantly higher than that in other treatments. 【Conclusion】 Optimizing irrigation amount can significantly increase dry matter accumulation in the aboveground part, and promote distribution of dry matter in the grain. In drought years with average annual natural precipitation between 364.2 and 390.7 mm, the optimum drip irrigation amount is 1 275 m3/hm2 for grain machine harvest maize (planting density is 7.5×104 plants/hm2) in the arid and semi-arid areas in central and western Inner Mongolia.

To explore the effect of the photoperiod on the accumulation and distribution of dry matter in potato, a pot experiment was carried out in 2021 and 2022 with two varieties (Atlantic and Hezuo 88). The varieties were used as the main plot, and light treatments (short-day and long-day) were used as the subplot. The results showed that extended hours of light delayed tuber formation in Hezuo 88, however, the effect was not obvious for the Atlantic. Comprehensive analyses were carried out using the potato developmental process, dynamic equation fitting of the tuber and whole-plant dry matter accumulation, and the dry matter accumulation and distribution rate of each organ of the two varieties under two photoperiods. The two photoperiods had different effects on the parameters of rapid tuber and whole-plant dry matter accumulation: the starting point of the period of the rapid dry matter accumulation (t1), the duration period of the rapid dry matter accumulation (Δt), and the average growth rate of the period of the rapid dry matter accumulation (Vmean). According to comprehensive analysis, tuber dry matter accumulation in Atlantic was the highest under the short-day condition, while Hezuo 88 showed the lowest tuber dry matter accumulation under the long-day condition and was the latest to enter the rapid tuber dry matter accumulation period. The whole-plant dry matter accumulation in Atlantic was the highest under the long-day condition and lowest in Hezuo 88; meanwhile, Hezuo 88 was the latest to enter the rapid whole-plant dry matter accumulation period. In terms of the dry matter accumulation and dry matter partitioning ratio of various organs, Hezuo 88 had the lowest mean tuber dry matter accumulation and partitioning ratio under the long-day condition but the highest mean stem, leaf, root, underground stem, and stolon dry matter partitioning ratio. On the contrary, Atlantic had the highest mean tuber dry matter accumulation and portioning ratio under the short-day condition but the lowest mean stem, leaf, root, underground stem, and stolon dry matter partitioning ratio. It was concluded that different varieties of potato respond differently to the photoperiod. In the case of Hezuo 88, prolonging the photoperiod affected the dynamics and distribution of dry matter accumulation; increased the stem, leaf, root, and underground stem dry matter partitioning ratio; and decreased the tuber dry matter partitioning ratio, which resulted in a decrease in tuber dry matter accumulation and consequently delayed the emergence of the equilibrium period between the aboveground and underground dry matter.

With the continuous progress and broad application of cutting-edge information technology such as big data, cloud computing, virtual reality and artificial intelligence, senior sports services has ushered in unprecedented development opportunities, especially the rise of senior intelligent sports services. In this study, we applied the principal component analysis method to conduct in-depth screening of evaluation indexes to assess the quality of the practice of senior intelligent sports services in Anhui Province. Through the comprehensive analysis of the eigenroots and the contribution ratio of variance, this paper successfully identified the key factors and realized the effective dimensionality reduction of the data. Meanwhile, we adopted the logistic equation to accurately estimate the relevant parameters. Through the comprehensive analysis of eigenroot and variance contribution ratio, this paper successfully identifies the key factors, realizes the effective dimensionality reduction of the data, and adopts the logistic equation to accurately estimate the relevant parameters. The analysis results show that in the senior intelligent sports service index system, the highest weight value of platform is the operation and management platform, which reaches 0.4754. In the aspect of the demand for sports information of the seniors, the demand for online sports knowledge and skills is the highest, and the demand for online sports knowledge and skills is the highest. Regarding the demand for sports information of the elderly, the online acquisition of sports knowledge and skills has the highest demand of 203, followed by the demand for regular online sports knowledge lectures of 181. In the demand for outdoor bright trails, the elderly strongly want to enter their fitness and energy consumption data for evaluation, with a high degree of demand of 351. In addition, the demand for heart rate testing of the intelligent body testing station is the highest, with a degree of 186, followed by body fat testing, with a degree of 179. The Research in this paper not only focuses on the current situation and problems of intelligent sports services for the elderly, but also explores the methods and strategies to solve these problems, aiming to provide practical reference and guidance for the effective implementation of intelligent sports services for the elderly.

