Related Experiment Video
Updated: Jan 28, 2026
08:13
Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects
Published on: May 10, 2019
6.8K
Generalized nonlinear weakly singular retarded integral inequalities with maxima and their applications
Yong Yan1, Derong Zhou2, Jianglin Zhao1
1School of Science and Technology, Sichuan Minzu College, Kangding, P.R. China.
Journal of Inequalities and Applications
|March 7, 2019
Summary
This study presents a new integral inequality for nonlinear equations with unknown functions. The findings help prove the uniqueness of solutions for specific singular integral equations.
Area of Science:
- Mathematical Analysis
- Integral Equations
- Nonlinear Analysis
Background:
- Integral inequalities are fundamental in analyzing differential and integral equations.
- Generalized Wendroff-type inequalities are crucial for establishing bounds on unknown functions.
- Singular integral equations with maxima present unique analytical challenges.
Purpose of the Study:
- To establish a novel generalized nonlinear weakly singular retarded Wendroff-type integral inequality.
- To develop a method for estimating the boundedness of unknown functions in these inequalities.
- To demonstrate the utility of the new inequality in weakening conditions for existing results and proving solution uniqueness.
Main Methods:
- A monotonization technique is employed, specifically avoiding separability and monotonicity of given functions.
- The technique is applied to estimate the boundedness of unknown functions within the inequality.
- The derived inequality is then utilized to analyze singular integral equations.
Main Results:
- A new generalized nonlinear weakly singular retarded Wendroff-type integral inequality is established.
- The monotonization technique effectively estimates the boundedness of unknown functions.
- The results provide a means to relax conditions in prior research concerning integral inequalities.
Conclusions:
- The developed integral inequality offers a valuable tool for the analysis of nonlinear equations.
- The findings contribute to the theoretical understanding of singular integral equations with maxima.
- The research potentially broadens the applicability of existing analytical techniques.
Related Concept Videos
03:21Weak Base Solutions
25.1K
Some compounds produce hydroxide ions when dissolved by chemically reacting with water molecules. In all cases, these compounds react only partially and so are classified as weak bases. These types of compounds are also abundant in nature and important commodities in various technologies. For example, global production of the weak base ammonia is typically well over 100 metric tons annually, being widely used as an agricultural fertilizer, a raw material for chemical synthesis of other...
25.1K
01:19Retarders
264
Retarders are chemical admixtures designed to extend the setting time, which is especially useful when there is a delay in sequential concrete pours to prevent cold joints and to achieve a cohesive structure. Retarders, when used in appropriate amounts, can also enhance the architectural appearance of exposed aggregate finishes.
The function of retarders is to delay the setting of concrete, and this effect can be measured using a penetration test. The retardation process involves adding...
The function of retarders is to delay the setting of concrete, and this effect can be measured using a penetration test. The retardation process involves adding...
264
04:02Weak Acid Solutions
43.0K
Few compounds act as strong acids. A far greater number of compounds behave as weak acids and only partially react with water, leaving a large majority of dissolved molecules in their original form and generating a relatively small amount of hydronium ions. Weak acids are commonly encountered in nature, being the substances partly responsible for the tangy taste of citrus fruits, the stinging sensation of insect bites, and the unpleasant smells associated with body odor. A familiar example of a...
43.0K
01:30Application of Integration: Problem Solving
92
The process of breathing involves the periodic intake and expulsion of air, known as the respiratory cycle, which typically lasts about five seconds. Modeling the volume of air inhaled into the lungs as a function of time provides insight into both the dynamics and efficiency of pulmonary ventilation. This volume is determined by integrating the airflow rate over time, which captures the cumulative effect of air entering the lungs.Sinusoidal Model of AirflowAirflow during respiration is not...
92
01:26Singularity Functions for Shear
440
In structural analysis, singularity functions are crucial in simplifying the representation of shear forces in beams under discontinuous loading. These functions describe discontinuous variations in shear force across a beam with varying loads by using a single mathematical expression, regardless of the complexity of the loading conditions. The singularity functions are derived from creating a free-body diagram of the beam and then making conceptual cuts at specific points to examine the...
440
01:22Nonlinear Pharmacokinetics: Causes of Nonlinearity
718
Nonlinearity in drug pharmacokinetics is caused by various factors influencing how a drug is absorbed, distributed, metabolized, and excreted. Understanding these nonlinear processes is crucial for predicting drug behavior in the body and optimizing drug dosing regimens.
Nonlinear drug absorption can occur when the process is rate-limited by solubility, carrier-mediated transport systems, or saturation of the presystemic gut wall or hepatic metabolism. For instance, high doses of riboflavin...
Nonlinear drug absorption can occur when the process is rate-limited by solubility, carrier-mediated transport systems, or saturation of the presystemic gut wall or hepatic metabolism. For instance, high doses of riboflavin...
718