Bounds for the Graham–Pollak theorem for hypergraphs

Let $f_r\left(n\right)$ represent the minimum number of complete $r$-partite $r$-graphs required to partition the edge set of the complete $r$-uniform hypergraph on $n$ vertices. The Graham–Pollak theorem states that $f_2\left(n\right)=n?1$. An upper bound of $(1+o\left(1\right))\left(\genfrac{}{}{0ex}{}{n}{?\frac{r}{2}?}\right)$ was known. Recently this was improved to $\frac{14}{15}(1+o\left(1\right))\left(\genfrac{}{}{0ex}{}{n}{?\frac{r}{2}?}\right)$ for even $r\ge 4$. A bound of $\left[\frac{r}{2}{\left(\frac{14}{15}\right)}^{\frac{r}{4}}+o\left(1\right)\right](1+o\left(1\right))\left(\genfrac{}{}{0ex}{}{n}{?\frac{r}{2}?}\right)$ was also proved recently. Let $c_r$ be the limit of $\frac{f_r\left(n\right)}{\left(\genfrac{}{}{0ex}{}{n}{?\frac{r}{2}?}\right)}$ as $n\to \infty$. The smallest odd $r$ for which $c_r<1$ that was known was for $r=295$. In this note we improve this to $c_{113}<1$ and also give better upper bounds for $f_r\left(n\right)$, for small values of even $r$.     

基于氨基酸的Cu(Ⅱ)-色氨酸MOF催化剂上环氧化物与CO_2环加成反应（英文）

由天然的/生物单元(氨基酸)构成的金属有机框架材料(MOFs)具有自然属性和丰富的酸/碱位和官能团,因而可用于CO_2化学中.本文报道了氨基酸系含铜MOF(CuTrp,Trp=L-色氨酸)的催化效率.以甲醇为溶剂,在室温采用直接混合法合成了CuTrp催化剂,该方法具有很高的能量效率.采用X射线衍射、红外光谱、热重分析、电感耦合等离子体发射光谱法、扫描电镜和BET分析等手段对该催化剂进行了表征.采用环氧化物与CO_2环加成制备环状碳酸酯反应评价了CuTrp催化剂活性.结果表明,在无溶剂条件下,CuTrp催化剂可与四丁基溴化铵助催化剂发生协同作用.通过条件实验确定了优化的反应条件,并基于该实验结果和前期的密度泛函理论计算结果提出了反应机理.另外,CuTrp催化剂在水中也表现出令人满意的稳定性,可重复使用三次以上而活性无明显下降.     

Four cocrystals of thymine with phenolic coformers: influence of the coformer on hydrogen bonding

Cocrystals are molecular solids composed of at least two types of neutral chemical species held together by noncovalent forces. Crystallization of thymine [systematic name: 5‐methylpyrimidine‐2,4(1H,3H)‐dione] with four phenolic coformers resulted in cocrystal formation, viz. catechol (benzene‐1,2‐diol) giving thymine–catechol (1/1), C₅H₆N₂O₂·C₆H₆O₂, (I), resorcinol (benzene‐1,3‐diol) giving thymine–resorcinol (2/1), 2C₅H₆N₂O₂·C₆H₆O₂, (II), hydroquinone (benzene‐1,4‐diol) giving thymine–hydroquinone (2/1), 2C₅H₆N₂O₂·C₆H₆O₂, (III), and pyrogallol (benzene‐1,2,3‐triol) giving thymine–pyrogallol (1/2), C₅H₆N₂O₂·2C₆H₆O₃, (IV). The resorcinol molecule in (II) occupies a twofold axis, while the hydroquinone molecule in (III) is situated on a centre of inversion. Thymine–thymine base pairing is common across all four structures, albeit with different patterns. In (I)–(III), the base pair is propagated into an infinite one‐dimensional ribbon, whereas it exists as a discrete dimeric unit in (IV). In (I)–(III), the two donor N atoms and one carbonyl acceptor O atom of thymine are involved in thymine–thymine base pairing and the remaining carbonyl O atom is hydrogen bonded to the coformer. In contrast, in (IV), just one donor N atom and one acceptor O atom are involved in base pairing, and the remaining donor N atom and acceptor O atom of thymine form hydrogen bonds to the coformer molecules. Thus, the utilization of the donor and acceptor atoms of thymine in the hydrogen bonding is influenced by the coformers.     

Structural characterization,photophysical and BSA binding interaction studies of 4,4′-bis(benzimidazolyl)-2,2′-bipyridine

The title compound is synthesized from the precursors 1,2-diaminobenzene and 2,2′-bipyridine-4,4′-dicarboxylic acid (dcbpy) and characterized using ESI-Mass, ¹H NMR, FT-IR and single crystal X-ray analysis. We are the first to report the crystal structure of the 4,4′-bis(benzimidazolyl)-2,2′-bipyridine (bimbpy) ligand. The photophysical properties of the compound in dimethyl sulfoxide and in the aqueous medium are studied. The interaction studies of bimbpy with bovine serum albumin (BSA) were performed with the fluorescence technique and it strongly binds with BSA.     

