Asymptotic Behaviour of Solutions of a Multidimensional Moving Boundary Problem Modeling Tumor Growth

We study a moving boundary problem modeling the growth of multicellular spheroids or in vitro tumors. This model consists of two elliptic equations describing the concentration of a nutrient and the distribution of the internal pressure in the tumor's body, respectively. The driving mechanism of the evolution of the tumor surface is governed by Darcy's law. Finally surface tension effects on the moving boundary are taken into account which are considered to counterbalance the internal pressure. To put our analysis on a solid basis, we first state a local well-posedness result for general initial data. However, the main purpose of our study is the investigation of the asymptotic behaviour of solutions as time goes to infinity. As a result of a centre manifold analysis, we prove that if the initial domain is sufficiently close to a Euclidean ball in the C ^m+μ-norm with m ≥ 3 and μ ∈ (0,1), then the solution exists globally and the corresponding domains converge exponentially fast to some (possibly shifted) ball, provided the surface tension coefficient γ is larger than a positive threshold value γ_*. In the case 0 < γ < γ_* the radially symmetric equilibrium is unstable.     

Some results of the worst-case analysis for flow shop scheduling with a learning effect

This article considers flow shop scheduling problems with a learning effect. By the learning effect, we mean that the processing time of a job is defined by a function of its position in a processing permutation. The objective is to minimize the total weighted completion time. Some heuristic algorithms by using the optimal permutations for the corresponding single machine scheduling problems are presented, and the worst-case bound of these heuristics are also analyzed.     

Rational design and synthesis of 3-heteroaromatics coumarin molecules with unusual solution and solid dual efficient luminescence

3-Imidazolyl coumarin molecules were synthesized under solvent-free condition and the optical properties both in solution and the solid state were determined. The compounds showed dual efficient luminescence, which were blue fluorescence with the highest fluorescence quantum yield being more than 0.9 and also exhibited favorable yellow solid-state fluorescence. Additionally, by using density functional theory (DFT) and time-dependent DFT (TD-DFT) calculation, all structures were optimized and the associated optical performances showed similar results as the experimental results.     

Sinuhirtins A and B,two uncommon norhumulene-type terpenoids from the South China Sea soft coral Sinularia hirta

Two new uncommon norhumulene-type norsesquiterpenoids, namely sinuhirtins A (1) and B (2), along with two known norcaryophyllene-type norsesquiterpenoids (3 and 4), were isolated from the South China Sea soft coral Sinularia hirta. The structures and absolute configurations of the new compounds were determined by extensive spectroscopic data analyses, and computer-assisted methods including GIAO ¹³C NMR and TDDFT-ECD calculations. A plausible biogenetic relationship of 1–4 was proposed.     

A Polypyridyl‐Based Layered Complex as Dual‐Functional Co‐catalyst for Photo‐Driven Organic Dyes Degradation and Water Splitting

With the ever‐increasing concerns on environmental pollution and energy crisis, it is of great urgency to develop high‐performance photocatalyst to eliminate organic pollutants from wastewater and produce hydrogen via water splitting. Herein, a polypyridyl‐based mixed covalent Cu^I/II complex with triangular {Cu₃} and rhombic {Cu₂Cl₄} subunits alternately extended by mixed SCN^– and Cl^– heterobridges [Cu₄(DNP)(SCN)Cl₄]_n ( 1 ) [DNP = 2,6‐bis(1,8‐naphthyridine‐2‐yl)pyridine] was solvothermally synthesized and employed as a dual‐functional co‐photocatalyst. Resulting from a narrowed band‐gap of 1.07 eV with suitable redox potential and unsaturated Cu^I/II sites, the complex together with H₂O₂ can effectively degrade Rhodamine B and methyl orange up to 87.4 and 88.2 %, respectively. Meanwhile, the complex mixed with H₂PtCl₆ can also accelerate the photocatalytic water splitting in the absence of a photosensitizer with the hydrogen production rate of 27.5 μmol · g^–1 · h^–1. These interesting findings may provide informative hints for the design of the multiple responsive photocatalysts.     

