Second order Randić index of phenylenes and their corresponding hexagonal squeezes

Given PH a phenylene, and HS its corresponding hexagonal squeeze, their second-order Randić indices are denoted by ²χ(P H) and ²χ(H S), respectively. The expressions of both ²χ(P H) and ²χ(H S) in terms of their inlet features are found, and a simple relation is estabblished between the second order Randić index of a phenylene and of the corresponding hexagonal squeeze.     

Computing weighted Szeged and PI indices from quotient graphs

The weighted (edge-)Szeged index and the weighted (vertex-)PI index are modifications of the (edge-)Szeged index and the (vertex-)PI index, respectively, because they take into account also the vertex degrees. As the main result of this article, we prove that if G is a connected graph, then all these indices can be computed in terms of the corresponding indices of weighted quotient graphs with respect to a partition of the edge set that is coarser than the Θ^*-partition. If G is a benzenoid system or a phenylene, then it is possible to choose a partition of the edge set in such a way that the quotient graphs are trees. As a consequence, it is shown that for a benzenoid system, the mentioned indices can be computed in sublinear time with respect to the number of vertices. Moreover, closed formulas for linear phenylenes are also deduced.     

PI indices of pericondensed benzenoid graphs

The Padmakar–Ivan (PI) index is a graph invariant defined as the summation of the sums of n _eu (e|G) and n _ev (e|G) over all the edges e = uv of a connected graph G, i.e., , where n _eu (e|G) is the number of edges of G lying closer to u than to v and n _ev (e|G) is the number of edges of G lying closer to v than to u. An efficient formula for calculating the PI index of a class of pericondensed benzenoid graphs consisting of three rows of hexagonal of various lengths.     

On normalized Laplacians,multiplicative degree-Kirchhoff indices,and spanning trees of the linear [n]phenylenes and their dicyclobutadieno derivatives

Let be the molecular graph of the linear [n] phenylene with n hexagons and n − 1 squares, and let be the graph obtained by attaching four-membered rings to the terminal hexagons of . In this article, the normalized Laplacian spectrum of consisting of the eigenvalues of two symmetric tridiagonal matrices of order 3n is determined. An explicit closed-form formula of the multiplicative degree-Kirchhoff index (respectively the number of spanning trees) of is derived. Similarly, explicit closed-form formulas of the multiplicative degree-Kirchhoff index and the number of spanning trees of are obtained. It is interesting to see that the multiplicative degree-Kirchhoff index of (respectively ) is approximately to one half of its Gutman index.     

Double hexagonal chains with maximal Hosoya index and minimal Merrifield–Simmons index

It is well known that the two graph invariants, “the Hosoya index” and “the Merrifield–Simmons index” are important ones in structural chemistry. The extremal hexagonal chains with respect to the Hosoya index and Merrifield–Simmons index are determined by Gutman and Zhang (J. Math. Chem., 12 (1993) 197–210, 27 (2000) 319–329 and J. Sys. Sci. Math. Sci., 18 (4) (1998) 460–465). In this paper, we will consider a type of the pericondensed hexagonal system. The double hexagonal chains with maximal Hosoya index and minimal Merrifield Simmons index are determined.     

Kirchhoff index of linear hexagonal chains

The resistance distance r_ij between vertices i and j of a connected (molecular) graph G is computed as the effective resistance between nodes i and j in the corresponding network constructed from G by replacing each edge of G with a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all pairs of vertices. In this work, according to the decomposition theorem of Laplacian polynomial, we obtain that the Laplacian spectrum of linear hexagonal chain L_n consists of the Laplacian spectrum of path P_2n+1 and eigenvalues of a symmetric tridiagonal matrix of order 2n + 1. By applying the relationship between roots and coefficients of the characteristic polynomial of the above matrix, explicit closed‐form formula for Kirchhoff index of L_n is derived in terms of Laplacian spectrum. To our surprise, the Krichhoff index of L_n is approximately to one half of its Wiener index. Finally, we show that holds for all graphs G in a class of graphs including L_n. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Novel PI Indices of Hexagonal Chains

Problems don't hung on trees. Formulation of a good problem is often the most important part of a (theoretical) research. New problems usually arise when you try to solve old problems. Ivan Gutman, June 27, 1995.The Padmakar–Ivan (PI) index of hexagonal chains (i.e., the molecular graphs of unbranched catacondensed benzenoid hydrocarbons) is examined. The index PI is a graph invariant defined as the summation of the sums of edges of n _eu and n _ev over all the edges of connected graph G, where n _eu is the number of edges of G lying closer to u than to v and n _ev is the number of edges of G lying closer to v than to u. An efficient calculation of formula for PI for hexagonal chains are put forward.     

