Structure analysis of single- and multi-frequency subspace migrations in inverse scattering problems

In this literature, we carefully investigate the structure of single- and multi-frequency imaging functions, that are usually employed in inverse scattering problems. Based on patterns of the singular vectors of the Multi-Static Response (MSR) matrix, we establish a relationship between imaging functions and the Bessel function. This relationship indicates certain properties of imaging functions and the reason behind enhancement in the imaging performance by multiple frequencies. Several numerical simulations with a large amount of noisy data are performed in order to support our investigation.Comment: 11 pages, 10 figure

On the anomaly of nonlocal symmetry in the chiral QED

We show that the anomaly of nonlocal symmetry can be canceled by the well-known Wess-Zumino acton which cancels the gauge anomaly in the two-dimensional chiral electrodynamics.Comment: 4 pages, latex, no figure

Entropy in the Kerr-Newman Black Hole

Entropy of the Kerr-Newman black hole is calculated via the brick wall method with maintaining careful attention to the contribution of superradiant scalar modes. It turns out that the nonsuperradinat and superradiant modes simultaneously contribute to the entropy with the same order in terms of the brick wall cutoff $\epsilon$. In particular, the contribution of the superradiant modes to the entropy is negative. To avoid divergency in this method when the angular velocity tends to zero, we propose to intr oduce a lower bound of angular velocity and to treat the case of the angular momentum per unit mass $a=0$ separately. Moreover, from the lower bound of the angular velocity, we obtain the $\theta$-dependence structure of the brick wall cutoff, which natu rally requires an angular cutoff $\delta$. Finally, if the cutoff values, $\epsilon$ and $\delta$, satisfy a proper relation between them, the resulting entropy satisfies the area law.Comment: 16 pages, Latex, no figures, References are included, Subsection A and B are reduced to subsection A, Abstract is rewritten, Minor corrections are include

Nanotechnology for Early Cancer Detection

Vast numbers of studies and developments in the nanotechnology area have been conducted and many nanomaterials have been utilized to detect cancers at early stages. Nanomaterials have unique physical, optical and electrical properties that have proven to be very useful in sensing. Quantum dots, gold nanoparticles, magnetic nanoparticles, carbon nanotubes, gold nanowires and many other materials have been developed over the years, alongside the discovery of a wide range of biomarkers to lower the detection limit of cancer biomarkers. Proteins, antibody fragments, DNA fragments, and RNA fragments are the base of cancer biomarkers and have been used as targets in cancer detection and monitoring. It is highly anticipated that in the near future, we might be able to detect cancer at a very early stage, providing a much higher chance of treatment