Entire large solutions of semilinear equations involving the fractional Laplacian

We investigate the existence and nonexistence of positive entire large solutions of a class of semilinear equations involving the fractional Laplacian. Sharp lower and upper bounds of the minimal solution, if it exists, are also given.     

Band structures of symmetrical graphene superlattice with cells of three regions

We study the electronic band structures of massless Dirac fermions in symmetrical graphene superlattice with cells of three regions. opening gaps and additional Dirac points. Finally, we inspect the potential effect on minibands, the anisotropy of group velocity and the energy bands contours near Dirac points. We also discuss the evolution of gap edges and cutoff region near the vertical Dirac points.     

Potassium Fluoride on Alumina: Condensation of 1,4-Diacetylpiperazine-2,5-Dione with Aldehydes. Dry Condensation Under Microwave Irradiation. Synthesis of Albonursin and Analogues

1,4-Diacetylpiperazine-2,5-dione (1) was condensated with aldehydes (2) with KF on alumina without solvent under microwaves or in at room temperature in the presence of DMF. The reaction was stereoselective and some natural products (4a-c) like albonursin(4c) were synthesized.     

A new distance measure including the weak preference relation: Application to the multiple criteria aggregation procedure for mixed evaluations

We introduce a new distance measure between two preorders that captures indifference, strict preference, weak preference and incomparability relations. This measure is the first to capture weak preference relations. We illustrate how this distance measure affords decision makers greater modeling power to capture their preferences, or uncertainty and ambiguity around them, by using our proposed distance measure in a multiple criteria aggregation procedure for mixed evaluations.     

Lower bound for the ratios of eigenvalues of Schrödinger with nonpositive single‐barrier potentials

Horváth and Kiss (Proc. Amer. Math. Soc., 2005) proved the upper bound estimate for Dirichlet eigenvalue ratios of the Schrödinger problem ?y^′′ + q(x)y = λy with nonnegative and single‐well potential q. In this paper, we prove that if q(x) is a nonpositive, continuous, and single‐barrier potential, then for λ_n > λ_m≥ ? 2q^?, where . In particular, if q(x) satisfies the additional condition , then λ₁ > 0 and for n > m ≥ 1. For this result, we develop a new approach to study the monotonicity of the modified Prüfer angle function.     

Quantum dot-in-a-well (QDWELL) laser dynamics under optical injection

We investigated theoretically the optical injection influence on the dynamics of a quantum dot in a quantum well (QDWELL) laser. The carrier dynamics is synchronized due to the optical injection, and QDWELL laser manifests a high performance at repetition frequencies up to 30 GHz.