A global differentiability result for solutions of nonlinear elliptic problems with controlled growths

Let Ω be a bounded open subset of ℝ ⁿ , n > 2. In Ω we deduce the global differentiability result

Higher order duality in multiobjective fractional programming with support functions

In this paper a new class of higher order (F,ρ,σ)-type I functions for a multiobjective programming problem is introduced, which subsumes several known studied classes. Higher order Mond-Weir and Schaible type dual programs are formulated for a nondifferentiable multiobjective fractional programming problem where the objective functions and the constraints contain support functions of compact convex sets in Rn. Weak and strong duality results are studied in both the cases assuming the involved functions to be higher order (F,ρ,σ)-type I. A number of previously studied problems appear as special cases.     

On solvability of boundary value problems for higher order nonlinear hyperbolic equations

In the rectangle Ω=[0,a]×[0,b] for the nonlinear hyperbolic equation

the boundary value problems of the type

are considered, where and are linear bounded functionals.Sufficient conditions of solvability and unique solvability of the general problem and its particular cases (Nicoletti type, Dirichlet, Lidstone and Periodic problems) are established.     

Global regularity for solutions to Dirichlet problem for discontinuous elliptic systems with nonlinearity q > 1 and with natural growth

In this paper we deal with the Hölder regularity up to the boundary of the solutions to a nonhomogeneous Dirichlet problem for second-order discontinuous elliptic systems with nonlinearity q > 1 and with natural growth. The aim of the paper is to clarify that the solutions of the above problem are always global Hölder continuous in the case of the dimension n = q without any kind of regularity assumptions on the coefficients. As a consequence of this sharp result, the singular sets $\Omega_0 \subset \OmegaIn this paper we deal with the H?lder regularity up to the boundary of the solutions to a nonhomogeneous Dirichlet problem for second-order discontinuous elliptic systems with nonlinearity q > 1 and with natural growth. The aim of the paper is to clarify that the solutions of the above problem are always global H?lder continuous in the case of the dimension n = q without any kind of regularity assumptions on the coefficients. As a consequence of this sharp result, the singular sets , are always empty for n = q. Moreover we show that also for 1 < q < 2, but q close enough to 2, the solutions are global H?lder continuous for n = 2.      

Facile Synthesis of Metallosalphen-Based 2D Conductive Metal-Organic Frameworks for NO2 Sensing: Metal Coordination Induced Planarization

As an emerging class of promising porous materials, the development of two-dimensional conductive metal organic frameworks (2D c-MOFs) is hampered by the few categories and tedious synthesis of the specific ligands. Herein, we developed a nonplanar hexahydroxyl-functionalized Salphen ligand (6OH-Salphen) through a facile two-step synthesis, which was further applied to construct layered 2D c-MOFs through in situ one pot synthesis based on the synergistic metal binding effect of the N₂O₂ pocket of Salphen. Interestingly, the C_2v-symmetry of ligand endows Cu-Salphen-MOF with periodically heterogeneous pore structures. Benefitting from the higher metal density and shorter in-plane metal-metal distance, Cu-Salphen-MOF showcased excellent NO₂ sensing performance with good sensitivity, selectivity and reversibility. The current work opens up a new avenue to construct 2D c-MOF directly from nonplanar ligands, which greatly simplifies the synthesis and provides new possibilities for preparing different topological 2D c-MOF based functional materials.     

Assessment model of classroom acoustics criteria for enhancing speech intelligibility and learning quality

In this paper, a new classroom acoustics assessment model (CAAM) based on analytic hierarchy process (AHP) for enhancing speech intelligibility and learning quality is proposed. The model is based on five main criteria that affect the learning process and related to classrooms acoustical properties. These include classroom specifications, noise sources inside and outside the classroom, teaching style, and vocal effort. The priority and weights of these major criteria along with their alternatives are identified using the views of students, staff, education consultants, and expertise by using a developed questionnaire, and the AHP methodology. This model can be considered as a helpful framework enabling universities decision makers to take effective decisions on classroom acoustics treatment issues. It also provides colleges’ higher authorities the suitable guidelines that help for determining necessary requirements that help to raise the quality and efficiency of the educational environment; in order to reach an excellent learning environment; and hence increasing students learning outcomes.