Perturbation theory for Hamiltonian matrices and the distance to bounded-realness

Motivated by the analysis of passive control systems, we undertake a detailed perturbation analysis of Hamiltonian matrices that have eigenvalues on the imaginary axis. We construct minimal Hamiltonian perturbations that move and coalesce eigenvalues of opposite sign characteristic to form multiple eigenvalues with mixed sign characteristics, which are then moved from the imaginary axis to specific locations in the complex plane by small Hamiltonian perturbations. We also present a numerical method to compute upper bounds for the minimal perturbations that move all eigenvalues of a given Hamiltonian matrix outside a vertical strip along the imaginary axis

Assessment of in-vivo anti-diabetic and anti-diarrheal effects of Flemingia stricta Roxb. leaf

The objective of this study was to evaluate the anti-diabetic and anti-diarrheal activity of methanol extract of Flemingia stricta Roxb. (Fabaceae) leaf. In anti-diabetic study, the extract was administered to alloxan-induce diabetic mice at two concentrations (200 mg/kg and 400 mg/kg body weight) for acute (12 hours) and prolong treatments (15 days) and blood glucose levels of diabetic mice were monitored at intervals of hours and days throughout the duration of treatment. Antidiarrheal test was conducted by castor oil induced diarrhea and enteropooling as well as intestinal motility in mice at three different concentration (100 mg/kg, 200 mg/kg and 400 mg/kg body weight). Treatment of alloxan induce diabetic mice with the extract caused a significant reduction in fasting blood glucose level of the diabetic mice both in acute (12 hours) and prolong treatment (15 days) and it was determined that the F. stricta methanol extract at both concentration (200 mg/kg and 400 mg/kg) showed the significant (P<0.05) hypoglycemic effect in comparison to the standard drug metformin. In the case of castor oil induced diarrheal test, enteropooling test and gastrointestinal motility test, the extract of F. stricta  at 100 mg/kg, 200 mg/kg and 400 mg/kg has given significant effect (P<0.05) compared to the standard drug loperamide. But 400 mg/kg demonstrated the highest activity amongst the three doses. These results suggested that the methanol extract of F. stricta Roxb. possess promising anti-diabetic effect on alloxan-induced mice and significant antidiarrheal effect on castor oil induced diarrheal mice. DOI: http://dx.doi.org/10.5281/zenodo.383974

On Spectral Approximation of Linear Operators

AbstractRefined error estimates are obtained for the approximation of discrete spectra of linear operators. It also provides an alternative approach to spectral approximation

On the construction of nearest defective matrices to a normal matrix

AbstractGiven an n-by-n normal matrix A having n distinct eigenvalues, we describe a simple procedure for constructing a defective matrix nearest to A. Our construction requires only an appropriate pair of eigenvalues of A and their corresponding eigenvectors