Roots in differential rings of ultradifferentiable functions

Let {M _k } be a logconvex sequence satisfying the differentiability condition $$\sup (M_{n + 1} /M_n )^{1/n} < \infty $$ . It is shown that the Carleman class C{k! M _k } contains all C ^∞ roots of its nonflat elements, i.e., if f ∈ C{k! M _k } and α > 0, then $$f^\alpha \in C\{ k!M_k \} whenever f^\alpha \in C^\infty $$ . If {M _k } also satisfies the additional condition M _n ^1/n → ∞, then the Beurling class C(k! M _k ) is also contains all C ^∞ roots of its nonflat elements.     

On solutions of real analytic equations

Analyticity of solutions , of systems of real analytic equations , is studied. Sufficient conditions for and power series solutions to be real analytic are given in terms of iterative Jacobian ideals of the analytic ideal generated by . In a special case when the 's are independent of , we prove that if a solution satisfies the condition , then is necessarily real analytic.

     

Biochemical Studies on Hemoglobin Modified with Reactive Oxygen Species (ROS)

Hemoglobin is the iron-containing oxygen transporting metalloprotein in the red cells of blood in mammals and other animals. Hemoprotein-mediated oxidative stress is thought to play a major role in pathophysiology of cerebral hemorrhage, blast pressure injury, crush injury, myocardial ischemia reperfusion injury. Hemoglobin undergoes oxidation-reduction reactions that lead to both generation and consumption of highly reactive oxygen and nitrogen species. In the present study, hemoglobin molecule was treated with hydrogen peroxide and the modification so incurred was analyzed by UV spectra, sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) and detection of carbonyl content. Our observations suggest that carbonyl content increases with increase in concentration of hydrogen peroxide. Production of hydroxyl radical was assessed by using benzoate degradation analysis. Our results was in tandem with the fact that hemoglobin on treatment with hydrogen peroxide rapidly generates free-radical species that can degrade benzoate to thiobarbituric acid reactive material which on reacting with thiobarbituric acid gives color. The increase in absorbance of ROS-modified hemoglobin at 532 nm shows the increase in benzoate degradation, which is a parameter of hydroxyl radical formation with increase in concentration of hydrogen peroxide. Modified hemoglobin was treated with catalase, mannitol, thiourea, glutathion, sodium benzoate and their effect were detected by spectroscopy and SDS-PAGE (12%). Substantial scavenging effect of aforementioned antioxidants reiterates the formation of hydroxyl radical. Catalase shows the maximum scavenging effect followed by thiourea and mannitol.