Nonlinear Difference Research Articles

On the directionality and non-linearity of halogen and hydrogen bonds.

Benchmark quality structures and interaction energies have been produced using explicitly correlated coupled cluster methods for a systematic series of hydrogen and halogen bonded complexes: B···HCCH, B···HCl and B···ClF, with six different Lewis bases B. Excellent agreement with experimental structures is observed, verifying the method used to deduce the equilibrium deviation from collinearity of the intermolecular bond via rotational spectroscopy. This level of agreement also suggests that the chosen theoretical method can be employed when experimental equilibrium data are not available. The application of symmetry adapted perturbation theory reveals differences in the underlying mechanisms of interaction for hydrogen and halogen bonding, providing insights into the differences in non-linearity. In the halogen bonding case it is shown that the dispersion term is approximately equal to the overall interaction energy, highlighting the importance of choosing the correct theoretical method for this type of interaction.

Positive Solutions for a Third Order Nonlinear Neutral Delay Difference Equation

The existence, multiplicity, and properties of positive solutions for a third order nonlinear neutral delay difference equation are discussed. Six examples are given to illustrate the results presented in this paper.

Socioeconomic inequalities of cardiovascular risk factors among manufacturing employees in the Republic of Ireland: A cross-sectional study.

Objectives: To explore socioeconomic differences in four cardiovascular disease risk factors (overweight/obesity, smoking, hypertension, height) among manufacturing employees in the Republic of Ireland (ROI). Methods: Cross-sectional analysis of 850 manufacturing employees aged 18–64 years. Education and job position served as socioeconomic indicators. Group-specific differences in prevalence were assessed with the Chi-squared test. Multivariate regression models were explored if education and job position were independent predictors of the CVD risk factors. Cochran–Armitage test for trend was used to assess the presence of a social gradient. Results: A social gradient was found across educational levels for smoking and height. Employees with the highest education were less likely to smoke compared to the least educated employees (OR 0.2, [95% CI 0.1–0.4]; p < 0.001). Lower educational attainment was associated with a reduction in mean height. Non-linear differences were found in both educational level and job position for obesity/overweight. Managers were more than twice as likely to be overweight or obese relative to those employees in the lowest job position (OR 2.4 [95% CI 1.3–4.6]; p = 0.008). Conclusion: Socioeconomic inequalities in height, smoking and overweight/obesity were highlighted within a sub-section of the working population in ROI.

Existence and Multiple of Positive Solution for Nonlinear Fractional Difference Equations with Parameter

Let,. We study the existence and multiple positive solutions of n-th nonlinear discrete fractional boundary value problem of the form By using a fixed-point theorem on cone, the parameter intervals of problem is established.

Numerical Simulation for the Soil-Pile-Structure Interaction under Seismic Loading

Piles are widely used as reinforcement structures in geotechnical engineering designs. If the settlement of the soil is greater than the pile, the pile is pulled down by the soil, and negative friction force is produced. Previous studies have mainly focused on the interaction of pile-soil under static condition. However, many pile projects are located in earthquake-prone areas, which indicate the importance of determining the response of the pile-soil structure under seismic load. In this paper, the nonlinear, explicit, and finite difference program FLAC3D, which considers the mechanical behavior of soil-pile interaction, is used to establish an underconsolidated soil-pile mode. The response processes of the pile side friction force, the pile axial force, and the soil response under seismic load are also analyzed.

Oscillation Criteria for Nonlinear Higher-Order Forced Functional Difference Equations

Some oscillation criteria for solutions of nonlinear higher-order forced difference equations are established. The investigations are carried out without assuming that the coefficients of the equations are of a definite sign and by showing that the forcing term needs not be the mth difference of an oscillatory function. The proposed results are supported with some examples.

Control of Cardiac Arrhythmia by Nonlinear Spatiotemporal Delayed Feedback

The dynamic feedback control of the cardiac pacing interval has been widely used to suppress alternans. In this paper, temporally and spatially suppressing the alternans for cardiac tissue consisting of a one-dimensional chain of cardiac units is investigated. The model employed is a nonlinear partial difference equation. The model's fixed points and their stability conditions are determined, and bifurcations and chaos phenomenon have been studied by numerical simulations. The main objective of this paper is to stabilize the unstable fixed point of the model. The proposed approach is nonlinear spatiotemporal delayed feedback, and the appropriate interval for controller feedback gain is calculated using the linear stability analysis. It is proven that the proposed approach is robust with respect to all bifurcation parameter variations. Also, set point tracking is achieved by employing delayed feedback with an integrator. Finally, simulation results are provided to show the effectiveness of the proposed methodology.

Continuous symmetries of certain nonlinear partial difference equations and their reductions

Abstract In this article, Quispel, Roberts and Thompson type of nonlinear partial difference equation with two independent variables is considered and identified five distinct nonlinear partial difference equations admitting continuous point symmetries quadratic in the dependent variable. Using the degree growth of iterates the integrability nature of the obtained nonlinear partial difference equations is discussed. It is also shown how to derive higher order ordinary difference equations from the periodic reduction of the identified nonlinear partial difference equations. The integrability nature of the obtained ordinary difference equations is investigated wherever possible.