Osmotic dehydration (OD) is an easy method for removing water from fruit and vegetable particles. In this study, apple slices were osmotically dehydrated in different hypertonic sucrose solutions and assisted with or without ultrasound. Sucrose concentrations, sonication power, and treatment time were the factors investigated concerning color parameters and surface area changes of the apple slices during OD. As the sonication power increased from 0W to 150W, the lightness (L*) index values of apple slices reduced from 80.01 to 74.33. Also, with increasing sucrose solution concentration from 30°Brix to 50°Brix the lightness index values of apple slices decreased from 79.23 to 75.65. The results showed that the mean of a* and b* indexes values of dehydrated apple slices increased during the OD period. The highest total color difference (∆E) index (23.4) and lowest surface area (7.98 cm 2 ) values were for the apple slices treated by the highest ultrasound power (150W, 40 kHz) and the highest sucrose solution concentration (50°Brix). The average surface area of fresh apple slices, dehydrated samples, hot -air drying samples, and rehydrated samples was 10.00 cm², 8.62 cm², 5.61 cm², and 6.99 cm², respectively. The results illustrated that the logistic equation was the best equation to explain the ∆ E index changes of untreated and treated apple slices during OD. [ABSTRACT FROM AUTHOR]

The aim of this study is to develop the Fibonacci wavelet method together with the quasi‐linearization technique to solve the fractional‐order logistic growth model. The block‐pulse functions are employed to construct the operational matrices of fractional‐order integration. The fractional derivative is described in the Caputo sense. The present time‐fractional population growth model is converted into a set of nonlinear algebraic equations using the proposed generated matrices. Making use of the quasi‐linearization technique, the underlying equations are then changed to a set of linear equations. Numerical simulations are conducted to show the reliability and use of the suggested approach when contrasted with methods from the existing literature. A comparison of several numerical techniques from the available literature is presented to show the efficacy and correctness of the suggested approach. [ABSTRACT FROM AUTHOR]

Power series, as an important means to analyze functions in different complex settings, are employed in various applied areas to solve differential equations and nonlinear problems and provide the assessment of intervals of convergence. Accordingly, the fuzzy logistic differential equation using the Caputo operator has been studied in this paper. Accordingly, the fuzzy logistic differential equation using the Caputo operator has been studied in this paper. The generalized Hukuhara difference and the generalized Hukuhara derivative are also used, and a power series representation is proposed for the solution of the fuzzy fractional logistic equation. Afterward, power series coefficients are obtained using a recursive formula. Finally, numerical experiments and illustrated results of the computations are presented to allow for more realistic decisions reflecting high complexity and underlying uncertainty. Thus, the numerical computations in our study reveal the effectiveness and accuracy of the power series method. Therefore, it is found that the fuzzy solution converges to the deterministic solution when uncertainty decreases, and, based on the technical analyses, it has been demonstrated that the results obtained are more fundamental in preventing geometric growth in nonlinear phenomena where uncertainties emerge due to impreciseness and inexactness. [ABSTRACT FROM AUTHOR]

This study investigates the evolutionary impact of applying artificial intelligence (AI) technology to foreign language education. By employing complex systems thinking, the relationship between foreign language education and AI technology is explored, and dynamic models are employed to analyze the evolutionary patterns of AI technology in foreign language education. Through model analysis and numerical simulations, the interactive effects between foreign language education and AI technology in different modes are revealed. The findings demonstrate that, under different coupling modes, foreign language education and AI technology can achieve self-organizing evolution. When the interaction coefficient between foreign language education and AI technology is appropriately set, AI technology exhibits emergent properties for foreign language education. Lastly, suggestions are presented to promote the sound development of foreign language education and AI technology. [ABSTRACT FROM AUTHOR]

We prove a uniqueness theorem for the obstacle problem for linear equations involving the fractional Laplacian with zero Dirichlet exterior condition. The problem under consideration arises as the limit of some logistic-type equations. Our result extends (and slightly strengthens) the known corresponding results for the classical Laplace operator with zero boundary condition. Our proof, as compared with the known proof for the classical Laplace operator, is entirely new, and is based on the probabilistic potential theory. Its advantage is that it may be applied to a wide class of integro-differential operators. [ABSTRACT FROM AUTHOR]

