Journal of Advances in Mathematics and Computer Science

In this paper we calculate the Witt groups of P¹. It's a known result, but we calculate it by another method: we use the localisation theorem of Balmer and the excision theorem of S. Gille.

In this paper, we shall continue a study of the CS-recovery of signals studied in [1]. Under the assumption that a m × n matrix A obeys the RIP of order s we decompose the space of unknown vectors into sets M₀; M₁; · · · ;M₇ de ned by a bias function p_x on a good location T₀ = {1; 2; · · · ; s} and research a good condition of CS-recovery.

Bernstein operators constitute a powerful tool allowing one to replace many inconvenient calculations performed for continuous functions by more friendly calculations on approximating polynomials. In this note we study a modi cation of Bernstein type operators and prove in particular that they satisfy Voronovskaya type theorems.

Aims: To propose a new chaff generation method and to compare the results with the standard Clancy’s Chaff Generation Method.

Place and Duration of Study: Department of Computer Science and Engineering, PEC University of Technology, Chandigarh during July 2012 and June 2013.

Methodology: Two databases are used to calculate the results. One is the FVC 2004-DB1 database which is approved by fingerprint recognition website. Other is the live database created using the Crossmatch’s Verifier 300 LC scanner. In both the databases 100 images of 10 different persons were compared with each other and performances are computed and compared.

Results: Results show that proposed algorithm takes less time to generate different number of chaff points (from 50 to 500) than Clancy’s algorithm. The performance metrics like Genuine Accept Ratio, False Accept Ratio and False Reject Ratio have same values of both the algorithms. Results are computed on both the databases.

Conclusion: Experiments results show that the proposed algorithm is faster than the Clancy’s algorithm in generating equal number of chaff points.

Our aim in the present article is to introduce and study a new type of chaotic graphs, namely chaotic graph on a sphere .We describe them by using chaotic matrices. This article introduces some operations on the chaotic graphs such as union and intersection; also both of the chaotic incidence matrices and the chaotic adjacency matrices representing the chaotic graphs induced from these operations will be introduced. Theorems governing these studies are obtained. Some applications on chaotic graphs are given.

This paper presents a fourth-order nonlinear conjugate gradient method in equality constrained optimization. The idea is to transform the constrained problem into unconstrained type through the Lagrange multipliers scheme. Using four terms of Taylor series development, we approximate the transformed function (augmented Lagrange function). Lastly, we employ the new fourth-order nonlinear conjugate gradient method in equality constrained optimization to solve the optimization problem. We present the algorithm in steps and some properties of the gradients are proved, using classical results. Also, the convergence analysis has been proved under classical and known assumptions. Furthermore, we present the obtained numerical results and compare them to some existing results. The analysis of results confirms that the new method is accurate.

The choice of quantization method and the requirement to achieve a trade-off between compressed image quality and degradation are very crucial in the overall performance of a lossy image compression algorithm. In this paper, uniform and non-uniform scalar quantization schemes of biometric fingerprint image were studied. Comparative analyses of non-uniform quantization methods were also conducted and these include dither-based quantization and the Lloyd-Max quantization methods.  The quality of the quantized output fingerprint image was determined in terms of Signal-to-Quantization Noise Ratio (SQNR). The degree of distortion or quantization error was determined in terms of the Mean Square Quantization Error (MSQE). The non-uniform quantization method performed better than the uniform quantization method in terms of the SQNR and MSQE values. It was also found out that, the performance of dither-based non-uniform quantization on biometric fingerprint image is not as efficient as the Lloyd-Max approach when the number of bits used in the quantization process increased. The results showed that the higher the number of bits used in the quantization process the higher the quality and the less the distortion in the resulting images.