A study on fuzzy semi inner product spaces

Mathematical models are often used to describe physical realities. However, the physical realities are imprecise while the mathematical concepts are required to be precise and perfect. The 1st chapter give a brief summary of the arithmetic of fuzzy real numbers and the fuzzy normed algebra M(I). Also we explain a few preliminary definitions and results required in the later chapters. Fuzzy real numbers are introduced by Hutton,B [HU] and Rodabaugh, S.E[ROD]. Our definition slightly differs from this with an additional minor restriction. The definition of Clementina Felbin [CL1] is entirely different. The notations of [HU]and [M;Y] are retained inspite of the slight difference in the concept.the 3rd chapter In this chapter using the completion M'(I) of M(I) we give a fuzzy extension of real Hahn-Banch theorem. Some consequences of this extension are obtained. The idea of real fuzzy linear functional on fuzzy normed linear space is introduced. Some of its properties are studied. In the complex case we get only a slightly weaker analogue for the Hahn-Banch theorem, than the one [B;N] in the crisp case

Induction of mitotic aberrations by Argon ion lasers in Vicia faba L. and Allium cepa L.

A comparat ive study of the effect oflaser in inducing chro mosomal aberrat ions at 4gg nm was done in View j aba L. (faba bean) and Allium ccpa L. (onion) with Argon ion laser (Spectra Physics Model 171). Seeds and bulbs of V.jaba and A. eepa were subjected to laser irra diation by 4gg nm excitations from Argon ion laser source at power levels 200 and 400 mW with power densities 2.25 mW em" and 4.49 mW em" and ditTerent exposure times (10, 20, 30 & 40 minutes). Similar to the effect of oth er physical and chemical mutagens, laser caused a dose dependent decrease in mitotic index and a rise in mitotic aberrations when compared to the control. In both plant species, mutations were observed in all stages of mitotic cell cycle. The total percentage of aberrations was two fold higher at 400 mW than at 200 mW exposure.