The present study validates growth models based on logistic equations to predict and analyze the use of fish viscera hydrolysates as a source of protein for rainbow trout (Oncorhynchus mykiss) diet. The study examines zootechnical variables such as body weight, total length, and biomass in the fingerling and rearing phases, during seven months of production. The treatments consist of isoproteic and isoenergetic diets with a content of 10%, 15%, and 20% of viscera hydrolysates. A commercial diet is used as a control. The results show that the logistic model explained more than 97% of the variation of the field data, proving to be adequate for assessing the efficiency of using 20% replacement hydrolyzed fish viscera. It is concluded that the logistic model developed here is a useful tool for diagnosing the effectiveness and quality of biological diets in each of the production phases of rainbow trout. [ABSTRACT FROM AUTHOR]

In this paper, we introduce logistic equations with Stieltjes derivatives and provide explicit solution formulas. As an application, we present a population model which involves intraspecific competition, periods of hibernation, as well as seasonal reproductive cycles. We also deal with various forms of Stieltjes integral equations, and find the corresponding logistic equations. We show that our work extends earlier results for dynamic equations on time scales, which served as an inspiration for this paper.

In this article, we study the sharp profiles of positive solutions to the diffusive logistic equation. By employing parameters and analyzing the corresponding perturbation equations, we find the effects of boundary and spatial heterogeneity on the positive solutions. The main results exhibit the sharp effects between boundary conditions and linear/nonlinear spatial heterogeneities on positive solutions.

Logistic sigmoids due to their flexibility seem to be natural candidates for modelling macrofinancial leverage behavior. The sigmoidal leverage transition towards its stationary value, which was driven by the yield spreads, could have replicated the dynamics of macrofinancial assets, debt and capital. The leverage transition, in its turn, has been a major factor in better balancing macrofinancial liabilities and assets. The sigmoidal leverage trajectories including their inflections and different phases were identified by a nonlinear transition function providing information necessary for steering the process towards its stable state. Solving the stationary Kolmogorov-Fokker-Plank logistic equation revealed that random leverage realizations might follow the gamma distribution. Parameters of its stationary probability density function, as well as the expected and the modal leverage, were dependent on the process variance and the yield spreads. Thus, the stochastic leverage behaviour reproduced a sequence of stylized phases similar to the observed in the US Treasuries market meltdown in 2020. In particular, larger yield spreads and smaller modal leverage signalled a "defensive" market response to sudden volatility increases. In addition, it was shown that the logistic leverage modelling could be helpful in the analysis of debt and money dynamics including some consequences of "minting a one trillion dollars coin".

The gelation kinetics of agar aqueous solutions were studied by means of the viscosity flow curves using a coaxial Couette cylinder viscometer. The viscosity curves show an unusual sigmoidal trend or an exponential decay to a viscous steady state. An original theory of gelation kinetics was developed considering the coarsening of increasingly larger and more stable clusters due to Ostwald ripening and the breakup of clusters that were too large due to the instability of rotating large particles induced by the shear rate. The developed Bounded Ripening Growth model takes into account the trend of the viscosity curves by means of an autocatalytic process with negative feedback on aggregation according to the logistic kinetic equation, in which the constants k1(γ) and k−(ν) are governed by the surface tension and shear rate, respectively. A dimensionless equation based on the difference between the Weber number and the ratio of the inverse kinetic constant to forward constant, accounts for the behavior of the dispersed phase in equilibrium conditions or far from the hydrostatic equilibrium.

We examine a multi-patch model of a population connected by nonlinear asymmetrical migration, where the population grows logistically on each patch. Utilizing the theory of cooperative differential systems, we prove the global stability of the model. In cases of perfect mixing, where migration rates approach infinity, the total population follows a logistic law with a carrying capacity that is distinct from the sum of carrying capacities and is influenced by migration terms. Furthermore, we establish conditions under which fragmentation and nonlinear asymmetrical migration can lead to a total equilibrium population that is either greater or smaller than the sum of carrying capacities. Finally, for the two-patch model, we classify the model parameter space to determine if nonlinear dispersal is beneficial or detrimental to the sum of two carrying capacities. [ABSTRACT FROM AUTHOR]

