An operator on ascent sequences

We solve two problems about ascent sequences: how to get the ascent sequence of the reflection of A with respect to its antidiagonal for a matrix A∈ Intn and its ascent sequences, and how to determine the ascent sequence of A+B for k×k matrices A∈ Intn and B∈ Intm. We give the other definition of ascent sequence and get M-sequence. For the first question, we define M-sequence of A and rewrite the ascent sequences as another form.We build the bijection between M-sequences and ascent sequences and prove that our bijection is well-defined. For the second question, we define an operation on M-sequences. On the basis of the operation and the bijections, we get the ascent sequences of the sum of two matrices.     

4-Formyl-2-（2H-benzotriazol-2-yl）-phenol： an ESIPT chromophore

In the present work, excited state intramolecular proton transfer （ESIPT） emission properties of a new benzotriazole derivative 4-formyl-2-（2H-benzotriazol-2-yl）- phenol （C1） were studied. 4-Formyl-2-（2H-benzotriazol-2- yl）-methoxy-benzene （C2）, 4-formyl-2-（2H-benzotriazol-2- yl）-phenyl acetate （C3） and 4-methyl-2-（2H-benzotriazol- 2-yl）-phenol （C4） were used as the reference molecules. ^1H NMR chemical shift of hydroxy group in C1 was located at more down field than that of C4 or p-hydroxy-benzaldehyde （C5）, respectively. C1 showed two absorption bands in the range of 260-400 nm zones in various solvents, while C2 and C3 exhibited single absorption band. The equal molar mixtures of C2/C5 or C3/C5 showed single absorption band. C2 and C3 displayed single fluorescence emission band in various solvents, while C1 exhibited dual emission bands in some strong polar solvents. Furthermore, the second emission band in these strong polar solvents showed the large Stokes shift. The results show that the second emission band of C1 was produced by ESIPT. C2 and C3 could not undergo ESIPT due to no hydroxy group. The geometry optimization calculation of enol and keto forms in the ground and excited states of C1 provided tough theoretical evidences of ESIPT.     

Synthesis, structure of iron(III)-containing imidazolium salts and their catalytic activity in the alkylation of aryl Grignard reagents

A series of iron(III)-containing imidazolium salts of the general formula [DRim][FeX₄] (R = 2,6-diisopropylphenyl, IPr, X = Cl, 1; R = IPr, X = Br, 2; R = tertbutyl, ^t Bu, X = Cl, 3; R = isopropyl, ⁱ Pr, X = Cl, 4; R = benzyl, Bn, X = Cl, 5; R = Bn, X = Br, 6) have been prepared in high yields via reactions of anhydrous ferric halides with equivalent of the corresponding N,N-dihydrocarby-limidazolium halides, where 2–6 are novel ones. All of the complexes were characterized by elemental analysis, Raman spectroscopy, electrospray ionization mass spectroscopy, and X-ray crystallography for 1 and 2. All of them were non-hygroscopic and air-stable, with four of them existing as solids (1–4) and two as liquids (5 and 6) at room temperature. A preliminary catalytic study on the coupling of 4-tolylmagnesium bromide with cyclohexyl bromide revealed that 1 and 3 possessed the highest activity. In comparison, 2, 4 and 5 exhibited moderate activity and the least active complex was 6.     

Synthesis and self-assembly of two 1,3-alternate thiacalix[4]arenes derivatives bearing amide groups

Two 1,3-alternate thiacalix[4]arene derivatives bearing amide groups, 1,3-alternate p-tert-butylthiacalix[4]arene tetraamide (4), and 1,3-alternate p-H-thiacalix[4]arene tetraamide (6) were prepared, and their crystal structures were determined by single-crystal X-ray diffraction method. The steric hindrances posed by tert-butyl groups play an important part in the synthesis and the self-assembly of the two compounds. Compound 6 was synthesized from the corresponding ester, which was obtained by the reaction of acid chloride with ammonia. In the crystal structure, compound 4 presents a highly symmetric molecular structure, while for compound 6, because of absence of tert-butyl groups, it presents a more flexible molecular structure.     

Synthesis, structure, optoelectronic properties of novel zinc Schiff-base complexes

Two novel zinc Schiff-base complexes, bis-(N-(2-hydroxybenzidene)-p-aminodimethylaniline)zinc(II) (2) and bis-(N-(2-hydroxy-1-naphthidene)-p-aminodimethylaniline)zinc(II) (4) were designed and synthesized. Both the complexes exhibit good solubility in organic solvents and excellent thermal stabilities. A single crystal of 2 was grown and its crystalline structure was determined from X-ray diffraction data. Analysis of the electronic structures of both the zinc complexes calculated by density functional theory reveals a localization of orbital. The UV-Vis absorption and photoluminescence profiles of 4 in thin film are similar to those of 2, but the emission for 4 is red-shifted compared to 2. Three-layered devices with a configuration of ITO/NPB/2/Alq 3 /LiF/Al and ITO/NPB/4/Alq 3 /LiF/Al show a yellow and red emission, respectively.     

