Cycle-maximal triangle-free graphs

We conjecture that the balanced complete bipartite graph _{K⌊n/2⌋,⌈n/2⌉}$K_{\lfloor n/2\rfloor ,\lceil n/2\rceil }$ contains more cycles than any other n$n$-vertex triangle-free graph, and we make some progress toward proving this. We give equivalent conditions for cycle-maximal triangle-free graphs; show bounds on the numbers of cycles in graphs depending on numbers of vertices and edges, girth, and homomorphisms to small fixed graphs; and use the bounds to show that among regular graphs, the conjecture holds. We also consider graphs that are close to being regular, with the minimum and maximum degrees differing by at most a positive integer k$k$. For k=1$k=1$, we show that any such counterexamples have n≤91$n\le 91$ and are not homomorphic to _C5$C_5$; and for any fixed k$k$ there exists a finite upper bound on the number of vertices in a counterexample. Finally, we describe an algorithm for efficiently computing the matrix permanent (a #P$\#P$-complete problem in general) in a special case used by our bounds.     

Gel-assisted synthesis of anatase TiO2 nanoparticles and application for electrochemical determination of L-tryptophan

Anatase titanium dioxide nanoparticles (TiO₂-NPs) were synthesized with and without gelatin via the sol-gel method. The TiO₂-NPs were characterized by a number of techniques, such as thermogravimetric analysis (TGA), X-ray diffraction analysis (XRD), transmission electron microscopy (TEM), fourier transform infrared spectroscopy (FT-IR) and ultraviolet visible spectroscopy (UV-Vis). The particle sizes of the TiO₂-NPs prepared with and without gelatin were ～13 and ～17 nm, respectively. The main advantage of using gelatin as a stabilizing agent is that it provides long-term stability for nanoparticles by preventing particles agglomeration. The results indicated that gelatin was a reliable green stabilizer, which can be used as a polymerization agent in the sol-gel method for synthesis of tiny size TiO₂-NPs. Moreover, the composite film was prepared by synthesized TiO₂-NPs nanoparticles and multi wall carbon nanotube (MWNT) on glassy carbon electrode (TiO₂-MWNT/GCE). The TiO₂-MWNT/GCE responded linearly to L-tryptophan (L-Trp) in the concentration of 1.0 × 10^?6 to 1.5 × 10^?4 M with detection limit of 5.2 × 10^?7 M at 3 using amperometry. The studied sensor exhibited good reproducibility and long-term stability.     

Redox Chemistry of a Hydroxyphenyl‐Substituted Borane

Chemical reduction of a hydroxyphenyl‐substituted borane triggers a sequential electron‐ and intramolecular hydrogen‐atom‐transfer process to afford a hydridoborate phenoxide dianion. On the other hand, hydrogen‐atom abstraction of the borane leads to the isolation of a neutral borylated phenoxyl radical, which can be transformed to the corresponding benzoquinone borataalkene derivative by reduction with cobaltocene.     

Crowning Proteins: Modulating the Protein Surface Properties using Crown Ethers

Crown ethers are small, cyclic polyethers that have found wide‐spread use in phase‐transfer catalysis and, to a certain degree, in protein chemistry. Crown ethers readily bind metallic and organic cations, including positively charged amino acid side chains. We elucidated the crystal structures of several protein‐crown ether co‐crystals grown in the presence of 18‐crown‐6. We then employed biophysical methods and molecular dynamics simulations to compare these complexes with the corresponding apoproteins and with similar complexes with ring‐shaped low‐molecular‐weight polyethylene glycols. Our studies show that crown ethers can modify protein surface behavior dramatically by stabilizing either intra‐ or intermolecular interactions. Consequently, we propose that crown ethers can be used to modulate a wide variety of protein surface behaviors, such as oligomerization, domain–domain interactions, stabilization in organic solvents, and crystallization.     

Dinitrosyl Iron Complex [K-18-crown-6-ether][(NO)2Fe(MePyrCO2)]: Intermediate for Capture and Reduction of Carbon Dioxide

Continued efforts are made for the utilization of CO₂ as a C₁ feedstock for regeneration of valuable chemicals and fuels. Mechanistic study of molecular (electro-/photo-)catalysts disclosed that initial step for CO₂ activation involves either nucleophilic insertion or direct reduction of CO₂. In this study, nucleophilic activation of CO₂ by complex [(NO)₂Fe(μ-^MePyr)₂Fe(NO)₂]²⁻ ( 2 , ^MePyr=3-methylpyrazolate) results in the formation of CO₂-captured complex [(NO)₂Fe(^MePyrCO₂)]⁻ ( 2-CO₂ , ^MePyrCO₂=3-methyl-pyrazole-1-carboxylate). Single-crystal structure, spectroscopic, reactivity, and computational study unravels 2-CO₂ as a unique intermediate for reductive transformation of CO₂ promoted by Ca²⁺. Moreover, sequential reaction of 2 with CO₂, Ca(OTf)₂, and KC₈ established a synthetic cycle, 2 → 2-CO₂ → [(NO)₂Fe(μ-^MePyr)₂Fe(NO)₂] ( 1 ) → 2 , for selective conversion of CO₂ into oxalate. Presumably, characterization of the unprecedented intermediate 2-CO₂ may open an avenue for systematic evaluation of the effects of alternative Lewis acids on reduction of CO₂.     