Here, the best ratio of slow-release nitrogen fertilizer to urea was determined to match the nitrogen demand of winter wheat. The fertilizer application structure was also optimized for the efficient use of nitrogen fertilizer and economic benefits. Seven fertilizer treatments were applied into the winter wheat in a two-year field trial: urea only (U), slow-release N fertilizer only (S), slow-release N fertilizer with the urea 1:3 (SU1), 1:1 (SU2), and 3:1 (SU3), no N fertilizer (N0) and no fertilizer (CK). A systematic investigation was made to explore the effects of slow-release N fertilizer application rates on the dry matter accumulation and transport, yield, and N fertilizer use efficiency of winter wheat. The results showed that there was an increase in the rapid growth period and the maximum accumulation rate of dry matter in the winter wheat with the proportion of slow-release N fertilizer. The average dry matter accumulation rate of slow-release nitrogen fertilizer combined with the urea increased by 1.90% to 19.91%, compared with the ordinary urea. The proportion of slow-release nitrogen fertilizer application posed a significant impact on the post post-flowering dry matter production. There was an increase in the pre and post post-flowering dry matter transport. Meanwhile, the post post-flowering dry matter production was contributed 53.18% to 71.83% of the grain yield. The yield increased significantly with the increasing proportion of slow-release N fertilizer, with the two-year yields of 7 243 and 8 021 kg/hm2 in the SU3, which were 7.25% and 16.07% higher than the S and U treatments, respectively, and their economic benefits were 15.18% and 25.67%, respectively. The cumulative nitrogen uptake of winter wheat increased by the application of slow-release nitrogen fertilizer with the urea. Specifically, the cumulative nitrogen uptake values were 24.08% to 36.63% higher than those in the SU3, compared with the U treatment. The slow-release N fertilizer with the urea was improved the N fertilizer use efficiency. The agronomic use efficiency, physiological use efficiency, and biased productivity were improved by 130.39%, 70.96%, 58.33%, and 23.05%, respectively, in the SU3, compared with the U treatment. But there was no significant difference between SU2 and SU3 treatments (P>0.05). The slowrelease N combined with the urea was significantly improved the N use efficiency, but there was no significant difference between SU2 and SU3 treatments (P>0.05). Therefore, the slow-release N fertilizer mixed with the urea can be expected to improve the winter wheat yield and N use efficiency. The dry matter growth period was significantly extended to promote the maximum accumulation rate for the post-flowering dry matter production and its transport rate to the seed. The fitting analysis showed that the high yield of winter wheat was achieved with 55% of slow-release N fertilizer in the combination with urea under the condition of 180 kg/hm2 of N application. Among them, the yield was 7 563 kg/hm2, and the nitrogen absorption efficiency was 50.23%. Agronomic utilization rate, physiological utilization rate, and partial production rate were 17.57, 31.97, and 43.59 kg/kg, respectively. The finding can provide the theoretical basis for the rational fertilization of winter wheat. Followup studies need to consider the environmental effects and carbon and nitrogen emissions, together with the impact of slowrelease nitrogen fertilizer combined with the urea on the soil nitrate nitrate-nitrogen distribution, ammonia volatilization, and greenhouse gas emissions. Further research can be conducted to determine the amount and proportion of slow-release nitrogen fertilizer and urea application for the high yield, high efficiency, and simultaneous emission reduction in winter wheat farmland.. [ABSTRACT FROM AUTHOR]

Modelers have choices in how they approach a problem, with different approaches potentially leading to different outcomes. Sometimes one approach gives a consistently lower (or higher) result than another. The theorem and corollaries in this study show that if the logistic equation or, equivalently, the SI model, are perturbed at time zero by a range of values with mean zero, the resulting trajectories must average to a value below (for logistic and I) or above (for S) the solution with average initial condition. The proof of the theorem shows that this phenomenon is the result of algebraic properties of the nonlinear quadratic term, although we note it can be extended to a larger class of systems. More importantly it shows that the only necessary criterion is that the perturbations average to zero. The source of them and the properties of their distribution does not matter to the result of the theorem but does affect the magnitude of the proven difference. [ABSTRACT FROM AUTHOR]

We consider a Dirichlet problem for a nonlinear, nonlocal equation driven by the degenerate fractional p‐Laplacian, with a logistic‐type reaction depending on a positive parameter. In the subdiffusive and equidiffusive cases, we prove existence and uniqueness of the positive solution when the parameter lies in convenient intervals. In the superdiffusive case, we establish a bifurcation result. A new strong comparison result, of independent interest, plays a crucial role in the proof of such bifurcation result. [ABSTRACT FROM AUTHOR]

