Concentration on minimal submanifolds for a singularly perturbed Neumann problem

We consider the equation −ε²Δu+u=up in Ω⊆RN, where Ω is open, smooth and bounded, and we prove concentration of solutions along k-dimensional minimal submanifolds of ∂Ω, for N?3 and for k∈{1,…,N−2}. We impose Neumann boundary conditions, assuming 1<p<(N−k+2)/(N−k−2) and ε→⁰⁺. This result settles in full generality a phenomenon previously considered only in the particular case N=3 and k=1.     

Stark broadening of isolated lines: calculation of the diagonal multiplet factor for complex configurations (n1l1 n n2l2 m n3l3 p)

Owing to the increasing sensitivity of detectors, accurate line profiles are needed for accurate stellar atmospheres modelling and for laboratory and technological plasmas as well. So, Stark broadening parameters of isolated lines of complex atoms and ions within the impact and quasistatic approximation are needed, even if the atomic abundance of the considered element is low. Angular factors of the diagonal line strength entering the quadrupole term appearing in the semi-classical expression of the width of line broadened by electron or ion perturbers, are needed. The aim of this paper is to extend the previous calculations of this diagonal multiplet factor which were obtained for configurations of the type lⁿ and l₁ ⁿl₂ ^m to more complex configurations in LS coupling. To study the Stark broadening of isolated lines in the impact and quasistatic approximation, we use the semi-classical-perturbation treatment, including both dipole and quadrupole contribution in the expansion of the electrostatic interaction between the optical electron and the perturber. We also use the Fano-Racah algebra. Angular factors of the diagonal line strength entering the quadrupole term appearing in the semi-classical expression of the width of line broadened by electron or ion perturbers, are calculated. New diagonal multiplet factor formulae for more complicated configurations such as (n₁l₁ ⁿ(L_nS_n)n₂l₂ ^m(L_mS_m)n₃l₃ ^p(L_pS_p)) are provided. These formulae can enter the computer Stark semi-classical perturbation codes.     

Voltage-controlled transmission through a dielectric slab doped with quantum dot molecules

Transmission and reflection of an electromagnetic pulse through a dielectric slab doped with the quantum dot molecules are investigated. It is shown that the transmission and reflection coefficients depend on the inter-dot tunneling effect and can be simply controlled by applying a gate voltage without any changing in the refractive index or thickness of the slab. Such simple controlling prepares an active beam splitter which can be used in all optical switching, optical limiting, and other optical systems.     

Rapid Sonosynthesis of N‐Doped Nano TiO2 on Wool Fabric at Low Temperature: Introducing Self‐cleaning,Hydrophilicity, Antibacterial/Antifungal Properties with low Alkali Solubility,Yellowness and Cytotoxicity

Nano nitrogen‐doped titanium dioxide was rapidly prepared by hydrolysis of titanium isopropoxide at 75–80°C using in situ sonochemical synthesis by introducing ammonia. Various concentrations of titanium isopropoxide were examined to deposit nano nitrogen‐doped titanium dioxide through impregnation of the wool fabric in ultrasound bath followed by curing. The antibacterial/antifungal activities of wool samples were assessed against two common pathogenic bacteria including Escherichia coli and Staphylococcus aureus and the diploid fungus Candida albicans. The sonotreated wool fabrics indicated no adverse effects on human dermal fibroblasts. The presence of nanoparticles on the sonotreated wool fabrics were confirmed by FE‐SEM images and EDS patterns and X‐ray mapping and the crystalline size of nanoparticles were estimated through XRD results. The role of both pH and precursor concentration on the various properties of the fabric was investigated and the optimized conditions introduced using response surface methodology.     

Hartman effect in one-dimensional photonic crystals with a three-level atomic defect layer

The Hartman effect in one-dimensional photonic crystals contained a defect layer doped with two-level, and three-level atoms is discussed. It is shown that the transmitted phase time in one-dimensional photonic crystals contained a defect layer reaches to a positive constant as the periodic number N increases. However, for a defect layer doped by two-level atoms, the transmitted phase time reaches to negative constant by increasing periodic number N. In addition, for defect layer doped by three-level atoms, the transmitted phase time can be controlled from positive to negative just by the Rabi-frequency of coupling field.     

Baer Criterion for Injectivity of Projection Algebras

Projection algebras are M-sets for the monoid M = (ℕ^∞, min) which are used by computer scientists for algebraic specification of process algebras. In contrast to the case of modules it is well known that the Baer Criterion does not generally hold for injectivity of M-sets for an arbitrary monoid M. Here, introducing a closure operator, we prove that the Baer Criterion does hold for injectivity of projection algebras.