Poisson distribution of a prime counting function corresponding to elliptic curves

Let $E$ be an elliptic curve defined over rational field $\mathbb{Q}$ and $N$ be a positive integer. Now, $M_E(N)$ denotes the number of primes $p$, such that the group $E_p(\mathbb{F}_p)$ is of order $N$. We show that $M_E(N)$ follows Poisson distribution when an average is taken over a large class of curves.Comment: 17 page

Upper Bounds for the Davenport Constant

We prove that for all but a certain number of abelian groups of order n its Davenport constant is atmost n/k+k-1 for k=1,2,..,7. For groups of order three we improve on the existing bound involving the Alon-Dubiner constant.Comment: article soumis, decembre 200

Mathematical Estimation of Logical Masking Capability of Majority/Minority Gates Used in Nanoelectronic Circuits

In nanoelectronic circuit synthesis, the majority gate and the inverter form the basic combinational logic primitives. This paper deduces the mathematical formulae to estimate the logical masking capability of majority gates, which are used extensively in nanoelectronic digital circuit synthesis. The mathematical formulae derived to evaluate the logical masking capability of majority gates holds well for minority gates, and a comparison with the logical masking capability of conventional gates such as NOT, AND/NAND, OR/NOR, and XOR/XNOR is provided. It is inferred from this research work that the logical masking capability of majority/minority gates is similar to that of XOR/XNOR gates, and with an increase of fan-in the logical masking capability of majority/minority gates also increases

Drag reduction effects in turbulent boundary layers over wavy walls

Two dimensional incompressible flow over wavy surfaces are analyzed numerically by spectral methods. Algorithms for periodic flows (Fourier modes in the periodic flow direction and Chebycheff modes in the normal direction), and inflow-outflow boundary conditions (Chebycheff modes used in both directions) are described. Results obtained using both codes are reported for laminar flows. Comparisons with known theoretical and experimental results are made

Analytical and numerical investigation of structural response of compliant wall materials

Surface motion of compliant walls in drag reduction experiments was analyzed. The spectrum of surface motion indicates that membranes over deep cavities respond at low frequencies and large wavelengths. The membrane over a deep cavity is therefore found not to yield the desired reponse predicted by the postulated mechanism. The membrane over a thin air gap is found to act as a wavelength chopper, and analysis of the nonlinear response of the compliant surface indicates its possible suitability for compliant wall experiments. Periodic structures are found to lock in the desired wavelengths of motion. Laminated structures are found to be very ineffective as compliant models, except when there is no bonding between the membrane and the backing. Computer programs developed for these analyses are documented

Analytical and design techniques for drag reduction studies on wavy surfaces

Numerical models for two dimensional turbulent boundary layers over wavy surfaces were investigated. Computations for wavy wall boundary layers indicate possibilities of overall drag reduction in a parameter range of the geometry of the wall. The correction technique using integral methods for analyzing arbitrary surfaces was found to be unsuitable for some cases of interest in drag reduction; a Navier-Stokes solver for wavy walls was built to test these problems. Test results of the Navier-Stokes solver indicate that the solution techniques are accurate enough to handle complex geometries and steep variations in fluid properties