The inhibition profiles of 4'-acylpyrrole–5-fluoroindolin-2-ones with a C-3' side chain for VEGFR2, PDGFR-β, and FGFR-1 protein kinases

In this study, we reported the inhibition profiles of 4′-acylpyrrole–5-fluoroindolin-2-one 3 with a C-3′ side chain for VEGFR2, PDGFR-β, and FGFR-1 protein kinases. The pyrrole-fused cyclohexanone moiety provided 3 with the best potency to inhibit the three kinases, and the C-3′ side chains contributed to the different inhibition profiles of 3 . Compound 3b with a C-3′ 2-carboxylethyl side chain showed good potency for the three kinase (IC₅₀: 25–260 nM), and compound 3g with a N,N-dialkyl-2-carbamoylethyl side chain was more active for VEGFR2 (IC₅₀: 59 nM) and PDGFR-β (IC₅₀: 16 nM) than FGFR-1 (IC₅₀: 1.7 μM). The C-3′ 3-(dialkylamino)propyl side chain accomplished 3h – j as selective PDGFR-β inhibitors (IC₅₀: 7.8–13 nM). Compound 3b was further investigated and found potent to inhibit VEGF- and FGF-dependent cell proliferation with moderate in vivo anticancer activity. Results from docking simulations revealed that the interactions of 3b with VEGFR2 and FGFR-1 which could account for the different inhibition profiles of 3 .     

Cascade One‐Pot Synthesis of Orange‐Red‐Fluorescent Polycyclic Cinnolino[2,3‐f]phenanthridin‐9‐ium Salts by Palladium(II)‐Catalyzed C−H Bond Activation of 2‐Azobiaryl Compounds and Alkenes

Quaternary ammonium salts were synthesized in moderate to good yields through double oxidative C?H bond activation on azobenzenes. The mechanism of the highly regioselective reaction of 2‐azobiaryls with alkenes to give orange‐red‐fluorescent cinnolino[2,3‐f]phenanthridin‐9‐ium salts and 15H‐cinnolino[2,3‐f]phenanthridin‐9‐ium‐10‐ide is proposed to involve ortho C?H olefination of the 2‐azobiaryl compound with the alkene, intramolecular aza‐Michael addition, concerted metalation–deprotonation (CMD), reductive elimination, and oxidation.     

Preparation of Tin Oxide-Based Metal Oxide Particles

Tin oxide-doped hybrid particles were prepared by a wet chemical process with organic-inorganic (phenyl/silica) hybrid particles in an alcoholic solution. The phenyl/silica hybrid particles, with a diameter of ca. 790 nm were used as a new support material for tin oxide (SnO₂) particles from tin(IV) chloride. The surface of the particles was modified via nitration of aromatic groups in the particles, to promote formation of the tin oxide coating on the particles. The thickness and surface morphology of the tin oxide layer coated on the nitrated-phenyl/silica hybrid particles could be controlled by varying the tin(IV) chloride concentration and reaction time. The size and morphology of the resultant particles were investigated with field emission scanning electron microscopy (FE-SEM) and transmission electron microscopy (TEM). The particles obtained were also characterised by infrared (FTIR) and solid-state ¹³C magic angle spinning nuclear magnetic resonance (¹³C-CP/MAS NMR) spectroscopy. The effect of processing parameters on the crystallinity and structure of the doped hybrids were confirmed by X-ray diffraction (XRD) patterns.     

The Relationship Between Stock Markets Of Major Developed Countries And Asian Emerging Markets

With the emergence of new capital markets and liberalization of stock markets in recent years, there has been an increase in investors' interest in international diversification. This is so because international diversification allows investors to have a larger basket of foreign securities to choose from as part of their portfolio assets, so as to enhance the reward-to-volatility ratio. This benefit would be limited if national equity markets tend to move together in the long run. This paper thus studies the issue of co-movement between stock markets in major developed countries and those in Asian emerging markets using the concept of cointegration. We find that there is co-movement between some of the developed and emerging markets, but some emerging markets do differ from the developed markets with which they share a long-run equilibrium relationship. Furthermore, it has been observed that there has been increasing interdependence between most of the developed and emerging markets since the 1987 Stock Market Crash. This interdependence intensified after the 1997 Asian Financial Crisis. With this phenomenon of increasing co-movement between developed and emerging stock markets, the benefits of international diversification become limited.