Dynamic Inequalities Research Articles

Unveiling the dynamic flows and spatial inequalities arising from agricultural methane and nitrous oxide emissions

Tracing the spatial transfer and heterogeneity of agricultural methane (CH4) and nitrous oxide (N2O) emissions in China is a prerequisite for the sustainable transformation of agricultural systems. In this study, we established a research framework for evaluating agricultural CH4 and N2O flows and convergence. Using this framework, we established an inventory of China's agricultural CH4 and N2O emissions calculated according to the IPCC inventory guidelines, built a food trade model to simulate the spatial transfer, and revealed the regional differences. Finally, we analyzed the influence mechanism by combining extended Kaya identity and the logarithmic mean divisia index (LMDI) model. We found that inter-regional transfer of agricultural CH4 and N2O emissions in China have intensified, increasing from 56.14 % of total transfers in 2000 to 67.28 % in 2019. The spatial inequalities of agricultural CH4 and N2O increased, and emission intensity varied more within regions than between regions, with per capita emissions showing a club convergence with “intragroup convergence and intergroup divergence”. Although the contribution of agricultural CH4 and N2O emissions varies across provinces, controlling emissions intensity and land use intensity while maintaining GDP per capita is the key to emission mitigation. Our study provides theoretical support for prioritizing policies to mitigate agricultural CH4 and N2O emissions.

Some Generalizations of Dynamic Hardy-Knopp-Type Inequalities on Time Scales

In the present paper, some new generalizations of dynamic inequalities of Hardy-type in two variables on time scales are established. The integral and discrete Hardy-type inequalities that are given as special cases of main results are original. The main results are proved by using the dynamic Jensen inequality and the Fubini theorem on time scales.

On Some New Dynamic Hilbert-Type Inequalities Across Time Scales

In this article, we present some novel dynamic Hilbert-type inequalities within the framework of time scales T. We achieve this by utilizing Hölder’s inequality, the chain rule, and the mean inequality. As specific instances of our findings (when T=N and T=R), we obtain the discrete and continuous analogues of previously established inequalities. Additionally, we derive other inequalities for different time scales, such as T=qN0 for q>1, which, to the best of the authors’ knowledge, is a largely novel conclusion.

Inventive dynamic inequalities of Pachpatte type on time scales and applications

In this article, we report a set of unique dynamic inequalities for different time scales that are based on delta-derivatives. These proposed inequalities prove to be useful tools for investigating both qualitative and quantitative facets of a class of time-scale dynamic equations, in addition to enhancing and extending several inequalities found in the literature. The introduced inequalities aid in a more thorough comprehension of the features of these equations, which involve an unknown function and its associated delta derivatives. The endpoint of this article includes numerical illustrations to emphasize the practical significance of the developed results.

Some generalizations of dynamic Opial-type inequalities on time scales

Some generalizations of dynamic Opial-type inequalities on time scales

On Grüss, Ostrowski and trapezoid-type inequalities via nabla integral on time scales

AbstractOstrowski inequality gives the absolute deviation of the function from its integral mean. Delta and nabla calculi are first two approaches to study time scales calculus. This article presents the Ostrowski inequality for univariate first order nabla differentiable function by using Montgomery identity established for nabla integrals. Some extensions of dynamic Ostrowski-type inequality are investigated with the help of integration by parts for nabla integrals, properties of the modulus and polynomials on time scales. Furthermore, dynamic Grüss and trapezoid-type inequalities are established in their generalized form for twice nabla differentiable functions by utilizing the Montgomery identity. In addition, the obtained inequalities are discussed for continuous and discrete time scales.

ON SOME INEQUALITIES FOR EXPONENTIALLY WEIGHTED FRACTIONAL HARDY OPERATORS WITH ∆-INTEGRAL CALCULUS

Dynamic equations, inequalities and operators are the indispensable cornerstones of harmonic analysis and time scale calculus. We know that the topics in question have many applications in different scientific fields. In this paper, some inequalities will be proved for variable exponentially weighted Hardy operators with ∆-integral calculus.