New terpenoids from the roots of Jatropha curcas

Two new sesquiterpenoids,(1S,2R)-dihydroxycycloax-4(15)-ene(1),14-dehydroxyl daucucarotol(2),and one new rhamnofalane diterpenoid,2-hydroxy-3-dehydroxycaniojane(3),together with two known compounds,curcusone D(4) and curcusone C(5),were isolated from the roots of Jatropha curcas.The chemical structures of these compounds were established by chemical methods and extensive 1D-and 2D-NMR spectroscopic data analyses.     

Synthesis and characterization of carbon-bridged bis(phenolate) lanthanum alkoxides and their catalytic behavior for the polymerization of L-lactide

Four lanthanum alkoxides stabilized by a carbon-bridged bis(phenolate) ligand were synthesized and their catalytic behavior for the ring-opening polymerization of L-lactide was explored. Reactions of [(MBMP)LaCp(THF) 2 ] (MBMP 2 = 2,2′-methylene-bis(6-tert-butyl-4-methyl phenoxo)) with HOCH 2 Ph, HOCH 2 CF 3 , HOCH(CH 3 ) 2 , and HOCH 2 CH 2 N(CH 3 ) 2 , respectively, in a 1:1 molar ratio in THF gave the dimeric lanthanum alkoxo complexes [(MBMP)Ln(μ-OR)(THF) 2 ] 2 (OR = OCH 2 Ph(1), OCH 2 CF 3 (2), OCH(CH 3 ) 2 (3), OCH 2 CH 2 N(CH 3 ) 2 (4)]. These complexes were well characterized, and the definitive molecular structure of complex 1 was determined. It was found that complexes 1 to 4 are efficient initiators for the ring-opening polymerization of L-lactide. The structure of the alkoxo groups has a significant effect on the catalytic behavior, and complex 2 can initiate L-lactide polymerization in a controlled manner.     

Development of Fe(III)-containing ether-functionalized imidazolium ionic liquids for aryl Grignard cross-coupling of alkyl halides

A series of Fe(Ⅲ)-containing imidazolium-based ionic liquids containing ether substituents,including[C3OMim][FeCl4](1,[C3OMim]=1-(2-methoxyethyl)-3-methylimidazolium),[C3OiPim][FeCl4](2,[C3OiPim]=1-isopropyl-3-(2-methoxyethyl)imidazolium),[C3OBim][FeCl4](3,[C3OBim]=1-butyl-3-(2-methoxyethyl)imidazolium),[(C3O)2im][FeCl4](4,[(C3O)2im]=1,3-bis(2-methoxyethyl)imidazolium),[C3OMim][FeBr4](5)and[(C3O)2im][FeBr4](6),were prepared and characterized by elemental analysis,Raman spectroscopy and electrospray ionization mass spectrometry.The catalytic performances of 1–6 and related Fe(III)-based catalysts in the cross-coupling of aryl Grignard reagents with alkyl halides bearing-hydrogens were studied,revealing that mono(ether)functionality improves the catalytic activity and that bis(ether)functionality improves the reusability.After simply decanting the product contained in the ethereal layer,complex 4,which containing bis(ether)-functionalized imidazolium cation,could be successfully recycled seven times.     

A practical process for the synthesis of translocator protein 18kDa imidazopyridine ligand

In this article, an effective feasible method to synthesize translocator protein 18kDa （TSPO） imidazopyridine ligand 7 is discussed. A new procedure for the synthesis of the key intermediate 17 has been developed in four steps （condensation, diazo reaction, hydrolysis, amidation） from 2-aminopyridine 18. The overall yield was increased from 18% to 31.6%. One of the key steps is using activated copper powder as a catalyst in several cycles. Finally, reduction of 17 with Zn dust completed the synthesis of TSPO imidazopyridine ligand 7 in 86% yield.     

Ionic iron（III） complex of aryloxo-linked bis（imidazolium） cations： efficient and recyclable catalyst for aryl Grignard cross-coupling of alkyl chlorides

A novel phenol-linked bis（imidazolium） salt, H3LCl2 （L = O-4-C（CH3）3-C6H2-2,6-di[CH2{C（NCHCH- NAr）}]2, Ar = 2,6-diisopropylphenyl, 1）, was designed and used to prepare an ionic iron（III） complex [H2L][FeCl4] （2）. Complex 2 was a highly efficient catalyst for aryl Grignard cross-coupling of alkyl chlorides bearing β-hydrogens. Furthermore, complex 2 was reusable and could be reused in at least eight times without significant loss in catalytic activity.     