Synthesis of graft copolymers onto styrenic polymer backbone via “grafting from” raft process

A new synthetic methodology is developed for preparing graft copolymers via RAFT polymerization method by the “R group approach” onto styrenic polymers. In this approach, latent sites of the styrenic polymer was brominated first and then converted into macro‐RAFT agents with pyrazole and thio dodecyl as the Z groups. This was used to synthesize graft copolymer such as polystyrene‐graft‐polymethyl methacrylate (PS‐g‐PMMA), polystyrene‐graft‐poly(isobornyl acrylate), polystyrene‐graft‐poly[2‐(acetoacetoxy)ethyl methacrylate] (PS‐g‐PAEMA), and poly(para‐methoxystyrene)‐graft‐polystyrene (P(p‐MS)‐g‐PS). The polymers are characterized by gel permeation chromatography, ¹H NMR, IR, and atomic force microscopy (AFM). The morphology of PS‐g‐PMMA in THF was investigated using AFM and island‐like features were noticed. The AFM studies of the PS‐g‐PAEMA graft copolymers revealed the formation of globules and ribbon‐like morphological features. The PS‐g‐PAEMA graft copolymers form complex with Fe(III) in dimethylformamide and the AFM studies suggest the formation of globular superstructures. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

First‐Row Transition‐Metal–Diborane and –Borylene Complexes

A combined experimental and quantum chemical study of Group 7 borane, trimetallic triply bridged borylene and boride complexes has been undertaken. Treatment of [{Cp*CoCl}₂] (Cp*=1,2,3,4,5‐pentamethylcyclopentadienyl) with LiBH₄ ? thf at ?78 °C, followed by room‐temperature reaction with three equivalents of [Mn₂(CO)₁₀] yielded a manganese hexahydridodiborate compound [{(OC)₄Mn}(η⁶‐B₂H₆){Mn(CO)₃}₂(μ‐H)] ( 1 ) and a triply bridged borylene complex [(μ₃‐BH)(Cp*Co)₂(μ‐CO)(μ‐H)₂MnH(CO)₃] ( 2 ). In a similar fashion, [Re₂(CO)₁₀] generated [(μ₃‐BH)(Cp*Co)₂(μ‐CO)(μ‐H)₂ReH(CO)₃] ( 3 ) and [(μ₃‐BH)(Cp*Co)₂(μ‐CO)₂(μ‐H)Co(CO)₃] ( 4 ) in modest yields. In contrast, [Ru₃(CO)₁₂] under similar reaction conditions yielded a heterometallic semi‐interstitial boride cluster [(Cp*Co)(μ‐H)₃Ru₃(CO)₉B] ( 5 ). The solid‐state X‐ray structure of compound 1 shows a significantly shorter boron–boron bond length. The detailed spectroscopic data of 1 and the unusual structural and bonding features have been described. All the complexes have been characterized by using ¹H, ¹¹B, ¹³C NMR spectroscopy, mass spectrometry, and X‐ray diffraction analysis. The DFT computations were used to shed light on the bonding and electronic structures of these new compounds. The study reveals a dominant B?H?Mn, a weak B?B?Mn interaction, and an enhanced B?B bonding in 1 .     

Visible‐Light/Photoredox‐Mediated sp3 CH Functionalization and Coupling of Secondary Amines with Vinyl Azides in Flow Microreactors

Structurally diverse imidazole derivatives were synthesized by a visible‐light/[Ru(bpy)₃][(PF₆)₂]‐mediated coupling of vinyl azides and secondary amines in flow microreactors. This operationally simple and atom‐economical protocol allows the formation of three new C?N bonds through the functionalization of sp³ C?H bonds adjacent to the secondary nitrogen atom. In order to get mechanistic insight of the coupling reaction, several control experiments were carried out and discussed.     

A convenient,rapid, and general synthesis of α-oxo thiocyanates using clay supported ammonium thiocyanate

A very rapid, convenient, and general method for the synthesis of α-oxo thiocyanates has been described by using clay supported ammonium thiocyanate. The procedure avoids the use of additional catalyst, solvent, aqueous work-up and the yields are high. Moreover, the method is applicable for a variety of aryl, heteroaryl, alkyl α-halo carbonyls, β-keto tosylates, α-halo β-dicarbonyl, α-tosyl, β-dicarbonyl, alkyl halide, and alkyl tosylates.     

Thiazole–Chalcone Hybrids as Prospective Antitubercular and Antiproliferative Agents: Design,Synthesis, Biological,Molecular Docking Studies and In Silico ADME Evaluation

Compounds bearing thiazole and chalcone pharmacophores have been reported to possess excellent antitubercular and anticancer activities. In view of this, we designed, synthesized and characterized a novel series of thiazole–chalcone hybrids (1–20) and further evaluated them for antitubercular and antiproliferative activities by employing standard protocols. Among the twenty compounds, chalcones 12 and 7, containing 2,4-difluorophenyl and 2,4-dichlorophenyl groups, showed potential antitubercular activity higher than the standard pyrazinamide (MIC = 25.34 µM) with MICs of 2.43 and 4.41 µM, respectively. Chalcone 20 containing heteroaryl 2-thiazolyl moiety exhibited promising antiproliferative activity against the prostate cancer cell line (DU-145), higher than the standard methotrexate (IC₅₀ = 11 ± 1 µM) with an IC₅₀ value of 6.86 ± 1 µM. Furthermore, cytotoxicity studies of these compounds against normal human liver cell lines (L02) revealed that the target molecules were comparatively less selective against L02. Additional computational studies using AutoDock predicted the key binding interactions responsible for the activity and the SwissADME tool computed the in silico drug likeliness properties. The lead compounds generated through this study, create a way for the optimization and development of novel drugs against tuberculosis infections and prostate cancer.