In this paper, we study the perturbation problem for the periodic logistic equation with indefinite weight functions and nonlocal dispersal. Our aim is to find the precisely asymptotic behavior of positive solutions when the perturbation (dispersal rate) is large or small. We establish that the positive solution uniformly tends to the maximum nonnegative solution of the kinetic equation as the dispersal rate goes to zero. However, the positive solution uniformly converges to the maximum nonnegative solution of kinetic equation, which is independent of spatial locations when the dispersal rate goes to infinity. The main results reveal that large dispersal rate corresponding to pure kinetic equation, whereas small dispersal rate corresponding to kinetic equation with parameters. [ABSTRACT FROM AUTHOR]

Understanding the fertility transition in Brazil at the municipal scale provides important support for designing and implementing local policies that incorporate spatial heterogeneity into local sociodemographic dimensions. To analyze the heterogeneity of the fertility transition process among Brazilian municipalities over the last two decades, we rewrite the logistic curve equation, estimate the parameters of the national logistic curve and allocate Brazilian municipalities in the national trend using their own total fertility rates. The lag between most and least developed areas persists in either the North or Northeast Region, opposite to what is observed in the South and Southeast. While some municipalities are beyond their time regarding the national average fertility transition, others are at the beginning of the transition. The very fast fertility decline experienced by late runners in the more recent period results in changes in age composition, configuring a challenge that social decision-makers should face.

In this paper, we introduce logistic equations with Stieltjes derivatives and provide explicit solution formulas. As an application, we present a population model which involves intraspecific competition, periods of hibernation, as well as seasonal reproductive cycles. We also deal with various forms of Stieltjes integral equations, and find the corresponding logistic equations. We show that our work extends earlier results for dynamic equations on time scales, which served as an inspiration for this paper. [ABSTRACT FROM AUTHOR]

In this article, we present a novel hybrid approach, by combining the Sawi transform with the homotopy perturbation method, to achieve the approximate and analytic solutions of nonlinear fractional differential equations (ODE as well as PDE) using the time-fractional Caputo derivative. The proposed algorithm is faster and simple compared to other iterative methods. The Sawi transform is used along with the homotopy perturbation method to accelerate the convergence of the series solution. The results discussed using calculations, graphs and tables are compatible for comparison with other known methods like the residual power series method and the exact solution which are discussed in the literature. [ABSTRACT FROM AUTHOR]

Copyright of Revista Latinoamericana de Población is the property of Revista Latinoamericana de Poblacion and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Logistic sigmoids due to their flexibility seem to be natural candidates for modelling macrofinancial leverage behavior. The sigmoidal leverage transition towards its stationary value, which was driven by the yield spreads, could have replicated the dynamics of macrofinancial assets, debt and capital. The leverage transition, in its turn, has been a major factor in better balancing macrofinancial liabilities and assets. The sigmoidal leverage trajectories including their inflections and different phases were identified by a nonlinear transition function providing information necessary for steering the process towards its stable state. Solving the stationary Kolmogorov-Fokker-Plank logistic equation revealed that random leverage realizations might follow the gamma distribution. Parameters of its stationary probability density function, as well as the expected and the modal leverage, were dependent on the process variance and the yield spreads. Thus, the stochastic leverage behaviour reproduced a sequence of stylized phases similar to the observed in the US Treasuries market meltdown in 2020. In particular, larger yield spreads and smaller modal leverage signalled a "defensive" market response to sudden volatility increases. In addition, it was shown that the logistic leverage modelling could be helpful in the analysis of debt and money dynamics including some consequences of "minting a one trillion dollars coin". [ABSTRACT FROM AUTHOR]

We consider the following doubly nonlocal nonlinear logistic problem driven by the fractional p-Laplacian (- Δ) p s u = f (x , u) - ∫ Ω | u (y) | r | x - y | α d y | u (x) | r - 2 u (x) in Ω , u = 0 in R N \ Ω. Here Ω ⊂ R N (N ≥ 2) is a bounded domain with C 1 , 1 boundary ∂ Ω , s ∈ (0 , 1) , p ∈ (1 , ∞) are such that p s < N . Also p s , α # ≤ r < ∞ , where p s , α # = (2 N - α) / 2 N . Under suitable and general assumptions on the nonlinearity f, we study the existence, nonexistence, uniqueness, and regularity of weak solutions. As for applications, we treat cases of subdiffusive type logistic Choquard problem. We also consider in the superdiffusive case the Brezis-Nirenberg type problem with logistic Choquard and show the existence of a nontrivial solution for a suitable choice of λ . Finally for a particular choice of f viz. f (x , t) = λ t q - 1 with 1 < p < 2 r < q , we show the existence of at least one energy nodal solution. [ABSTRACT FROM AUTHOR]

