The second part of the notes are written jointly with my collaborator from University of Illinois, M. B. Erdogan. We developed the material with two goals in mind. First to prove existence and uniqueness results in the case of dispersive PDE evolving from initial data that are periodic in the space variable. Secondly we develop new tools to address the problem of wellposedness of solutions, in ...

Sum Rules equations for pick-up reactions are presented for the first time for the energy centroids of states both for the isospin T<(≡ T0 − 1 2) and T>(≡ T0 + 1 2) of the final nucleus when a nucleon is picked up from a general multishell target state with isospin T0. These equations contain two-body correlation terms, < H01 >, which, at the present moment, are difficult to handle analytically...

L-arginine is an amino acid semiessencial considered a precursor of nitric oxide, a gas mainly produced in endothelial cells. Nutritional supplements based on the amino acid L-arginine have been broadly marketed in order to increase vasodilation and the blood supply to muscle in order to optimize metabolic responses induced by exercise. The main objective of this study was to evaluate the effec...

An economically important species of Citharus linguatula was investigated in the Sea Marmara (Eastern Mediterranean, Turkey). Length-weight relationships, growth parameters, reproductive time, and first sexual maturity length were determined. A total 236 individuals analyzed, weight varied from 7.5 to 26.5 cm TL (17.11±3.62 cm) 2.67 180.81 g (44.07±1.84 g), respectively. The length-weight relat...

Uniqueness and continuous dependence of solutions of (2) can thus be derived from the well-posedness of the Cauchy problem for (3). We remark that the genuine nonlinearity of (1) implies that the total variation of u(t0, ·) is locally bounded, for each t0 > 0. Hence the well posedness of the Cauchy problem (3) with initial data x(t0) = x0 follows from [2]. It is worth noting that in [3] the wel...

Theorems on the Fredholm alternative and well-posedness of the Darboux problem ∂2u(t, x) ∂t ∂x = `(u)(t, x) + q(t, x), u(t, x0) = φ(t) for t ∈ [a, b], u(t0, x) = ψ(x) for x ∈ [c, d] are established, where ` : C(D;R) → L(D;R) is a linear bounded operator, q ∈ L(D;R), t0 ∈ [a, b], x0 ∈ [c, d], φ : [a, b]→ R, ψ : [c, d]→ R are absolutely continuous functions, and D = [a, b] × [c, d]. New sufficien...