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.     

Equivalency for Disconjugate Operators

The solutions of the dfferential equation L_nx + a₀(t)x = 0, where L_n is a disconjugate operator and a₀ is of one sign, are studied according to their behavior as t → ∞. We prove equivalence theorems between solutions of this equation and its adjoint in terms of property A and property B. These theorems generalize the results known for n = 3 and for odd order binomial equations. Some applications are given too.     

粘土担载的钼基催化剂的制备、结构及CO加氢合成醇性能

采用溶胶凝胶法与等体积浸渍相结合制备了一系列以粘土为载体的K-Co-Mo催化剂. 采用XRD、N₂等温吸脱附、H_{26+的还原,但对Mo⁴⁺和Co²⁺的还原没有明显的影响. 催化剂经还原后,在其表面生成了一种更低价态的Mo^δ+(1<δ<4)物种,被认为是合成醇的活性中心. 与非负载催化剂相比,粘土担载的K-Co-Mo具有更高的合成醇性能. 负载型催化剂具有较高的活性物种分散度,并且其介孔结构在一定程度上延长了合成醇反应中间体的滞留时间,从而促进了低碳醇的生成. 经773 K还原的催化剂具有较高的活性,其原因可为催化剂表面具有较高含量的Mo^δ+物种.}     

Domain Wall with Strange Quark Matter in Kaluza-Klein Type Cosmological Model

In this study we have analyzed the Kaluza-Klein type Robertson Walker (RW) cosmological model by considering variable cosmological constant term Λ of the form: , and Λ∼ρ in the presence of strange quark matter with domain wall. The various physical aspects of the model are also discussed.     

Partial regularity and singular sets of solutions of higher order parabolic systems

In the present paper we provide a broad survey of the regularity theory for non-differentiable higher order parabolic systems of the type

Variational integrals of splitting-type: higher integrability under general growth conditions

Besides other things we prove that if , , locally minimizes the energy