On initial boundary-value problems for symmetric nonhyperbolic systems of partial differential equations

We obtain examples of continuous maps of initial boundary-value problem data into approximate solutions of symmetric, linear, nonhyperbolic first-order systems of partial differential equations. This discussion is motivated by recurring hyperbolicity failure in models of two-fluid flow, and provides a possible means of evaluating the validity of the underlying physical and mathematical assumptions in the limit of vanishing viscosity.This work was completed while the author was visiting at The Fields Institute, Toronto, Canada.     

Exact Pseudospin Symmetric Solution of the Dirac Equation for Pseudoharmonic Potential in the Presence of Tensor Potential

Under the pseudospin symmetry, we obtain exact solution of the Dirac equation for the pseudoharmonic potential in the presence of the tensor potential with arbitrary spin–orbit coupling quantum number κ. The energy eigenvalue equation of the Dirac particles is found and the corresponding radial wave functions are presented in terms of confluent hypergeometric functions. We investigate the tensor potential dependence of the energy of the each state in the pseudospin doublet. It is shown that degeneracy between members of the pseudospin doublet is removed by tensor interaction. Furthermore, the radial node structure of the Dirac spinor is discussed.     

Characterizations of proximinal,semichebychevian and chebychevian subspaces in real normed spaces

A simple model optimal control problem for continuous casting with state-space constraints is approximated, as usual, by a penalty method and by a numerical discretization of the nonlinear heat equation. The convergence of the approximate problems directly to the original problem is proven under a stability criterion linking the penalty parameter with the discretization parameters. For this purpose, known discretization error estimates for the Stefan problem are extended for the case of time varying boundary conditions.     

Approximate Analytical Solutions of the Dirac Equation for Yukawa Potential Plus Tensor Interaction with Any κ-Value

Approximate analytical solutions of the Dirac equation are obtained for the Yukawa potential plus a tensor interaction with any κ-value for the cases having the Dirac equation pseudospin and spin symmetry. The potential describing tensor interaction has a Yukawa-like form. Closed forms of the energy eigenvalue equations and the spinor wave functions are computed by using the Nikiforov–Uvarov method. It is observed that the energy eigenvalue equations are consistent with the ones obtained before. Our numerical results are also listed to see the effect of the tensor interaction on the bound states.     

Preparation,Characterization and ex vivo Intestinal Permeability Studies of Ibuprofen Solid Dispersion

The aim of the present study was to improve the solubility and dissolution rate of ibuprofen and to evaluate, ex vivo, the intestinal permeation. Solid dispersions (SD) were prepared with Kollicoat IR^® by solvent evaporation technique in different drug:carrier ratios. The permeation intestinal of ibuprofen was evaluated by inverted intestinal sac method. The SD was characterized by solubility equilibrium, FT-IR, DSC, PXRD, SEM, and dissolution rate. The solubility, dissolution rate, and permeability were significantly greater for SD 1:2. The PXRD, SEM and DSC indicated a partial change in the crystalline state of ibuprofen. The solubility equilibrium of SD (1:2) was approximately 15 times greater than the solubility of ibuprofen. Dissolution rate enhancement was attributed to the decreased crystallinity of the ibuprofen, and increase of wettability and decrease of particle size. In conclusion, dissolution rate and intestinal permeability of ibuprofen were enhanced by the use of Kollicoat IR^® carrier in the SD formulation.     

Time Dependence of Joint Entropy of Oscillating Quantum Systems

The time dependent entropy (or Leipnik’s entropy) of harmonic and damped harmonic oscillator systems is studied by using time dependent wave function obtained by the Feynman path integral method. The Leipnik entropy and its envelope change as a function of time, angular frequency and damping factor. Our results for simple harmonic oscillator are in agreement with the literature. However, the joint entropy of damped harmonic oscillator shows remarkable discontinuity with time for certain values of damping factor. The envelope of the joint entropy curve increases with time monotonically. These results show the general properties of the envelope of the joint entropy curve for quantum systems.     

Nonrelativistic Euler–Maxwell systems

Results of two previous papers are used to reexamine Galilean symmetric Euler–Maxwell systems as candidate models of magnetohydrodynamic flow. For a single, electrically charged fluid, the results are largely negative. Under expected physical conditions, inclusion of the magnetic force on the fluid all but necessarily results in a modified Lundquist system. However the treatment is unsatisfactory in several respects.     

Novel quantum description of time-dependent molecular interactions obeying a generalized non-central potential

Nonlinear Dynamics - Quantum features of time-dependent molecular interactions are investigated by introducing a time-varying Hamiltonian that involves a generalized non-central potential....