Controlling Switching in Bistable [2]Catenanes by Combining Donor–Acceptor and Radical–Radical Interactions

Zhu, Zhixue,Fahrenbach, Albert C.,Li, Hao,Barnes, Jonathan C.,Liu, Zhichang,Dyar, Scott M.,Zhang, Huacheng,Lei, Juying,Carmieli, Raanan,Sarjeant, Amy A.,Stern, Charlotte L.,Wasielewski, Michael R.,Sto American Chemical Society 2012 JOURNAL OF THE AMERICAN CHEMICAL SOCIETY - Vol.134 No.28

<P>Two redox-active bistable [2]catenanes composed of macrocyclic polyethers of different sizes incorporating both electron-rich 1,5-dioxynaphthalene (DNP) and electron-deficient 4,4′-bipyridinium (BIPY<SUP>2+</SUP>) units, interlocked mechanically with the tetracationic cyclophane cyclobis(paraquat-<I>p</I>-phenylene) (CBPQT<SUP>4+</SUP>), were obtained by donor–acceptor template-directed syntheses in a threading-followed-by-cyclization protocol employing Cu(I)-catalyzed azide–alkyne 1,3-dipolar cycloadditions in the final mechanical-bond forming steps. These bistable [2]catenanes exemplify a design strategy for achieving redox-active switching between two translational isomers, which are driven (i) by donor–acceptor interactions between the CBPQT<SUP>4+</SUP> ring and DNP, or (ii) radical–radical interactions between CBPQT<SUP>2(•+)</SUP> and BIPY<SUP>•+</SUP>, respectively. The switching processes, as well as the nature of the donor–acceptor interactions in the ground states and the radical–radical interactions in the reduced states, were investigated by single-crystal X-ray crystallography, dynamic <SUP>1</SUP>H NMR spectroscopy, cyclic voltammetry, UV/vis spectroelectrochemistry, and electron paramagnetic resonance (EPR) spectroscopy. The crystal structure of one of the [2]catenanes in its trisradical tricationic redox state provides direct evidence for the radical–radical interactions which drive the switching processes for these types of mechanically interlocked molecules (MIMs). Variable-temperature <SUP>1</SUP>H NMR spectroscopy reveals a degenerate rotational motion of the BIPY<SUP>2+</SUP> units in the CBPQT<SUP>4+</SUP> ring for both of the two [2]catenanes, that is governed by a free energy barrier of 14.4 kcal mol<SUP>–1</SUP> for the larger catenane and 17.0 kcal mol<SUP>–1</SUP> for the smaller one. Cyclic voltammetry provides evidence for the reversibility of the switching processes which occurs following a three-electron reduction of the three BIPY<SUP>2+</SUP> units to their radical cationic forms. UV/vis spectroscopy confirms that the processes driving the switching are (i) of the donor–acceptor type, by the observation of a 530 nm charge-transfer band in the ground state, and (ii) of the radical–radical ilk in the switched state as indicated by an intense visible absorption (ca. 530 nm) and near-infrared (ca. 1100 nm) bands. EPR spectroscopic data reveal that, in the switched state, the interacting BIPY<SUP>•+</SUP> radical cations are in a fast exchange regime. In general, the findings lay the foundations for future investigations where this radical–radical recognition motif is harnessed in bistable redox-active MIMs in order to achieve close to homogeneous populations of co-conformations in both the ground and switched states.</P><P><B>Graphic Abstract</B> <IMG SRC='http://pubs.acs.org/appl/literatum/publisher/achs/journals/content/jacsat/2012/jacsat.2012.134.issue-28/ja3037355/production/images/medium/ja-2012-037355_0011.gif'></P><P><A href='http://pubs.acs.org/doi/suppl/10.1021/ja3037355'>ACS Electronic Supporting Info</A></P>

NORMALITY CRITERIA FOR A FAMILY OF HOLOMORPHIC FUNCTIONS CONCERNING THE TOTAL DERIVATIVE IN SEVERAL COMPLEX VARIABLES

Cao, Tingbin,Liu, Zhixue Korean Mathematical Society 2016 대한수학회지 Vol.53 No.6

In this paper, we investigate a family of holomorphic functions in several complex variables concerning the total derivative (or called radial derivative), and obtain some well-known normality criteria such as the Miranda's theorem, the Marty's theorem and results on the Hayman's conjectures in several complex variables. A high-dimension version of the famous Zalcman's lemma for normal families is also given.