An analysis of hybrid impulsive prey-predator-mutualist system on nonuniform time domains

Abstract In this work, we propose a hybrid impulsive prey-predator-mutualist model on nonuniform time domains. We have investigated the permanence/persistence results for the proposed model using the comparison theorems of impulsive differential equations and some dynamic inequality on the nonuniform time domains. In addition, we have established certain necessary requirements for the uniform asymptotic stability of the almost periodic solution and global attractivity of the proposed model. Furthermore, we provide several numerical examples on nonuniform time domains with computer simulation to demonstrate the viability of the results of the acquired analytical work.

Panama: An Analysis Of Class Location And Income Distribution

Abstract In this article, the theoretical perspective centered on “dynamic inequality” and inter-category or individual differences is questioned, while the structural approach of extra-categorical analysis is sustained as essential and pertinent to sociological discussions of inequality and, further, attributable to social class, rather than internal or individual differences as posited by some theorists of inequality. From this position, an attempt is made to offer a frame of reference for the analysis and understanding the distributive structure of income in contemporary Panama. Despite presenting one of the best positioned minimum wage and average income structures in Latin America, Panama occupies one of the worst income distributions in the region. The approach subscribed to in this investigation is based on the theoretical assumption that links the conditions of income inequality with the structures of occupation and class location of the workers. The purpose is to build an empirical model of class structures associated with the occupational categories of the workers and, from this, to analyze the trends in the distribution of income in the country. The data analysis was carried out based on the Labor Market Survey of the National Institute of Statistics and Census of the Comptroller General of the Republic for 2000 and 2021.

Diamond-Type Dirac Dynamic System in Mathematical Physics

In order to merge continuous and discrete analyses, a number of dynamic derivative equations have been put out in the process of developing a time-scale calculus. The investigations that incorporated combined dynamic derivatives have led to the proposal of improved approximation expressions for computational application. One such expression is the diamond alpha (⋄α) derivative, which is defined as a linear combination of delta and nabla derivatives. Several dynamic equations and inequalities, as well as hybrid dynamic behavior—which does not occur in the real line or on discrete time scales—are analyzed using this combined concept. In this study, we consider a ⋄α Dirac system under boundary conditions on a uniform time scale. We examined some basic spectral properties of the problem we are considering, such as the simplicity, the reality of eigenvalues, orthogonality of eigenfunctions, and self adjointness of the operator. Finally, we construct an expression for the eigenfunction of the ⋄α Dirac boundary value problem (BVP) on a uniform time scale.

Norm-Based Finite-Time Convergent Recurrent Neural Network for Dynamic Linear Inequality

Norm-Based Finite-Time Convergent Recurrent Neural Network for Dynamic Linear Inequality

Generalized Dynamic Inequalities of Copson Type on Time Scales

This paper introduces novel generalizations of dynamic inequalities of Copson type within the framework of time scales delta calculus. The proposed generalizations leverage mathematical tools such as Hölder’s inequality, Minkowski’s inequality, the chain rule on time scales, and the properties of power rules on time scales. As special cases of our results, particularly when the time scale T equals the real line (T=R), we derive some classical continuous analogs of previous inequalities. Furthermore, when T corresponds to the set of natural numbers including zero (T=N0), the obtained results, to the best of the authors’ knowledge, represent innovative contributions to the field.

Switched max-plus linear-dual inequalities: cycle time analysis and applications

AbstractP-time event graphs are discrete event systems suitable for modeling processes in which tasks must be executed in predefined time windows. Their dynamics can be represented by max-plus linear-dual inequalities (LDIs), i.e., systems of linear dynamical inequalities in the primal and dual operations of the max-plus algebra. We define a new class of models called switched LDIs (SLDIs), which allow to switch between different modes of operation, each corresponding to a set of LDIs, according to a sequence of modes called schedule. In this paper, we focus on the analysis of SLDIs when the considered schedule is fixed and either periodic or intermittently periodic. We show that SLDIs can model a wide range of applications including single-robot multi-product processing networks, in which every product has different processing requirements and corresponds to a specific mode of operation. Based on the analysis of SLDIs, we propose algorithms to compute: i. minimum and maximum cycle times for these processes, improving the time complexity of other existing approaches; ii. a complete trajectory of the robot including start-up and shut-down transients.