Effect of the Spacer Chain Length of Organic Dicarboxylic Acid on the Supramolecular Assembly of Two Ternary Zinc (II) Coordination Polymers Derived from Mixed Ligands

Two new Zn^II coordination polymers (CPs), [Zn₂(SA)₂(L)₂]_n ( 1 ) and [Zn(AA)(L)]_n ( 2 ) [L = 1,6‐bis(benzimidazol‐1‐yl)hexane, H₂SA = succinic acid, H₂AA = adipic acid], were synthesized via hydrothermal method and characterized by elemental analysis, infrared spectroscopy, and single‐crystal X‐ray diffraction. CP 1 possesses a sql network, which is further extended into a 3D supramolecular skeleton by non‐classical C–H ··· O hydrogen bonding interactions. CP 2 exhibits a 1D linear chain, which is further assembled into a 2D supramolecular layer by π ··· π stacking interactions. The solid state fluorescence properties of two Zn^II CPs were investigated. Both CPs present high photocatalytic activities for the degradation of methylene blue (MB) under UV light irradiation. The photodegradation efficiency using CP 1 as catalyst is 91.3 % and using CP 2 as catalyst is 85.0 %, respectively.     

A Scalable Methylamine Gas Healing Strategy for High‐Efficiency Inorganic Perovskite Solar Cells

An easy and scalable methylamine (MA) gas healing method was realized for inorganic cesium‐based perovskite (CsPbX₃) layers by incorporating a certain amount of MAX (X=I or Br) initiators into the raw film. It was found that the excess MAX accelerated the absorption of the MA gas into the CsPbX₃ film and quickly turned it into a liquid intermediate phase. Through the healing process, a highly uniform and highly crystalline CsPbX₃ film with enhanced photovoltaic performance was obtained. Moreover, the chemical interactions between a series of halides and MA gas molecules were studied, and the results could offer guidance in further optimizations of the healing strategy.     

Directed Evolution of a Bacterial Laccase (CueO) for Enzymatic Biofuel Cells

Escherichia coli's copper efflux oxidase (CueO) has rarely been employed in the cathodic compartment of enzymatic biofuel cells (EBFCs) due to its low redox potential (0.36 V vs. Ag/AgCl, pH 5.5) towards O₂ reduction. Herein, directed evolution of CueO towards a more positive onset potential was performed in an electrochemical screening system. An improved CueO variant (D439T/L502K) was obtained with a significantly increased onset potential (0.54 V), comparable to that of high‐redox‐potential fungal laccases. Upon coupling with an anodic compartment, the EBFC exhibited an open‐circuit voltage (V_oc) of 0.56 V. Directed enzyme evolution by tailoring enzymes to application conditions in EBFCs has been validated and might, in combination with molecular understanding, enable future breakthroughs in EBFC performance     

Platinum/Nickel Bicarbonate Heterostructures towards Accelerated Hydrogen Evolution under Alkaline Conditions

Heterostructured nanomaterials, generally have physicochemical properties that differ from those of the individual components, and thus have potential in a wide range of applications. New platinum (Pt)/nickel bicarbonate (Ni(HCO₃)₂) heterostructures are designed for an efficient alkaline hydrogen evolution reaction (HER). Notably, the specific and mass activity of Pt in Pt/Ni(HCO₃)₂ are substantially improved compared to the bare Pt nanoparticles (NPs). The Ni(HCO₃)₂ provides abundant water adsorption/dissociation sites and modulate the electronic structure of Pt, which determine the elementary reaction kinetics of alkaline HER. The Ni(HCO₃)₂ nanoplates offer a platform for the uniform dispersion of Pt NPs, ensuring the maximum exposure of active sites. The results demonstrate that, Ni(HCO₃)₂ is an effective catalyst promoter for alkaline HER.     

Cleavage of C(aryl)−CH3 Bonds in the Absence of Directing Groups under Transition Metal Free Conditions

Organic chemists now can construct carbon–carbon σ‐bonds selectively and sequentially, whereas methods for the selective cleavage of carbon–carbon σ‐bonds, especially for unreactive hydrocarbons, remain limited. Activation by ring strain, directing groups, or in the presence of a carbonyl or a cyano group is usually required. In this work, by using a sequential strategy site‐selective cleavage and borylation of C(aryl)?CH₃ bonds has been developed under directing group free and transition metal free conditions. Methyl groups of various arenes are selectively cleaved and replaced by boryl groups. Mechanistic analysis suggests that it proceeds by a sequential intermolecular oxidation and coupling of a transient aryl radical, generated by radical decarboxylation, involving a pyridine‐stabilized persistent boryl radical.