Abstract:
In hep-th/0111281 the complete set of eigenvectors and eigenvalues of Neumann matrices was found. It was shown also that the spectral density contains a divergent constant piece that being regulated by truncation at level L equals (log L)/(2\pi). In this paper we find an exact analytic expression for the finite part of the spectral density. This function allows one to calculate finite parts of various determinants arising in string field theory computations. We put our result to some consistency checks.

Abstract:
Imaging with sub-wavelength resolution using a lens formed by periodic metal-dielectric layered structure is demonstrated. The lens operates in canalization regime as a transmission device and it does not involve negative refraction and amplification of evanescent modes. The thickness of the lens have to be an integer number of half-wavelengths and can be made as large as required for ceratin applications, in contrast to the other sub-wavelength lenses formed by metallic slabs which have to be much smaller than the wavelength. Resolution of $\lambda/20$ at 600 nm wavelength is confirmed by numerical simulation for a 300 nm thick structure formed by a periodic stack of 10 nm layers of glass with $\epsilon=2$ and 5 nm layers of metal-dielectric composite with $\epsilon=-1$. Resolution of $\lambda/60$ is predicted for a structure with same thickness, period and operating frequency, but formed by 7.76 nm layers of silicon with $\epsilon=15$ and 7.24 nm layers of silver with $\epsilon=-14$.

Abstract:
In the annihilation of a positron with a bound atomic electron, the virtual gamma photon created may excite the atomic nucleus. We put forward this effect as a spectroscopic tool for an energy-selective excitation of nuclear transitions. This scheme can efficiently populate nuclear levels of arbitrary multipolarities in the MeV regime, including monopole transitions and giant resonances. In certain cases, it may have a higher cross sections than the conventionally used Coulomb excitation.

Abstract:
We reveal extraordinary electromagnetic properties for a general class of uniaxially polarizable media. Depending on parameters, such metamaterials may have wide range of nontrivial shapes of isofrequency contours including lemniscate, diamond and multiply connected curves with connectivity number reaching five. The possibility of the dispersion engineering paves a way to more flexible manipulation of electromagnetic waves. Employing first-principle considerations we prove that uniaxially polarizable media should be described in terms of the nonlocal permittivity tensor which by no means can be reduced to local permittivity and permeability even in the long-wavelength limit. We introduce an alternative set of local material parameters including quadrupole susceptibility capable to capture all of the second-order spatial dispersion effects.

Abstract:
Let $W$ be an infinite word over finite alphabet $A$. We get combinatorial criteria of existence of interval exchange transformations that generate the word W.

Abstract:
Let us call subdivision {\it good}, if 1) set corresponding to each symbol is convex (i.e. interval or (semi)closed interval). 2) If points $A$ and $B$ corresponds to the some color and interval $(A,B)$ has discontinuity point, then $f(A)$ and $f(B)$ has different color. Every subdivision can be further divided into good subdivision, old superword can be obtained from new one by gluing letters. Hence in the section ``Equivalence of the set of uniformly recurrent words generated by piecewise-continuous transformation to the set of words generated by interval exchange transformation'' one can consider only good subdivision.

Abstract:
Double-antennas EHF AM transceiver measuring system (TRX MS) for to measure signals scattered by objects, when the system is situated in its near-field zone, is briefly described. Physical Optic (PO) simulation of the radar system and experimental measuring of signals scattered by the conductive sphere of 30 wavelengths diameter, which were measured in distances to the sphere from ~ 10 up to 2000 wavelengths are presented and discussed.

Abstract:
Evanescent wave amplification is observed, for the first time to our knowledge, inside a half-wavelength-thick wire medium slab used for subwavelength imaging. The wire medium is analyzed using both a spatially dispersive finite-difference time-domain (FDTD) method and a full-wave commercial electromagnetic simulator CST Microwave Studio. In this work we demonstrate that subwavelength details of a source placed at a distance of one-tenth of a wavelength from a wire medium slab can be detected inside the slab with a resolution of approximately one-tenth of a wavelength in spite of the fact that they cannot be resolved at the front interface of the device, due to the rapid decay of evanescent spatial harmonics in free space.