Sharif Digital Repository

In this thesis, it has been introduced Hardy inequality and it’s extends. The fractional Hardy inequality for Ω ⊆ Rn and f ∈ C ∞ (Ω) is:1f (x) − f ( y)2∫α +n2dx dy ≥ kn,α ∫f (x)dx( )αΩ×Ωx − yΩ M α x In this thesis we are going to introduce the fractional and derivative forms of Hardy inequality then the Hardy inequality will be proved to fractional form on Euclidean and Hyperbolic domains, and finally we will get right into Hardy inequality with remainder.
 

Quantum correlations are among most intriguing problems in physics. Bell’s inequality which was proved in 1964 provides with us the possibility of comparing the predictions of quantum theory with what an underlying local realistic theory may reproduce for some given observables in correlated states. The violation of Bell’s inequality in practice prohibits the existance of such underlying theories. Yet, it is not clear which of the assumption, i.e., locality or reality is responsible for explaining the experimentally verified violations. In 2003, a Nobel prizewinner A. J. Leggett proved a new inequality in which the locality assumption was not crucial. Here, we explore different aspects of... 

This study examins effects of trade liberalization on the wage inequality across industries and between genders within these industries by utilizing the data of micro-level Households’ Income and Expenditures surveys and trade statistics over 2001-2011. The analysis is carried based on the Heckscher–Ohlin’s theory in international trade and Baker’s taste discrimination theory at firms. We use Quantile regression and ordinary least squares (OLS) to consider the wage discrimination across entire distribution wage distribution and at wages mean as well. The results of Blinder-Oaxaca decomposition approach (inequality at mean wage) and Machado and Mata’s model (inequality of wage at entire... 

The ratio of the two first non-trivial Dirichlet eigenvalues is the subject of the Payne-Polya-Weinburger Conjecture and Inequality. The PPW Conjecture was proven by M. Ashbaugh and R. Benguria. Ashbaugh and Benguria later proved a similar result for domains on the n-sphere. On the other hand, discrete counterparts of universal inequalities from (continuous) have been studied in the graph theory setting. This thesis surveys results related to the PPW inequality on graphs  

One of the most common problems encountered in multivariable systems is the interactions between the system inputs and outputs. Interaction causes difficulties in control of these systems. Hence reduction of interaction in multivariable systems is an important design objective. One way to do this is to employ a pre-compensator in the open loop systems. Several approaches with different design methods and optimization criterions have been proposed thus far. In this study the problem of interaction reduction for a square stable system is considered and a pre-compensator matrix is designed which reduces interactions in the interacting multivariable system.In this case the purpose is to use... 

Quantum Mechanics, as the most famous physical theory was founded about 85 years ago; but still there are a lot of debates about its interpretation. In this work, we review some basic concepts of Quantum Mechanics in form of questions about uncertainty principle, measurement problem and complementarily. We also review Bell inequality which has great philosophical and recently technological results. Bell derived his inequality regardless of modeling the measuring apparatus; we show, by take a realistic model for measuring apparatus, Bell inequality would be deduced. Finally we review a mathematical language which was used to show the duality of wave and particle. Quantum...