Radically Enhanced Molecular Switches

Fahrenbach, Albert C.,Zhu, Zhixue,Cao, Dennis,Liu, Wei-Guang,Li, Hao,Dey, Sanjeev K.,Basu, Subhadeep,Trabolsi, Ali,Botros, Youssry Y.,Goddard, William A.,Stoddart, J. Fraser American Chemical Society 2012 JOURNAL OF THE AMERICAN CHEMICAL SOCIETY - Vol.134 No.39

<P>The mechanism governing the redox-stimulated switching behavior of a tristable [2]rotaxane consisting of a cyclobis(paraquat-<I>p</I>-phenylene) (CBPQT<SUP>4+</SUP>) ring encircling a dumbbell, containing tetrathiafulvalene (TTF) and 1,5-dioxynaphthalene (DNP) recognition units which are separated from each other along a polyether chain carrying 2,6-diisopropylphenyl stoppers by a 4,4′-bipyridinium (BIPY<SUP>2+</SUP>) unit, is described. The BIPY<SUP>2+</SUP> unit acts to increase the lifetime of the metastable state coconformation (MSCC) significantly by restricting the shuttling motion of the CBPQT<SUP>4+</SUP> ring to such an extent that the MSCC can be isolated in the solid state and is stable for weeks on end. As controls, the redox-induced mechanism of switching of two bistable [2]rotaxanes and one bistable [2]catenane composed of CBPQT<SUP>4+</SUP> rings encircling dumbbells or macrocyclic polyethers, respectively, that contain a BIPY<SUP>2+</SUP> unit with either a TTF or DNP unit, is investigated. Variable scan-rate cyclic voltammetry and digital simulations of the tristable and bistable [2]rotaxanes and [2]catenane reveal a mechanism which involves a bisradical state coconformation (BRCC) in which only one of the BIPY<SUP>•+</SUP> units in the CBPQT<SUP>2(•+)</SUP> ring is oxidized to the BIPY<SUP>2+</SUP> dication. This observation of the BRCC was further confirmed by theoretical calculations as well as by X-ray crystallography of the [2]catenane in its bisradical tetracationic redox state. It is evident that the incorporation of a kinetic barrier between the donor recognition units in the tristable [2]rotaxane can prolong the lifetime and stability of the MSCC, an observation which augurs well for the development of nonvolatile molecular flash memory devices.</P><P><B>Graphic Abstract</B> <IMG SRC='http://pubs.acs.org/appl/literatum/publisher/achs/journals/content/jacsat/2012/jacsat.2012.134.issue-39/ja306044r/production/images/medium/ja-2012-06044r_0014.gif'></P><P><A href='http://pubs.acs.org/doi/suppl/10.1021/ja306044r'>ACS Electronic Supporting Info</A></P>

ON MEROMORPHIC SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL-DIFFERENCE EQUATIONS OF FIRST ORDER IN SEVERAL COMPLEX VARIABLES

Qibin Cheng,Yezhou Li,Zhixue Liu 대한수학회 2023 대한수학회보 Vol.60 No.2

This paper is concerned with the value distribution for meromorphic solutions $f$ of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions $f$ are uniquely determined by the poles of $f$ and the zeros of $f-c, f-d$ (counting multiplicities) for two distinct small functions $c, d$.

