Linear and Nonlinear Discrete Inequalities in n Independent Variables

1987 ◽  
pp. 303-318 ◽  
Author(s):  
Ravi P. Agarwal
Keyword(s):  
Independent Variables ◽  
Discrete Inequalities ◽  
Linear And Nonlinear

scholarly journals Some New Volterra-Fredholm-Type Discrete Inequalities and Their Applications in the Theory of Difference Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-24 ◽  
Author(s):  
Bin Zheng ◽  
Qinghua Feng
Keyword(s):  
Difference Equations ◽  
Fredholm Type ◽  
Qualitative And Quantitative ◽  
Independent Variables ◽  
Discrete Inequalities ◽  
Quantitative Properties ◽  
Two Independent Variables

Some new Volterra-Fredholm-type discrete inequalities in two independent variables are established, which provide a handy tool in the study of qualitative and quantitative properties of solutions of certain difference equations. The established results extend some known results in the literature.

scholarly journals ON LIEB AND THIRRING TYPE DISCRETE INEQUALITIES

1991 ◽  
Vol 22 (2) ◽  
pp. 145-151
Author(s):  
B. G. PACHPATTE
Keyword(s):  
Independent Variables ◽  
Discrete Inequalities ◽  
Forward Differences

Discrete inequalities of the Lieb and Thirring type involving functions of several independent variables and their forward differences are established. The proofs given here are elementary and the results established provide new estimates on these types of inequalities.

Sharp discrete inequalities inn independent variables

1995 ◽  
Vol 72 (2-3) ◽  
pp. 97-112 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Peter Y.H. Pang
Keyword(s):  
Independent Variables ◽  
Discrete Inequalities

Comparison of Fisheries Control Systems That Utilize Catch and Effort Data

1979 ◽  
Vol 36 (12) ◽  
pp. 1477-1489 ◽  
Author(s):  
Ray Hilborn
Keyword(s):  
Control Systems ◽  
Data Series ◽  
Independent Variables ◽  
Simulation Techniques ◽  
Estimation Problems ◽  
Fisheries Regulation ◽  
Linear And Nonlinear ◽  
Catch Per Effort ◽  
Average Catch ◽  
Two Independent Variables

The relative merits of various methods for estimating the parameters of the Schaefer model from catch and effort data and of controlling the fishery are compared by simulation techniques. Estimation procedures compared are the linear and nonlinear methods for the discretized Schaefer model and Schnute's method for the continuous form of the Schaefer model. The control systems compared are feedback effort limitation, quota control for fixed escapement policies, and application of equilibrium effort. It is found that all estimation systems frequently fail to provide reasonable estimates of the Schaefer model and will produce poor catches, especially when managing long-lived, low productivity species. These estimation problems are most severe when the catch and effort data series begins after the stock has been heavily exploited. The failure of the estimation systems is primarily due to insufficient contrasts in the two independent variables of the multiple regression used for estimation, effort and catch per effort. The need for alternative policies that will explore the effort, catch per effort space is discussed. Application of the equilibrium effort may frequently be preferred to a fixed escapement policy; average catch may not be reduced, and variability in catch is much lower. Quota regulation is dangerous when the stock is heavily exploited and the biological parameters of the stock uncertain; at other times the quota method produces results comparable with effort limitation. Key words: Schaefer model, feedback control, catch and effort, fisheries regulation, adaptive control

scholarly journals DISCRETE POINCARE-TYPE INEQUALITIES

1998 ◽  
Vol 29 (2) ◽  
pp. 145-153
Author(s):  
WING-SUM CHEUNG
Keyword(s):  
Discrete Analogue ◽  
Integral Inequalities ◽  
Independent Variables ◽  
Type Integral ◽  
Discrete Inequalities ◽  
Poincaré Type Inequalities

In this paper some discrete analogue of Poincare-type integral inequalities involving many independent variables are established. These in turn can be used to serve as generators of other interesting discrete inequalities.

scholarly journals A Generalization of Linear and Nonlinear Retarded Integral Inequalities in Two Independent Variables

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Ying Jiang ◽  
Guojing Xing ◽  
Chenghui Zhang
Keyword(s):  
Integral Inequalities ◽  
Qualitative Properties ◽  
Analysis Techniques ◽  
Independent Variables ◽  
Amplification Method ◽  
Paper Work ◽  
Explicit Bounds ◽  
Linear And Nonlinear ◽  
Qualitative Properties Of Solutions ◽  
Two Independent Variables

Integral inequalities, which provide explicit bounds on unknown functions, are used to serve as handy tools in the study of the qualitative properties of solutions to differential and integral equations. By utilizing some analysis techniques, such as amplification method, differential, and integration, several new types of linear and nonlinear retarded integral inequalities in two independent variables are provided. These results generalize and complement previous ones. An illustrative example is given to support the obtained results. The study of the numerical example shows that the new results presented in this paper work well in the analysis of retarded integral inequalities in two independent variables.

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