Improved S/N meter

Signal-to-noise ratios /S/N/ meter containing a variable-frequency notch filter measures noise plus interference in the presence of carrier or modulation signals. A noise source and calibration signal source are included in the instrument for calibration purposes

Classical pattern distributions in Sn(132)\mathcal{S}_{n}(132) and Sn(123)\mathcal{S}_{n}(123)

Classical pattern avoidance and occurrence are well studied in the symmetric group $\mathcal{S}_{n}$. In this paper, we provide explicit recurrence relations to the generating functions counting the number of classical pattern occurrence in the set of 132-avoiding permutations and the set of 123-avoiding permutations.Comment: 23 pages, 5 fugure

The Florentin Smarandache Function S(n)

A program SMARAND has been designed to generate S(n) up to a preset limit N (N up to 1000000 has been used in some applications)

Bubbling 1/4 BPS solutions in type IIB and supergravity reductions on S^n x S^n

We extend the construction of bubbling 1/2 BPS solutions of Lin, Lunin and Maldacena (hep-th/0409174) in two directions. First we enquire whether bubbling 1/2 BPS solutions can be constructed in minimal 6d supergravity and second we construct solutions that are 1/4 BPS in type IIB. We find that the S^1 x S^1 bosonic reduction of (1,0) 6d supergravity to 4d gravity coupled to 2 scalars and a gauge field is consistent only provided that the gauge field obeys a constraint (F \wedge F=0). This is to be contrasted to the case of the S^3 x S^3 bosonic reduction of type IIB supergravity to 4d gravity, 2 scalars and a gauge field, where consistency is achieved without imposing any such constraints. Therefore, in the case of (1,0) 6d supergravity we are able to construct 1/2 BPS solutions, similar to those derived in type IIB, provided that this additional constraint is satisfied. This ultimately prohibits the construction of a family of 1/2 BPS solutions corresponding to a bubbling AdS_3 x S^3 geometry. Returning to type IIB solutions, by turning on an axion-dilaton field we construct a family of bubbling 1/4 BPS solutions. This corresponds to the inclusion of back-reacted D7 branes to the solutions of Lin, Lunin and Maldacena.Comment: 30 pages, Latex citations adde