Certain Novel Dynamic Inequalities Applicable in the Theory of Retarded Dynamic Equations and Their Applications

In this article, we establish certain time-scale-retarded dynamic inequalities that contain nonlinear retarded integral equations on various time scales. These inequalities extend and generalize some significant inequalities existing in the literature to their more general forms. The qualitative and quantitative characteristics of solutions to various dynamic equations on time scales involving retarded integrals can be studied using these inequalities. The results presented in this manuscript furnish a powerful tool to analyze the boundedness of nonlinear integral equations with retarded integrals on several time scales. In the end, we also include numerical illustrations to signify the applicability of these results to power nonlinear retarded integral equations on real and quantum time scales.

Study on the Spatial-temporal Evolution Characteristics and Trajectory of the Coupling Coordination Degree between Carbon Emission Intensity and High-quality Development of Energy-intensive Industries

This paper constructs the index of high-quality development of energy-intensive industries and calculates the coupling coordination degree between high-quality development and carbon emission intensity. In this study, the dynamic evolution process, regional inequality and convergence characteristics of the coupling coordination degree are investigated using kernel density estimation, Dagum Gini coefficient, and convergence analysis. The results show that (1) the full-sample coupling coordination degree fluctuates in medium levels, showing a two-stage inverted U-shaped trend. In addition, the highest coupling coordination degree occurred in the eastern region, followed by western provinces, and the lowest in the central regions. (2) Results of kernel density estimation showed a shift in coupling coordination degree from bipolar to unipolar; (3) the Dagum Gini coefficient shows that the general, inter-regional, and intra-regional variations all show an upward trend, suggesting a significant elevated polarization effect. Additionally, the primary determinants influencing the Dagum Gini coefficient reveal a pattern of “inter-regional variation - antagonism - hypervariable density.” (4) absolute convergence exists in the overall sample and in the eastern region, while it is not significant in the central and western regions. Based on the aforementioned findings, this study proposes policy implications for different regions in China.

Some dynamic Hardy-type inequalities with negative parameters on time scales nabla calculus

<abstract><p>In this paper, we establish some new dynamic Hardy-type inequalities with negative parameters on time scales nabla calculus by applying the reverse H ölder's inequality, integration by parts, and chain rule on time scales nabla calculus. As special cases of our results (when $ \mathbb{ T = R} $), we get the continuous analouges of inequalities proven by Benaissa and Sarikaya, and when $ \mathbb{T = N}_{0} $, the results to the best of the authors' knowledge are essentially new.</p></abstract>

Some weighted dynamic inequalities of Hardy type with kernels on time scales nabla calculus

Some weighted dynamic inequalities of Hardy type with kernels on time scales nabla calculus

Some New Dynamic Inequalities Involving The Dyanamic Hardy Operator With Kernels

Some New Dynamic Inequalities Involving The Dyanamic Hardy Operator With Kernels

Delta Calculus on Time Scale Formulas That Are Similar to Hilbert-Type Inequalities

In this article, we establish some new generalized inequalities of the Hilbert-type on time scales’ delta calculus, which can be considered similar to formulas for inequalities of Hilbert type. The major innovation point is to establish some dynamic inequalities of the Hilbert-type on time scales’ delta calculus for delta differentiable functions of one variable and two variables. In this paper, we use the condition aj(sj)=0 and aj(sj,zj)=aj(wj,nj)=0, ∀j=1,2,…,n. These inequalities will be proved by applying Hölder’s inequality, the chain rule on time scales, and the mean inequality. As special cases of our results (when T=N and T=R), we obtain the discrete and continuous inequalities. Also, we can obtain other inequalities in different time scales, like T=qZ−, q>1.

Linear fractional dynamic equations: Hyers–Ulam stability analysis on time scale

The article’s purpose is to examine ăthe Hyers–Ulam stability (HUS) for some linear fractional dynamic equations (FDEs) with the Caputo Δ−derivative on time scale. If we swap out a certain FDE for a fractional dynamical inequality, we want to know how close the solutions of the fractional dynamical inequality are to the solutions of the exact FDEs. Meanwhile, the generalized HUS result is obtained as a direct corollary. To achieve this goal, we solve the aforementioned equations utilizing the time scale version of the Laplace transform. Subsequently, the HUS is investigated in accordance with theseăsolutions.