Analysis of Surge Shaft Excavation Process Based on 3-Dimensional Finite Difference Method

As an important part of the structure of hydroelectric power station, surge shaft is embedded in the rock mass, whose body size and loading conditions are typically complex. Thus, it is necessary to evaluate safety of the design scheme in order to ensure construction safety. With upper background, three dimensional finite difference model of the surge shaft and surrounding rock of a hydroelectric project in Zambia were established based on three dimensional nonlinear finite difference analysis method. Calculation of the surge shaft stepped excavation with supporting at all levels of the construction process was done. The deformation and stress state of the surrounding rock of surge shaft and its variation law in excavation process was analyzed. Furthermore, the stability of surrounding rocks and rationality of the designed support measures were evaluated.

On asymptotic exit-time control problems lacking coercivity

The research on a class of asymptotic exit-time problems with a vanishing Lagrangian, begun in [M. Motta and C. Sartori, Nonlinear Differ. Equ. Appl. Springer (2014).] for the compact control case, is extended here to the case of unbounded controls and data, including both coercive and non-coercive problems. We give sufficient conditions to have a well-posed notion of generalized control problem and obtain regularity, characterization and approximation results for the value function of the problem.

A Class of Nonlinear Singular Difference Inequality in Engineering

In this paper, we discuss a class of new nonlinear weakly singular difference inequality. Using change of variable, discrete Jensen inequality, amplification method, the mean-value theorem for integrals and Gamma function, explicit bounds for the unknown functions in the inequality is given clearly. The derived results can be applied in the study of fractional difference equations in Engineering.

A novel approach to exponential stability of nonlinear non-autonomous difference equations with variable delays

In this paper, by using a novel approach, we first prove a new generalization of discrete-type Halanay inequality. Based on our new generalized inequality, a novel criterion for the exponential stability of a certain class of nonlinear non-autonomous difference equations is proposed. Numerical examples are given to illustrate the effectiveness of the obtained results.

Quantifying and Reducing the Signal Noise Using Nonlinear Stochastic Difference Equations

This paper deals with quantification of the noise located in the digital signal by an innovative process. This process is associated with the filter that represents the novel information conveyed by the desired signal, residual interference and residual noise which are used to reduce the noise. A typical uniform quantization operation of a sampled signal is identified and interpreted with the framework of stochastic difference equation. A new theorem is proposed with all possible assumptions to support our result to signal noise ratio. AMS [200] Subject Classification: 39A10, 39A30, 39A60, 39B82, 39B99.

Positive Solution for Boundary Value Problem of Nonlinear Three-Order Difference Equation

In this paper we investigate the existence of positive solution of the following nonlinear discrete third-order two-point boundary value problem. whereis continuous and there existssuch that . Our approach relies on the Krasnosel'skii fixed point theorem. An example is given to demonstrate the application of the theorem obtained.

On a second-order nonlinear discrete multi-point eigenvalue problem

We study the existence and non-existence of positive solutions of a system of nonlinear second-order difference equations with eigenvalues subject to multi-point boundary conditions.

Oscillation of Second-Order Nonlinear Impulsive Difference Equations with Continuous Variables

The paper deals with a second-order nonlinear impulsive difference equation with continuous variable. Sufficient conditions for the oscillation of impulsive difference equation are obtained by using a nonimpulsive inequality.

Nonexistence and Existence Results for a Fourth-Order p-Laplacian Discrete Mixed Boundary Value Problem

In this paper, a fourth-order nonlinear p-Laplacian difference equation is considered. Using the critical point theory, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for mixed boundary value problem and give some new results. Recent results in the literature are generalized and significantly complemented.

New Oscillation Criteria for Third-Order Nonlinear Mixed Neutral Difference Equations

Some new oscillation criteria are established for a third-order nonlinear mixed neutral difference equation. Our results improve and extend some known results in the literature. Several examples are given to illustrate the importance of the results.

Stability in nonlinear neutral difference equations

In this paper we use fixed point method to prove asymptotic stability results of the zero solution of a nonlinear neutral difference equation with variable delay. An asymptotic stability theorem with a sufficient condition is proved, which improves and generalizes some results due to Raffoul (J Math Anal Appl 324:1356–1362 2006), Yankson (Electron J Qual Theory Differ Equ 8:1–7 2009), Jin and Luo (Georgian Math J 16:683–691 2009) and Chen (A fixed point approach towards stability of delay differential equations with applications to neural networks 2013).

Estimation on Unknown Function of a Class of Generalized Nonlinear Volterra-Fredholm Type Difference Inequality

The main objective of this paper is to establish a class of new nonlinear Volterra-Fredholm type difference inequality. Upper bound estimations of unknown functions are given by technique of change of variable, amplification method, difference and summation and inverse function. The derived results can be applied in the study of solutions of Volterra-Fredholm type difference equations.