The main mathematical result in this paper is that change of variables in the ordinary differential equation (ODE) for the competition of two infections in a Susceptible– Infected–Removed (SIR) model shows that the fraction of cases due to the new variant satisfies the logistic differential equation, which models selective sweeps. Fitting the logistic to data from the Global Initiative on Sharing All Influenza Data (GISAID) shows that this correctly predicts the rapid turnover from one dominant variant to another. In addition, our fitting gives sensible estimates of the increase in infectivity. These arguments are applicable to any epidemic modeled by SIR equations. [ABSTRACT FROM AUTHOR]

We consider applications of a comparison method for obtaining some exact solutions of nonlinear partial differential equations (PDEs) through their traveling wave reductions. The method, proposed by N. A. Kudryashov, 39(18), 5733–5742, Applied Mathematical Modelling, is extended to encompass not only solutions expressible in terms of the logistic function but also to the tanh$$ \tanh $$‐class of functions in a unified manner. The standard set of second‐order ordinary differential equations (ODEs) admitting the logistic and tanh$$ \tanh $$ functions as solutions is derived and extensions to the third‐order case are enunciated. A number of examples are included to illustrate the method. [ABSTRACT FROM AUTHOR]

Food industry effluents represent one of the major concerns when it comes to environmental impact; hence, their valorization through different chemical and biological routes has been suggested as a possible solution. The vast amount of organic and inorganic nutrients present in food industry effluents makes them suitable substrates for microbial growth. This study suggests two valorization routes for whey as dairy industry effluent and flotation wastewater from the wine industry through microbial conversion to biocontrol agents as value-added products. Cultivations of the biocontrol strain Bacillus sp. BioSol021 were performed in a 16 L bioreactor to monitor the bioprocess course and investigate bioprocess kinetics in terms of microbial growth, sugar substrate consumption and surfactin synthesis, as an antimicrobial lipopeptide. The produced biocontrol agents showed high levels of biocontrol activity against mycotoxigenic strains of Aspergillus flavus, followed by a significant reduction of sugar load of the investigated effluents by the producing microorganisms. With proven high potential of whey and winery flotation wastewater to be used as substrates for microbial growth, this study provides grounds for further optimization of the suggested valorization routes, mostly in terms of bioprocess conditions to achieve maximal techno-economical feasibility, energy saving and maximal reduction of effluents' organic and inorganic burden. [ABSTRACT FROM AUTHOR]

This work discusses the existence of the limit as p goes to 1 of the nontrivial solutions to the one-dimensional problem: - | u x | p - 2 u x x = λ | u | p - 2 u - | u | q - 2 u 0 < x < 1 u (0) = u (1) = 0 , where λ is a positive parameter and the exponents p, q satisfy 1 < p < q . We prove that solutions do converge to a limit function, which solves in a proper sense a Dirichlet problem involving the 1-Laplacian operator. [ABSTRACT FROM AUTHOR]

The problem of testing in education is relevant for many countries. Testing solves three problems. The first task is to assess the quality of current training. The second task is to conduct a comparative analysis of learning outcomes. The third task is the management of the educational process in a particular educational institution and in the education sector. This determines the relevance of testing and the relevance of developing new methods for assessing test results. The article proposes a new method for assessing test results for different situations: “teacher– student”, computer test, virtual testing model, test on a mixed reality model and others. To solve the problem, a special quasi-sigmoidal function is introduced. It is analogous to the logistic function, but takes into account the peculiarities of real testing of students. The logistic function ranges from minus infinity to plus infinity. There are no negative assessments in education. The introduced function lies only in the positive range of the argument. It describes actual positive scores when testing students. The authors called this function the complexity function. With its help, the complexity of the subject is assessed according to the test results. To substantiate the method, the function of the logarithms of the odds, logistic regression and the resulting Rush method are investigated. The article notes two shortcomings of the Rush method. The testing principle has been defined for the new function, which is used to estimate complexity. The article introduces two new concepts: the test difficulty function and the integral test score. Integral assessment of testing is a smooth function and makes it possible to go from a stepwise dependence to a continuous one. The cumulative test score translates the point test results into a continuous function and creates a correlation between the scores. The results of an experiment with the participation of RTU MIREA students are presented. The experimental results are analyzed. The possibility of using the method in educational processes is shown. The method is an alternative to the Rush method.