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

Noninvasive depth estimation using tissue optical properties and a dual-wavelength fluorescent molecular probe in vivo

Translation of fluorescence imaging using molecularly targeted imaging agents for real-time assessment of surgical margins in the operating room requires a fast and reliable method to predict tumor depth from planar optical imaging. Here, we developed a dual-wavelength fluorescent molecular probe with distinct visible and near-infrared excitation and emission spectra for depth estimation in mice and a method to predict the optical properties of the imaging medium such that the technique is applicable to a range of medium types. Imaging was conducted at two wavelengths in a simulated blood vessel and an in vivo tumor model. Although the depth estimation method was insensitive to changes in the molecular probe concentration, it was responsive to the optical parameters of the medium. Results of the intra-tumor fluorescent probe injection showed that the average measured tumor sub-surface depths were 1.31 ± 0.442 mm, 1.07 ± 0.187 mm, and 1.42 ± 0.182 mm, and the average estimated sub-surface depths were 0.97 ± 0.308 mm, 1.11 ± 0.428 mm, 1.21 ± 0.492 mm, respectively. Intravenous injection of the molecular probe allowed for selective tumor accumulation, with measured tumor sub-surface depths of 1.28 ± 0.168 mm, and 1.50 ± 0.394 mm, and the estimated depths were 1.46 ± 0.314 mm, and 1.60 ± 0.409 mm, respectively. Expansion of our technique by using material optical properties and mouse skin optical parameters to estimate the sub-surface depth of a tumor demonstrated an agreement between measured and estimated depth within 0.38 mm and 0.63 mm for intra-tumor and intravenous dye injections, respectively. Our results demonstrate the feasibility of dual-wavelength imaging for determining the depth of blood vessels and characterizing the sub-surface depth of tumors in vivo

Nonequilibrium tricriticality in one dimension

We show the existence of a nonequilibrium tricritical point induced by a repulsive interaction in one dimensional asymmetric exclusion process. The tricritical point is associated with the particle-hole symmetry breaking introduced by the repulsion. The phase diagram and the crossover in the neighbourhood of the tricritical point for the shock formation at one of the boundaries are determined.Comment: 6 pages; 4 figure

TYPE II DNA: when the interfacial energy becomes negative

An important step in transcription of a DNA base sequence to a protein is the initiation from the exact starting point, called promoter region. We propose a physical mechanism for identification of the promoter region, which relies on a new classification of DNAs into two types, Type-I and Type-II, like superconductors, depending on the sign of the energy of the interface separating the zipped and the unzipped phases. This is determined by the energies of helical ordering and stretching over two independent length scales. The negative interfacial energy in Type II DNA leads to domains of helically ordered state separated by defect regions, or blobs, enclosed by the interfaces. The defect blobs, pinned by non-coding promoter regions, would be physically distinct from all other types of bubbles. We also show that the order of the melting transition under a force is different for Type I and Type II.Comment: 4 pages, 2 figures, Eq.(4) corrected in 4th versio