On the second largest Laplacian eigenvalues of graphs

The second largest Laplacian eigenvalue of a graph is the second largest eigenvalue of the associated Laplacian matrix. In this paper, we study extremal graphs for the extremal values of the second largest Laplacian eigenvalue and the Laplacian separator of a connected graph, respectively. All simple connected graphs with second largest Laplacian eigenvalue at most 3 are characterized. It is also shown that graphs with second largest Laplacian eigenvalue at most 3 are determined by their Laplacian spectrum. Moreover, the graphs with maximum and the second maximum Laplacian separators among all connected graphs are determined.     

Improving artificial bee colony with one-position inheritance mechanism

Artificial bee colony (ABC) algorithm simulates the foraging behavior of honey bees. It shows good performance in many application problems and large scale optimization problems. However, variation of a solution in the ABC algorithm is only employed on one dimension of the solution. This would sometimes hamper the convergence speed of the ABC algorithm, especially for large scale optimization. This paper proposes a one-position inheritance (OPI) mechanism to overcome this drawback. The OPI mechanism aims to promote information exchange amongst employed bees of the ABC algorithm. For separable function, OPIABC has a higher probability resulting in function value improvement of the worst positions than ABC. Through one-position information exchange, the OPI mechanism can assist the ABC algorithm to find promising solutions. This mechanism has been tested on a set of 25 test functions with $D= 30$ and on CEC 2008 test suite with $D= 100$ and 1,000. Experimental results show that the OPI mechanism can speed up the convergence of the ABC algorithm. After the use of OPI, the performance of the ABC algorithm is significantly improved for both rotated problems and large scale problems. OPIABC is also competitive on both test suites comparing with other recently proposed swarm intelligence metaheuristics (e.g. SaDE and PSO2011). Furthermore, the OPI mechanism can greatly enhance the performance of other improved ABC algorithms.     

L（j,k）-number of Direct Product of Path and Cycle

For positive numbers j and k, an L(j,k)-labeling f of G is an assignment of numbers to vertices of G such that |f(u)-f(v)|≥j if uv∈E(G), and |f(u)-f(v)|≥k if d(u,v)=2. Then the span of f is the difference between the maximum and the minimum numbers assigned by f. The L(j,k)-number of G, denoted by λj,k(G), is the minimum span over all L(j,k)-labelings of G. In this paper, we give some results about the L(j,k)-number of the direct product of a path and a cycle for j≤k.     

Cyclic bandwidth with an edge added

B_c(G) denotes the cyclic bandwidth of graph G. In this paper, we obtain the maximum cyclic bandwidth of graphs of order p with adding an edge as follows:

     

Syntheses and Structural Characterization of 1D Coordination Polymers of Transition‐Metal Atoms Containing 2,4‐Pyridinedicarboxylate Bridges

By employing one bridging ligand, 2,4‐pyridinedicarboxylate (2,4‐pda^2?), three one‐dimensional (1D) coordination polymers of [Cu(2,4‐pda)(H₂O)₂]_∞ ( 1 ), {[Cu₄(2,4‐pda)₄(H₂O)₈]·3H₂O}_∞ ( 2 ), and {[Cd(2,4‐pda)(H₂O)₃]·H₂O}_∞ ( 3 ) were synthesized. A simple zigzag polymeric chain is observed for both 1 and 3 , but a railroad‐like zigzag polymeric chain is observed for 2. Almost all water molecules, whether coordinated or not, are involved in hydrogen bonding interactions and help to tie up the 1D polymeric chains of 1‐3 into a three‐dimensional (3D) network. A comparison about the coordination geometries in all similar coordination polymers available to date is also included.     

Photoinduced Reaction of α-Bromoacetophenone with Thiosulfonate: Synthesis of β-Keto Thiosulfone

A photoinduced synthesis of β-keto thiosulfone/β-keto selenosulfone by the reaction of α-bromoacetophenone with thiosulfonate/selenosulfonate under metal-free and visible light irradiation conditions is developed. Two C−S bonds or one C−S bond and one C−Se bond were constructed simultaneously.     

Zn2+@Polyvinylpyrrolidone and Urushiol Preparation of Nanofibrous Membranes and Their Synergistic Effect

In this study, lacquer is gathered from a lacquer tree and rotary evaporation is used to remove impurities to obtain urushiol. Next, 10 mL of anhydrous ethanol serves as the solvent for blending polyvinylpyrrolidone (PVP) at a specified content (0.7 g and 0.2–0.7 g urushiol) to form an electrospinning solution. Electrospinning is carried out with a voltage of 18 kV to prepare PVP/urushiol nanofibrous membranes. At a ratio of 7/4, the PVP/urushiol nanofibrous membranes are not eroded in 98% sulfuric acid and these membranes also demonstrate a 50–60% antibacterial effect against Staphylococcus aureus and Escherichia coli. Moreover, the antibacterial effect can be boosted to 98% with the incorporation of zinc ions. The results indicate that anhydrous ethanol can remove the sensitization of urushiol from PVP/urushiol membranes. Furthermore, animal test results indicate that when rats are in contact with PVP/urushiol anhydrous ethanol for 48 h, their skins are free from dark brown skin allergy. The presence of PVP eliminates the sensitization of urushiol, and the nanofibrous membranes demonstrate low toxicity. Hence, urushiol is the only natural material that enables PVP to withstand 98% sulfuric acid as well as acquire hydrolyzability, thereby qualify PVP as a medical material.     

Accelerated direct electrochemistry of hemoglobin based on hemoglobin-carbon nanotube (Hb-CNT) assembly

In this study, we have demonstrated that hemoglobin can be coupled to acid-treated multiwall carbon nanotubes in the presence of 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide (EDC) and assembled as hemoglobin-carbon nanotube (Hb-CNT) composites. Our observations of the electrochemical studies demonstrate that the electrochemical response of Hb-CNT assembled in the presence of EDC is much higher than that in the absence of EDC. It is evident that the direct electron transfer of hemoglobin could be effectively accelerated in the Hb-CNT assembly by using EDC on a glassy carbon electrode (GCE), and the relative electron transfer rate constant K(s) is found to be 1.02+/-0.05 s(-1). The results of our studies illustrate that the assembly of hemoglobin-multiwall carbon nanotubes using EDC could provide a novel strategy to effectively facilitate the direct electrochemistry of heme-containing proteins, which could be further utilized as a promising biosensor for some specific biological substrate and related biological process.     

Selective Determination of Vitamin B2 at Electrochemically Activated Glassy Carbon Electrode

Electrochemically activated glassy carbon electrodes were applied to the preconcentration and electroanalysis of Vitamin B₂ (VB₂) in multivitamin preparation. Voltammetric peak currents showed linear response for VB₂ concentrations in the range between 0.1 to 3.0 M with a large slope of 12.2 AM^-1 and a correlation coefficient of 0.996. The reproducibility of the voltammetric measurements was usually less than 7% RSD for five replicate measurements. Common vitamin and metal species did not interfere the determination.     

A novel electrochemical approach for fabrication of photoluminescent erbium-doped porous silicon

21 /cm³. After this new ECD treatment, PS:Er was found to emit much more intense room-temperature visible photoluminescence than both the porous silicon control and the PS:Er prepared by constant-current ECD. Room-temperature IR photoluminescence around 1.54 μm was observed for the first time without any post-doping annealing. Received: 3 September 1998/Accepted: 9 September 1998