Some Paranormed Difference Sequence Spaces of Order mm Derived by Generalized Means and Compact Operators

We have introduced a new sequence space $l(r, s, t, p ;\Delta^{(m)})$ combining by using generalized means and difference operator of order $m$. We have shown that the space $l(r, s, t, p ;\Delta^{(m)})$ is complete under some suitable paranorm and it has Schauder basis. Furthermore, the $\alpha$-, $\beta$-, $\gamma$- duals of this space is computed and also obtained necessary and sufficient conditions for some matrix transformations from $l(r, s, t, p; \Delta^{(m)})$ to $l_{\infty}, l_1$. Finally, we obtained some identities or estimates for the operator norms and the Hausdorff measure of noncompactness of some matrix operators on the BK space $l_{p}(r, s, t ;\Delta^{(m)})$ by applying the Hausdorff measure of noncompactness.Comment: Please withdraw this paper as there are some logical gap in some results. 20 pages. arXiv admin note: substantial text overlap with arXiv:1307.5883, arXiv:1307.5817, arXiv:1307.588

Relating transverse structure of various parton distributions

We present the results of T-even TMDs in a light front quark-diquark model of nucleons with the wave functions constructed from the soft-wall AdS/QCD prediction. The relations amongst TMDs are discussed. The $p_\perp$ dependence of the TMDs are compared with the $t$-dependence of the GPDs. AdS/QCD wave function provides an explanation behind the approximate $x$ and $p_\perp$ factorization observed in lattice TMD calculations.Comment: 11 pages, 8 figures, modified extensively, added new results and discusssion

Dynamic phase transition in the conversion of B-DNA to Z-DNA

The long time dynamics of the conformational transition from B-DNA to Z-DNA is shown to undergo a dynamic phase transition. We obtained the dynamic phase diagram for the stability of the front separating B and Z. The instability in this front results in two split fronts moving with different velocities. Hence, depending on the system parameters a denatured state may develop dynamically eventhough it is thermodynamically forbidden. This resolves the current controversies on the transition mechanism of the B-DNA to Z-DNA.Comment: 5 pages, 4 figures. New version with correction of typos, new references, minor modifications in Fig 2, 3. To appear in EP

Phenomenological features of turbulent hydrodynamics in sparsely vegetated open channel flow

YesThe present study investigates the turbulent hydrodynamics in an open channel flow with an emergent and sparse vegetation patch placed in the middle of the channel. The dimensions of the rigid vegetation patch are 81 cm long and 24 cm wide and it is prepared by a 7× 10 array of uniform acrylic cylinders by maintaining 9 cm and 4 cm spacing between centers of two consecutive cylinders along streamwise and lateral directions respectively. From the leading edge of the patch, the observed nature of time averaged flow velocities along streamwise, lateral and vertical directions is not consistent up to half length of the patch; however the velocity profiles develop a uniform behavior after that length. In the interior of the patch, the magnitude of vertical normal stress is small in comparison to the magnitudes of streamwise and lateral normal stresses. The magnitude of Reynolds shear stress profiles decreases with increasing downstream length from the leading edge of the vegetation patch and the trend continues even in the wake region downstream of the trailing edge. The increased magnitude of turbulent kinetic energy profiles is noticed from leading edge up to a certain length inside the patch; however its value decreases with further increasing downstream distance. A new mathematical model is proposed to predict time averaged streamwise velocity inside the sparse vegetation patch and the proposed model shows good agreement with the experimental data.Debasish Pal received financial assistance from SRIC Project of IIT Kharagpur (Project code: FVP