Nabla Discrete fractional Calculus and Nabla Inequalities

Here we define a Caputo like discrete nabla fractional difference and we produce discrete nabla fractional Taylor formulae for the first time. We estimate their remaiders. Then we derive related discrete nabla fractional Opial, Ostrowski, Poincare and Sobolev type inequalities

Soliton X-junctions with controllable transmission

We propose new planar X-junctions and multi-port devices written by spatial solitons, which are composed of two (or more) nonlinearly coupled components in Kerr-type media. Such devices have no radiation losses at a given wavelength. We demonstrate that, for the same relative angle between the channels of the X-junctions, one can vary the transmission coefficients into the output channels by adjusting the polarizations of multi-component solitons. We determine analytically the transmission properties and suggest two types of experimental embodiments of the proposed device.Comment: 3 pages, 2 figure

Ostrowski Type Inequalities over Spherical Shells

2000 Mathematics Subject Classification: 26D10, 26D15.Here are presented Ostrowski type inequalities over spherical shells. These regard sharp or close to sharp estimates to the difference of the average of a multivariate function from its value at a point

Representations and Ostrowski type inequalities on time scales

AbstractHere, we give univariate and multivariate representations of the Montgomery type for hybrid functions on time scales. Based on these, we establish univariate and multivariate Ostrowski type inequalities on time scales domains. These compare the average of a function to its values. The estimates involve the higher order delta and nabla derivatives and partial derivatives. We finish with applications on the time scales R and Z

On a discrete Korovkin theorem

AbstractIn [G. A. Anastassiou, A discrete Korovkin theorem, J. Approx. Theory 45 (1985), pp. 383–388, Theorem 3], a discrete Korovkin theorem was given. We restate the theorem here and its proof, correcting a mistake in the above reference

Are Tax Incentive Provisions Always Operative? Evidence From The Greek Manufacturing Industry

Tax incentives have been provided in many countries with the ultimate goal of making the cost of capital cheaper and thus enabling the development process through the increase of investment expenditures. The study of the role of tax incentives in investment spending has been made possible through the use of the neoclassical theory of optimum capital accumulation. This theory has been used in this article to indicate that incentive provisions may not always be operative at the margin, and thus having no effect in  the formulation of the value of depreciation allowances and further on the value of the implicit rental price of capital. Variations in the value of the user cost of capital can make an investment project cheaper or more expensive in relation to various time periods. This could not be proved for the case of Greece