Existence and Exponential Decay of Solutions for a Wave Equation with Integral Nonlocal Boundary Conditions of Memory Type

In this paper, we consider a wave equation with integral nonlocal boundary conditions of memory type. First, we establish two local existence theorems by using Faedo–Galerkin method and standard arguments of density. Next, we give a su?cient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical results.     

Unbounded Components in the Solution Sets of Strictly Quasiconcave Vector Maximization Problems

Let (P) denote the vector maximization problem

Particle Model for the Reservoirs in the Simple Symmetric Exclusion Process

Journal of Statistical Physics - In this paper, we will study the long time behavior of the simple symmetric exclusion process in the “channel” $$varLambda _N=[1,N]cap mathbb {N}$$...     

Linear and Cyclic Hybrids of Alternating Thiophene–Amino Acid Units: Synthesis and Effects of Chirality on Conformation and Molecular Packing

The dipeptide isostere 5‐aminothiophene carboxylic acid has been combined with L ‐phenylalanine moieties to provide linear and cyclic hybrid oligopeptides. A suitable protecting group strategy and appropriate coupling methods have been developed to guarantee a high degree of enantiopurity of the resulting amides. Cyclic tetraamides have been efficiently obtained by macrocyclization of the linear derivatives. In the case of racemized cyclization precursors, two diastereomeric macrocycles (S,S/R,R and meso) have been isolated. Their crystal structures show clear effects of the stereogenic centers on the ring conformations and molecular packing.     

An oxacalix[2]arene[2]pyrimidine-bis(Zn-porphyrin) tweezer as a selective receptor towards fullerene C70

An oxacalix[2]arene[2]pyrimidine-bis(Zn^II-porphyrin) conjugate was readily prepared via nucleophilic aromatic substitution of a phenolic AB₃-Zn-porphyrin on the upper rim of a (1,3-alternate) 5,17-bis(methylsulfonyl)oxacalix[4]arene precursor. Efficient 1:1 complex formation between the ‘jaws’ bisporphyrin tweezer and fullerene C₇₀ was evidenced by ¹H NMR titrations (K = 3.0 × 10⁴ M⁻¹), while no detectable complexation could be observed with C₆₀. On the other hand, an analogous oxacalix[4]arene-bis(Cu-corrole) conjugate did not show any measurable (C₆₀ or C₇₀) fullerene binding.     

Functional group effects on metal-organic framework topology

Functionalization of the ligand 1,3,5-tris(4-carboxyphenyl)benzene (H(3)BTB) has been realized with methoxy (H(3)BTB-[OMe](3)) and hydroxy (H(3)BTB-[OH](3)) groups. Combining H(3)BTB-[OMe](3) and Zn(ii) results in the formation of the first isostructural, functionalized analogue of MOF-177 (MOF-177-OMe), while the combination of H(3)BTB-[OH](3) and Zn(ii) generates a rare, interpenetrated pcu-e framework.     

A rapid way to synthesize Brønsted acidic ionic liquid and its application as an efficient catalyst for esterification

A novel and time-saving method to prepare a Brønsted acidic ionic liquid, 1-carboxymethyl-3-methylimidazolium hydrogen sulfate ([CMI][HSO₄]), in high yield and purity was performed under microwave irradiation. The ionic liquid showed an incomparable catalytic efficiency in the microwave-accelerated esterification of arenecarboxylic acids. Moreover, its ability of being recovered and reused many times without loss of activity has made [CMI][HSO₄] more favorable from the viewpoint of green chemistry.     

Hydrogenated Graphene and Hydrogenated Silicene: Computational Insights

Density functional calculations are performed to study the energetic, structural, and electronic properties of graphene and silicene functionalized with hydrogen. Our calculations predict that H atoms bind much more strongly to silicene than to graphene. The adsorbed H atoms tend to cooperatively stabilize each other leading to a two‐dimensional nucleation and growth mechanism. The different structural and electronic modifications induced by H in fully functionalized graphene and silicene (known as graphane and silicane) are also explained. Finally, the electronic properties of defective graphane with multiple hydrogen vacancies are investigated. Engineering the vacancies in graphane offers a way to modify the electronic properties of this material.