Connectivity of Direct Products of Graphs

Let $\kappa(G)$ be the connectivity of $G$ and $G\times H$ the direct product of $G$ and $H$. We prove that for any graphs $G$ and $K_n$ with $n\ge 3$, $\kappa(G\times K_n)=min\{n\kappa(G),(n-1)\delta(G)\}$, which was conjectured by Guji and Vumar.Comment: 5 pages, accepted by Ars Com

Rogue Waves of Nonlinear Schrödinger Equation with Time-Dependent Linear Potential Function

The rogue waves of the nonlinear Schrödinger equation with time-dependent linear potential function are investigated by using the similarity transformation in this paper. The first-order and second-order rogue waves solutions are obtained and the nonlinear dynamic behaviors of these solutions are discussed in detail. In addition, the amplitudes of the rogue waves under the effect of the gravity field and external magnetic field changing with the time are analyzed by using numerical simulation. The results can be used to study the matter rogue waves in the Bose-Einstein condensates and other fields of nonlinear science

Multimodal Contrast Agents for Optoacoustic Brain Imaging in Small Animals

Optoacoustic (photoacoustic) imaging has demonstrated versatile applications in biomedical research, visualizing the disease pathophysiology and monitoring the treatment effect in an animal model, as well as toward applications in the clinical setting. Given the complex disease mechanism, multimodal imaging provides important etiological insights with different molecular, structural, and functional readouts in vivo. Various multimodal optoacoustic molecular imaging approaches have been applied in preclinical brain imaging studies, including optoacoustic/fluorescence imaging, optoacoustic imaging/magnetic resonance imaging (MRI), optoacoustic imaging/MRI/Raman, optoacoustic imaging/positron emission tomography, and optoacoustic/computed tomography. There is a rapid development in molecular imaging contrast agents employing a multimodal imaging strategy for pathological targets involved in brain diseases. Many chemical dyes for optoacoustic imaging have fluorescence properties and have been applied in hybrid optoacoustic/fluorescence imaging. Nanoparticles are widely used as hybrid contrast agents for their capability to incorporate different imaging components, tunable spectrum, and photostability. In this review, we summarize contrast agents including chemical dyes and nanoparticles applied in multimodal optoacoustic brain imaging integrated with other modalities in small animals, and provide outlook for further research

Mechanical and biodeterioration behaviours of a clayey soil strengthened with combined carrageenan and casein

In the last decade, biopolymers have been used as organic soil binders in ground improvement and earthen construction material modification. Although biopolymer-treated soils have substantially enhanced mechanical strength, the deformation characteristics under external loads and material durability (e.g. biodeterioration due to microbial activity) have not yet been fully understood, which limits the in situ practical application of the biopolymer-based soil treatment technology. This study investigated the efficiency of combined carrageenan and casein in strengthening a clayey soil with the biodeterioration consideration. Both mechanical tests (e.g. unconfined compressive strength and one-dimensional consolidation) and biological tests (e.g. high throughput sequencing and rating of mould growth) were conducted. Results indicated that the usage of the carrageenan–casein mixture induced a higher soil compressive strength compared with either carrageen or casein, due to the formation of a three-dimensional gel network. In addition, carrageenan–casein mixture and casein decreased the compressibility of the clayey soil, which might be attributed to the casein’s peculiarity of self-associating into micelles, leading to minimal interactions with water molecules. Carrageenan, due to its affinity for water, increased the soil compressibility. Under the impact of microbial activity, the biopolymer-treated soils underwent deterioration in both surface appearance (i.e. coloured stains and patches caused by mould growth) and compressive strength. A linear relationship was proposed, in which a reduction in compressive strength by approximately 11% is expected while the rating of mould growth is increased by one in a five-rating system. The current research demonstrates that the soil reinforcement with combined carrageenan and casein is able to improve both soil strength and deformation behaviours. It is also suggested to take into account the biodeterioration considerations in the design and implementation of biopolymer-based soil reinforcement practices

Synthesis and structures of O-anthrylmethyl-substituted hexahomotrioxacalix[3]arenes

O-Alkylation of 7,15,23-tri-tert-butyl-25,26,27-trihydroxy-2,3,10,11,18,19-hexahomo-3,11,19-trioxacalix[3]arene (1H₃) with 9-chloromethylanthracene 5 was carried out under different reaction conditions. Variation of the number of anthrylmethyl group introduced at the phenolic rim of hexahomotrioxacalix[3]arene 1H₃ was achieved through selective O-alkylation using stoichiometric amounts of 9-chloromethylanthracene 5 in acetone to afford the mono-O-alkylated product 2H₂An, the di-O-alkylated product 3HAn₂ and the tri-O-alkylated product partial-cone-4An₃, respectively. Interestingly, by using an acetone/benzene (1:1 v/v) mixed solvent system, the cone-4An₃ was successfully synthesized. These results suggest that the solvent can also control the conformation of the O-alkylation products. The possible reaction routes of the cone-4An₃ and partial-cone-4An₃ are also discussed