Normality criteria for a family of holomorphic functions concerning the total derivative in several complex variables

Ting-Bin Cao,Zhixue Liu 대한수학회 2016 대한수학회지 Vol.53 No.6

In this paper, we investigate a family of holomorphic functions in several complex variables concerning the total derivative (or called radial derivative), and obtain some well-known normality criteria such as the Miranda's theorem, the Marty's theorem and results on the Hayman's conjectures in several complex variables. A high-dimension version of the famous Zalcman's lemma for normal families is also given.

Xinhuang Tablets Improve Intestinal Barrier Function via Regulating Epithelial Tight Junctions in Dextran Sulfate Sodium-Induced Ulcerative Colitis Mice

Meizhu Wu,Aling Shen,Youqin Chen,Liya Liu,Li Li,Senthilkumar Sankararaman,Hongwei Chen,Bin Guan,Zhixue Zhan,Shuhua Nan,Thomas J. Sferra,Jun Peng 한국식품영양과학회 2021 Journal of medicinal food Vol.24 No.1

Intestinal mucosal barrier dysfunction is involved in the pathogenesis of inflammatory bowel disease, including ulcerative colitis (UC). Xinhuang tablets (XHTs) have been prescribed for several kinds of inflammatory diseases, including UC, whereas its possible underlying molecular mechanisms had never been explored. Mouse model of UC was constructed by DSS treatment and followed by XHT treatment. Disease activity index, histopathological of colonic tissue, tumor necrosis factor-alpha (TNF-α), and serum amyloid A (SAA) levels in serum were further assessed. The underlying mechanism was further explored by determination of the expression of epithelial tight junction-related protein. XHT administration ameliorated dextran sulfate sodium (DSS)-induced clinical symptoms, colonic histological injury, and decreased the circulating levels of TNF-α and SAA. Moreover, XHT treatment significantly increased the protein levels of zona occludens (ZO)-1, whereas decreased the levels of phosphorylation of Elk-1. In conclusion, this study confirmed the therapeutic effects of XHT treatment on UC in a DSS-induced mouse model, and indicated that by increasing expression of epithelial tight junctions and decreasing phosphorylation of Elk-1 might be one of the underlying mechanisms of XHT treatment on UC.

Modelling and Simulating the Spatio-Temporal Correlations of Clustered Wind Power Using Copula

Ning Zhang,Chongqing Kang,Qianyao Xu,Changming Jiang,Zhixu Chen,Jun Liu 대한전기학회 2013 Journal of Electrical Engineering & Technology Vol.8 No.6

Modelling and simulating the wind power intermittent behaviour are the basis of the planning and scheduling studies concerning wind power integration. The wind power outputs are evidently correlated in space and time and bring challenges in characterizing their behaviour. This paper provides a methodology to model and simulate the clustered wind power considering its spatiotemporal correlations using the theory of copula. The sampling approach captures the complex spatiotemporal connections among the wind farms by employing a conditional density function calculated using multidimensional copula function. The empirical study of real wind power measurement shows how the wind power outputs are correlated and how these correlations affect the overall uncertainty of clustered wind power output. The case study validates the simulation technique by comparing the simulated results with the real measurements.

Modelling and Simulating the Spatio-Temporal Correlations of Clustered Wind Power Using Copula

Zhang, Ning,Kang, Chongqing,Xu, Qianyao,Jiang, Changming,Chen, Zhixu,Liu, Jun The Korean Institute of Electrical Engineers 2013 Journal of Electrical Engineering & Technology Vol.8 No.6

Modelling and simulating the wind power intermittent behaviour are the basis of the planning and scheduling studies concerning wind power integration. The wind power outputs are evidently correlated in space and time and bring challenges in characterizing their behaviour. This paper provides a methodology to model and simulate the clustered wind power considering its spatio-temporal correlations using the theory of copula. The sampling approach captures the complex spatio-temporal connections among the wind farms by employing a conditional density function calculated using multidimensional copula function. The empirical study of real wind power measurement shows how the wind power outputs are correlated and how these correlations affect the overall uncertainty of clustered wind power output. The case study validates the simulation technique by comparing the simulated results with the real measurements.