In this paper, we prove that the solvability of dynamic equations of second order is sufficient for the validity of some Hardy and Opial type inequalities with two different weights on time scales. In particular, the results give new characterizations of two different weights in inequalities containing Hardy and Opial operators. The main contribution in this paper is the characterizations of weights in discrete inequalities that will be formulated from our results as special cases.

In this paper, we employ some algebraic equations due to Hardy and Littlewood to establish some conditions on weights in dynamic inequalities of Hardy and Copson type. For illustrations, we derive some dynamic inequalities of Wirtinger, Copson and Hardy types and formulate the classical integral and discrete inequalities with sharp constants as particular cases. The results improve some results obtained in the literature.

In this paper, we prove some new Opial-type dynamic inequalities on time scales. Our results are obtained in frame of convexity property and by using the chain rule and Jensen and Hölder inequalities. For illustration purpose, we obtain some particular Opial-type inequalities reported in the literature.

In this article, we develop a 1-D traveltime tomography method to calculate the seismic Pwave velocity of a medium. We use the results of 1-D tomography to obtain linear inhomogeneity parameters in a specific layer. To get the trustworthiness of the method, we perform several synthetic experiments. We show that the inverted model parameters are reasonably accurate and stable. To examine the results of linear inhomogeneity parameters using a different method, we also develop an inversion method based on a two-parameter velocity model. Finally, we apply both the methods to Vertical Seismic Profile (VSP) data and do a study comparing their results.

The paper explains the essence of derivatives and identifies the different types of that exist. The article examines the technologies of credit derivatives application in the financial markets, especially the most common ones, credit default swaps. Both positive and negative aspects of their application to risk management have been revealed. Moreover, the grounds for their considering to be responsible for the global crisis aggravation have been identified. The prospects of CDS utilization in the development of a new global financial order have been illustrated. The paper briefly explains how derivative activity level can be monitored and then takes a look at the benefits, risks and opportunities of derivative in Bangladesh.