Generalized inverse eigenvalue problem for (<Emphasis Type="Italic">P</Emphasis>,<Emphasis Type="Italic">Q</Emphasis>)-conjugate matrices and the associated approximation problem

In this paper, the generalized inverse eigenvalue problem for the (P,Q)-conjugate matrices and the associated approximation problem are discussed by using generalized singular value decomposition (GSVD). Moreover, the least residual problem of the above generalized inverse eigenvalue problem is studied by using the canonical correlation decomposition (CCD). The solutions to these problems are derived. Some numerical examples are given to illustrate the main results.     

A new second-order Mehrotra-type predictor-corrector algorithm for SDO

In Zhang's recent works,a second-order Mehrotra-type predictor-corrector algorithm for linear optimization was extended to semidefinite optimization and derived that the algorithm for semidefinite optimization had O(n~(3/2)log(X~0)~T·S~0/ε) iteration complexity based on the NT direction as Newton search direction. In this paper, we extend the second-order Mehrotra-type predictor-corrector algorithm for linear optimization to semidefinite optimization and discuss the polynomial convergence of the algorithm by modifying the corrector direction and new iterates. It is proved that the iteration complexity is reduced to O(n~(3/2)log(X~0)~T·S~0/ε), which coincides with the currently best iteration bound of Mehrotra-type predictor-corrector algorithm for semidefinite optimization.     

A wide neighborhood arc-search interior-point algorithm for convex quadratic programming

In this paper, we propose an arc-search interior-point algorithm for convex quadratic programming with a wide neighborhood of the central path, which searches the optimizers along the ellipses that approximate the entire central path. The favorable polynomial complexity bound of the algorithm is obtained, namely O(nlog(( x~0)~TS~0/ε)) which is as good as the linear programming analogue. Finally, the numerical experiments show that the proposed algorithm is efficient.     

Synthesis, spectra, structure and quantum chemistry study on two novel oxovanadium complexes with hydrotris （pyrazolyl） borate ligands

Vanadium is a trace element in lives. Though vana- dium was investigated in life science from 1876, the importance of vanadium in lives was not recognized until 1971[1,2]. Since bromoperoxidase and nitrogenase were found and proved that vanadium plays an …     

A quantum algorithm that deletes marked states from an arbitrary database

We present a general quantum deletion algorithm that deletes M marked states from an N-item quantum database with arbitrary initial distribution. The general behavior of this algorithm is analyzed, and analytic result is given. When the number of marked states is no more than 3N/4 , this algorithm requires just a single query, and this achieves exponential speedup over classical algorithm.     

Design, synthesis and nonlinear optical properties of “dendronized hyperbranched polymers”

A new type of dendritic polymer, named dendronized hyperbranched polymer (DHP), was prepared successfully by the macro-monomer approach. Thanks to the perfect 3D isolation effects, DHPG1 exhibited good NLO property with d 33 value of 133 pm/V, higher than its analogues of dendronized polymer and dendrimer, and its stability of NLO effect was also enhanced.     

The Reverse Hoelder Classes in Martingale Setting

In martingale setting, it has been shown that Ap weights can be factorized in terms of A1 weights. This factorization benefits many problems very much. ]n this paper, the new class of RH~ plays the same role for RHs, which makes the reverse HOlder inequalities hold with exponent s＞1, that the class A1 does for Ap class. Therefore, the Jones‘ factorization theorem for Ap weights was extended to include some information about the reverse HOlder classes. And it is the most convenient obiect in weight theory indeed.     

A generalized funk’s section theorem for measures

If L is a star body in R~n whose central(n-i)-slices have the same(n-i)-dimensional measure μ_(n-i)(with appropriate density)as the central(n-i)-slices of an origin-symmetric star body K,then the corresponding n-dimensional measures μ_n of K and L satisfy μ_n(K)≤μ_n(L).This extends a generalized Funk’s section theorem for volumes to that for measures.     

Binding number,minimum degree and bipancyclism in bipartite graphs

Let G =(V_1,V_2,E) be a balanced bipartite graph with2 n vertices.The bipartite binding number of G,denoted by B(G),is defined to be n if G =K_n and min i∈{1,2}|N(S)|n min |N(S)|/|S|otherwise.We call G bipancyclic if it contains a cycle of every even length m for 4 ≤ m ≤ 2n.A theorem showed that if G is a balanced bipartite graph with 2n vertices,B(G) 3 / 2 and n 139,then G is bipancyclic.This paper generalizes the conclusion as follows:Let 0 c 3 / 2 and G be a 2-colmected balanced bipartite graph with 2n(n is large enough) vertices such that B(G) c and δ(G)(2-c)n/(3-c)+2/3.Then G is bipancyclic.