Synthesis and characterization of alkaline‐soluble triazine‐based poly(phenylene sulfide)s with high refractive index and low birefringence

High‐refractive‐index (high‐n) polymers (HRIPs) with a high optical transparency are highly needed in advanced optoelectronic devices. In this work, we report the synthesis and characterization of a series of high‐n, transparent, totally colorless, and high‐sulfur‐containing poly(phenylene sulfide)s (PPSs) bearing a triazine unit. Two new triazine monomers T1 and T2 with hydroxyl and tert‐butyl acetate side chains, respectively, were designed and synthesized to develop PPSs with high‐n and high alkaline solubility. These PPSs were prepared by the single‐phase polycondensation from T1 / T2 and commercial aromatic dithiols such as 4,4′‐thiobisbenzenethiol ( TBT ) and benzene‐1,3‐dithiol ( BDT ), achieving very high‐n up to 1.7530 at 633 nm, a high optical transparency (T% > 90% @400 nm) and low birefringence (Δn = 0.0014–0.0080), and exhibiting high potential on the application of high‐n photoresists. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 724–731     

The evaluation of spectral moments for molecular graphs of phenylenes

The evaluation of some spectral moments for phenylenes is considered. Explicit topological formulae for the fourth, sixth and eighth moments are derived. This was achieved by adopting the method of Hall [1], which was originally applied to benzenoid systems, and applying it to molecular graphs of phenylenes. It is shown that the moments considered in this paper can be expressed in terms of three mutually independent graphical invariants. Received: 17 October 1996 / Accepted: 18 April 1997     

烷基的憎水指数

本文提出憎水指数HBI来定量烷基的憎水能力, 结果表明: 烷基的憎水指数能较好地预报有机物在水中的溶解度、在正辛醇/水两相中的分配系数。     

Quantitative characterization of optical anisotropy in high refractive index films

Waveguide coupling measurements of polymers have largely concentrated on the application of mode analysis to the study of thin supported films (such as spin coatings). The use of prism coupling to study thick, freestanding polymer films, however, has not been reported. In this paper, the ability of prism coupling to characterize the three-dimensional optical properties of thick, freestanding polymer films and sheets is demonstrated. A modified prism coupling procedure is described that allows the determination of all three principal refractive indices in thick, three-dimensionally anisotropic freestanding films. A Metricon prism coupler is used in a manner similar to an Abbé refractometer for the measurement of isotactic polypropylene, poly(ethylene terephthalate), PMDA-ODA polyimide, and poly(phenylene sulfide). Three series of PMDA-ODA films are also investigated in this study. The first series has been drawn to different extensions from three-dimensionally random films. The second series has random orientation in the plane of the film but different degrees of planarity with respect to the through direction. The third series are commercial films of varying thickness. These three series of films are compared as to the optical an-isotropy that is developed from the three different fabrication processes. © 1993 John Wiley & Sons, Inc.     

On the normalized Laplacian of Möbius phenylene chain and its applications

Let denote a molecular graph of linear [n] phenylene with n hexagons and n squares, and let the Möbius phenylene chain be the graph obtained from the by identifying the opposite lateral edges in reversed way. Utilizing the decomposition theorem of the normalized Laplacian characteristic polynomial, we study the normalized Laplacian spectrum of , which consists of the eigenvalues of two symmetric matrices ℒ _R and ℒ _Q of order 3n. By investigating the relationship between the roots and coefficients of the characteristic polynomials of the two matrices above, we obtain an explicit closed-form formula of the multiplicative degree-Kirchhoff index as well as the number of spanning trees of . Furthermore, we determine the limited value for the quotient of the multiplicative degree-Kirchhoff index and the Gutman index of .     

Enumeration of the isomers of phenylenes

Summary The [h]phenylene C_6h H_2h+4 isomers are enumerated up toh=12. The numbers are compared with old and new data for C _n H₅ isomers of benzenoids, fluoranthenoids and biphenylenoids.

