scholarly journals A generalized nonlinear sums-difference inequality and its applications

2018 ◽  
pp. 77-94
Author(s):  
Zi un Li
Keyword(s):  
Difference Inequality

scholarly journals ON FINITE DIFFERENCE INEQUALITY OF LYAPUNOV TYPE

1992 ◽  
Vol 23 (3) ◽  
pp. 213-221
Author(s):  
GOU-SHENG YANG ◽  
SHIOW-FU HUANG
Keyword(s):  
Finite Difference ◽  
Difference Inequality

ON FINITE DIFFERENCE INEQUALITY OF LYAPUNOV TYPE

A Class of Singular Volterra-Fredholm Type Difference Inequality in Engineering

2014 ◽  
Vol 571-572 ◽  
pp. 132-138
Author(s):  
Wu Sheng Wang ◽  
Chun Miao Huang
Keyword(s):  
Beta Function ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Jensen Inequality ◽  
Fredholm Type ◽  
Difference Inequality ◽  
Amplification Method ◽  
Change Of Variable ◽  
Explicit Bounds ◽  
The Mean

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

All Bad Things Do Not Go Together: A Comment on Echeverri-Gent

2009 ◽  
Vol 42 (04) ◽  
pp. 639-643 ◽  
Author(s):  
Nicolas van de Walle
Keyword(s):  
Development Process ◽  
Task Force ◽  
Difference Inequality ◽  
The Core ◽  
International Inequality ◽  
Developing Societies

John Echeverri-Gent's (2009) fine article in this symposium makes a compelling case for a greater focus on the study of inequality by political scientists. A topic we have too often neglected, its dynamics go to the core of our disciplinary concerns and we clearly should have more to offer to its understanding. APSA is to be commended for supporting the work of the Task Force on Difference, Inequality, and Developing Societies (2008), which Echeverri-Gent led, and which, in large part, informs his article in these pages. It should generate a renewed focus by political scientists on international inequality and on the role of domestic inequality in the development process.

A Class of Nonlinear Singular Difference Inequality in Engineering

2014 ◽  
Vol 577 ◽  
pp. 824-827
Author(s):  
Wu Sheng Wang ◽  
Zong Yi Hou
Keyword(s):  
Mean Value ◽  
Mean Value Theorem ◽  
Jensen Inequality ◽  
Fractional Difference ◽  
Difference Inequality ◽  
Amplification Method ◽  
Weakly Singular ◽  
Change Of Variable ◽  
Explicit Bounds ◽  
The Mean

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.

Energy Decay of Global Solutions for a System of Petrovsky Equations

2013 ◽  
Vol 405-408 ◽  
pp. 3160-3164
Author(s):  
Yao Jun Ye
Keyword(s):  
Boundary Value Problem ◽  
Bounded Domain ◽  
Decay Estimate ◽  
Boundary Value ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Energy Decay ◽  
Difference Inequality ◽  
Initial Boundary Value

The initial-boundary value problem for a class of nonlinear Petrovsky systems in bounded domain is studied. We prove the energy decay estimate of global solutions through the use of a difference inequality.

scholarly journals Concentration Inequalities on the Multislice and for Sampling Without Replacement

2021 ◽  
Author(s):  
Holger Sambale ◽  
Arthur Sinulis
Keyword(s):  
Correction Factor ◽  
Convex Functions ◽  
Empirical Measure ◽  
Concentration Inequalities ◽  
Sobolev Inequalities ◽  
Kolmogorov Distance ◽  
Sampling Without Replacement ◽  
Difference Inequality ◽  
Finite Sampling ◽  
Multilinear Polynomials

AbstractWe present concentration inequalities on the multislice which are based on (modified) log-Sobolev inequalities. This includes bounds for convex functions and multilinear polynomials. As an application, we show concentration results for the triangle count in the G(n, M) Erdős–Rényi model resembling known bounds in the G(n, p) case. Moreover, we give a proof of Talagrand’s convex distance inequality for the multislice. Interpreting the multislice in a sampling without replacement context, we furthermore present concentration results for n out of N sampling without replacement. Based on a bounded difference inequality involving the finite-sampling correction factor $$1 - (n / N)$$ 1 - ( n / N ) , we present an easy proof of Serfling’s inequality with a slightly worse factor in the exponent, as well as a sub-Gaussian right tail for the Kolmogorov distance between the empirical measure and the true distribution of the sample.

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