EXPLORING SOME NEW IDEAS ON SMARANDACHE TYPE SETS, FUNCTIONS AND SEQUENCES

In this article I have defined a number of SMARANDACHE type sets ,sequences which I found very interesting. The problems and conjectures proposed would give food for thought and would pave ways for more work in this field

SOME MORE IDEAS ON SMARANDACHE FACTOR PARTITIONS

We define here the SMARANDACHE FACTOR PARTITION FUNCTION (SFP)

Calculation of sidewall boundary-layer parameters from rake measurements for the Langley 0.3-meter transonic cryogenic tunnel

Correction of airfoil data for sidewall boundary-layer effects requires a knowledge of the boundary-layer displacement thickness and the shape factor with the tunnel empty. To facilitate calculation of these quantities under various test conditions for the Langley 0.3 m Transonic Cryogenic Tunnel, a computer program was written. This program reads the various tunnel parameters and the boundary-layer rake total head pressure measurements directly from the Engineering Unit tapes to calculate the required sidewall boundary-layer parameters. Details of the method along with the results for a sample case are presented

Modifications to Langley 0.3-m TCT adaptive wall software for heavy gas test medium, phase 1 studies

The scheme for two-dimensional wall adaptation with sulfur hexafluoride (SF6) as test gas in the NASA Langley Research Center 0.3-m Transonic Cryogenic Tunnel (0.3-m TCT) is presented. A unified version of the wall adaptation software has been developed to function in a dual gas operation mode (nitrogen or SF6). The feature of ideal gas calculations for nitrogen operation is retained. For SF6 operation, real gas properties have been computed using the departure function technique. Installation of the software on the 0.3-m TCT ModComp-A computer and preliminary validation with nitrogen operation were found to be satisfactory. Further validation and improvements to the software will be undertaken when the 0.3-m TCT is ready for operation with SF6 gas

Corrections for attached sidewall boundary-layer effects in 2-dimensional airfoil testing

The problems of sidewall boundary-layer effects in airfoil testing is treated by considering the changes in the flow area due to boundary-layer thinning under the influence of the airfoil flowfield. Using von Karman's momentum integral equation, it is shown that the sidewall boundary-layer thickness in the region of the airfoil can reduce to about half the undisturbed value under the conditions prevailing in testing of supercritical airfoils. A Mach number correction due to this increased width of the flow passage is proposed. Using the small disturbance approximation, the effect of the sidewall boundary-layers is shown to be equivalent to a change in the test Mach number and also in the airfoil thickness. Comparison of the results of this approach with other similarity rules and correlation of the experimental data demonstrate the applicability of the analysis presented from low speeds to transonic speeds

Moonshine in Fivebrane Spacetimes

We consider type II superstring theory on $K3 \times S^1 \times \mathbb{R}^{1,4}$ and study perturbative BPS states in the near-horizon background of two Neveu-Schwarz fivebranes whose world-volume wraps the $K3 \times S^1$ factor. These states are counted by the spacetime helicity supertrace $\chi_2(\tau)$ which we evaluate. We find a simple expression for $\chi_2(\tau)$ in terms of the completion of the mock modular form $H^{(2)}(\tau)$ that has appeared recently in studies of the decomposition of the elliptic genus of K3 surfaces into characters of the N=4 superconformal algebra and which manifests a moonshine connection to the Mathieu group $M_{24}$.Comment: 32 page