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Anzahl möglicher Isomerer von Phenylenen

Zusammenfassung Die Anzahl der [h]Phenylen-Isomeren C_6h H_2h+4 wurde bish=12 ausgewertet. Die Zahlen wurden mit alten und neuen Daten für C _n H _s -Isomere von Benzenoiden, Fluoranthenoiden und Biphenyloiden verglichen.

     

Isoform Selective PI3K-beta Inhibitors

Although PI3K/AKT has undoubtedly been one of the most important pathways that impact tumorigenesis and proliferation, PI3K‐beta has not been considered as a stand‐alone target for potential cancer treatment until the recent discovery of the key role that PI3K‐beta plays in phosphatase and TENsin homolog (PTEN)‐deficient tumors. Medicinal chemistry efforts from the pharmaceutical industry and academia in the past few years have led to significant advancements in understanding beta isoform selectivity and in the development of a clinical drug candidate.     

Design,synthesis and biological evaluation of acylhydrazone derivatives as PI3K inhibitors

Since the PI3K signaling pathway is the most commonly activated in human cancers,inhibition of PI3K is a promising approach to cancer therapy.In this study,a series of 2-methyl-5-nitrobenzeneacylhydrazones were designed and synthesized.All the new derivatives were tested by p110α enzymatic and Rh30 cellular assays.Further enzyme selectivity profiling proved that 6e and 7 were potential selective PI3K inhibitors.     

聚苯胺在聚酰亚胺膜基体表面的原位沉积成膜机理

采用分散聚合方法,在聚酰亚胺(PI)膜基体表面原位成膜,制备聚苯胺-聚酰亚胺-聚苯胺(PANI-PI-PANI)导电复合膜.通过反应历程跟踪、扫描电镜(SEM)及静滴接触角-界面张力测量仪研究了PANI在PI基体表面原位成膜的过程及其驱动力.结果表明,PANI在PI基体表面的成膜过程有3个阶段:含苯胺的结构单元(包括An盐酸盐、An阳离子自由基及低聚物)在PI表面吸附成核阶段、膜快速增长阶段和增长完成阶段;PANI膜由PANI小颗粒逐渐堆积而成,直至覆盖整个PI膜表面;PANI成膜的主要驱动力来自亲水-疏水相互作用.     

The reinforcing effect of clay on the mechanical properties of nitric acid–treated fluorosilicone rubber filled PI composites

The mechanical behaviour of fluorosilicone rubber–filled PI composites with and without clay was investigated. The clay filled fluorosilicone rubber composite had the highest interlaminar shear strength value of all the combinations because its higher bond strength may have hindered a large fibre/matrix debonding. The maximum tensile strength was observed for 20 vol% fluorosilicone rubber/PI/5vol%clay composite. The interlaminar shear strength of clay filled fluorosilicone rubber/PI composite was greater than that of fluorosilicone rubber/PI composite, which shows that the adhesion factor of the combination of the PI and fluorosilicone rubber was greater.     

Effect of 2-D BN on enhanced corona-resistant characteristic of PI/AlN+BN composite investigated by quasi-in-situ technology

Incorporating two-dimensional (2-D) boron nitride (BN) into polyimide/aluminum nitride (PI/AlN) renders a simple strategy in producing new ternary composite films with longer corona aging life and higher breakdown strength compared with PI/AlN. During corona aging process, the effects of 2-D BN on adjusting the microstructure evolution of ternary composites were investigated using quasi-in-situ technology systematically as follow: (SEM), (AFM), (FTIR), (XRD) and (SAXS) at different corona time. Quasi-in-situ characterization results show that the corona aging modes of the two composite films are quite different, the introduction of BN nanosheets could protect the C–N–C and C–O–C bonds from breaking as well as accelerate the fillers expose via autoxidation reaction. In addition, BN nanosheets could induce the distance between PI molecular chains to shorten during the corona process, resulting in more dense structures coordinating with AlN and PI. Different corona aging mechanism compared with that of the PI/AlN composite films was proposed. This work demonstrated the effect of 2-D BN nanosheets in the PI/AlN+BN ternary composites, which can be used to expand their application in insulating polymer based composites.