Modern Scientific Press

ABSTRACT: Norm -attainability of elementary operators on Hilbert and Banach spaces have been Characterized by many mathematicians. However, there is little information on Norm-attainability of generalized finite operators on C*-algebra. A pair of bounded linear operators A,B on a complex Hilbert space H is called generalized finite operators if ||AX- XB- I ||≥ 1 for each xϵB(H). This paper therefore determines the norm attainability of these generalized finite operators on C*-algebra when implemented by norm attainable operators A,B.

ABSTRACT: Generally-speaking there are three tests for specification error in the context of regression analysis in the statistical literature: (1) The Durbin-Watson statistic, (2) The Ramsey RESET (Regression Equation Specification Error Test) t-test, and (3) The Breusch-Godfrey serial correlation LM test. The first and third tests assume that the presence of serial correlation in the regression residuals is a sign of misspecification, while the second test is more appropriate when non-linear functional forms prevail. In the RESET test, non-linearity is detected by including the squares of the fitted dependent variable in the original model, and undertaking a t-test on the coefficient of the included fitted variable. This paper introduces an alternative test for misspecification, which consists of including the squares of the actual dependent variable in the original regression. This alternative test is studied for the case of misspecification when a quadratic explanatory term is omitted. Two separate simulations are carried out. One assumes that the variables are generated by a normal distribution, and the other by a uniform distribution. The results strongly find that the alternative testing procedure suggested here dominates the other 3 tests available in the literature. This is especially true when the variables are set to follow a normal distribution.

ABSTRACT: Many phenomena’s in engineering, biology, fluid mechanics and other sciences can be modeled as both linear and nonlinear partial differential equations (PDEs). In this paper, we proposed wavelet based lifting schemes for the numerical solution of Poisson equations using Orthogonal and Biorthogonal wavelets filter coefficients. The numerical results obtained by the scheme are compared with the exact solution to exhibit the accuracy and also speeds up the convergence in lesser computational time as compared with the existing schemes. Some of the problems are presented for the applicability and validity of the scheme.