The Riemann-Hilbert Problem for Mixed Complex Equations of First Order with Degenerate Rank 0

This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed （elliptic- hyperbolic） complex equations of first order with degenerate rank 0. Firstly, we give the representation theorem and prove the uniqueness of solutions for the boundary value problem. Afterwards, by using the method of successive iteration, the existence and estimates of solutions for the boundary value problem are verified. The above problem possesses the important applications to the Tricomi problem of mixed type equations of second order. In this article, the proof of HSlder continuity of a singular double integer is very difficult and interesting as in this Section 4 below.

Riemann-Hilbert problem for first order complex equations of mixed type with degenerate curve

This paper considers the Riemann-Hilbert problem for linear mixed（elliptichyperbolic） complex equations of first order with degenerate curve in a simply connected domain. We first give the representation theorem and uniqueness of solutions for such boundary value problem. Then by using the methods of successive iteration and parameter extension, the existence of solutions for this problem is proved.

Mixed d/f Complexes Zn(H2L)Ln(NO3)3(Ln=Sm,Tb and Dy)：Crystal Structure,Fluorescence and Thermal Stability

A series of isostructural d/f molecular compounds Zn（H2L）Ln（NO3）3·CH3OH（Ln = Dy（1）, Tb（2） and Sm（3）） were synthesized by the introduction of a designed multifunctional ligand N,N？,N？？,N？？？-tetra（2-hydroxy-3-methoxy-5-methylbenzyl）-1,4,7,10-tetraazacyclododecan（H4L = C（44）H（60）N4O8）. In the isostructural molecules, each crystallographically independent Zn2＋ and Ln3＋ centers are connected by two phenolic oxygen atoms. For the six-coordinate Zn-（2＋） ion, the coordination geometry can be viewed as a regular bicapped square pyramid. While for the ten-coordinate Ln-（3＋） ion, if each O,O？-chelated nitrate ligand is seen as a single coordination site, the coordination geometry can be viewed as a distorted pentagonal bipyramid. The fluorescent spectra show that compounds 2 and 3 exhibited characteristic sharp emissions of Tb-（3＋） and Sm-（3＋）, respectively, while compound 1 was found to be a single-component white-light-emitting complex in the solid state. Thermal stabilities of the three compounds were investigated by using thermal gravimetric analysis. In addition, the thermal decomposition of compound 1 was confirmed by temperature-dependent powder X-ray diffraction technique.

Synthesis and Crystal Structure of Quaternary Mixed Anion Complexes of Lanthanide Containing 1,10-Phenanthroline

A series of novel quaternary mixed anion complexes of lanthanide containing 1,10 phenanthroline(phen) were synthesized from the water/ethanol solution with slightly acidic solution and characterized by elemental analysis, IR and UV spectra, thermal analysis and single crystal X ray diffraction analysis. The crystal of [Ce(CH 3COO) 2(NO 3)(phen)] 2 belongs to monoclinic system, lattice type C centered, space group C 2/m, a =1 5444(6) nm, b =1 2273(5) nm, c =1 2776(5) nm, β =131 89(2)°, V =1 802(1) nm 3, Z =2, R =0 024, R w =0 032.

Synthesis Crystal Structureof Quaternary Mixed AnionComplex of Lanthanides[Ln(CCl_3COO)_2 (CH_3COO)(phen) (H_2O)]_2

Three new quaternary mixed anion complexes of lanthanides were prepared from thewater-ethanol solution under slightacidity condition and characterizedby elemental analysis, IR, UVspectrum and single crystal X-raydiffraction analysis. The crystal ofLa(CCl3COO)2 (CH3COO) (phen)(H2O)·DMF]2 belongs to tricliniccrystal system, space group P1with a=1 .2510 (4) nm, b=1.3460(5) nm, c=1.0343 (3)nm, α=102.47(3)°, β=102.34(2)°, γ=113.82 (2)°, μ(MoKa) = 20.47 cm-1, Z= 1, Dc=1. 800 g·cm-3, F (000) =780. 00. The acetate tends to coordinate with the center ion as abridge and trichloroacetate has fourkinds of coordination modes, somany coordination modes were observed in their co-ligand system.

STUDIES ON THE CHROMOPHORIC REACTIONS OF MIXED POLYNUCLEAR COMPLEXES OF RARE EARTH-ARSENAZO Ⅲ-COPPERO-PHENANTHROLINE

In an acidic solution the mixed polynuclear complexes could be formed by association of rareearth-arsenazo Ⅲ complexing anions with copper o-phenanthrolinate cations.In this paper the formationconditions of lanthanum-arsenazo Ⅲ-copper-o-phenanthroline complex and its related reaction mechanismhave been studied in detail.The complex exhibits an absorption maximum at 663 nm and its apparent molarabsorptivity is found to be 1.22×105L·mol-1·cm-1.The molar ratio of the components in the complex isestimated to be La:arsenazo Ⅲ:Cu:Phen=1:1:1:3.Its possible molecular formula can expressed as[Cu（Phen）3]（La-arsenazo Ⅲ）.The reaction is used to determine micro amounts of lanthanum（or rareearths）in copper containning synthetic samples and satisfactory results are obtained.

SYNTHESIS, MAGNETIC PROPERTY AND X-RAY CRYSTAL STUCTURE OF MIXED VALENT COBALT COMPLEX SALT [Co~Ⅲ Cl_2(py)_4][Co~Ⅱ Cl_3(py)]

Complex salt Co_2Cl_5(py)_5 (py=pyridine) was obtained by the reaction of CoCl_2·6H_2O with Bu_4NMnO_4 in pyridine in the presence of benzoic acid. It is monoclinic and crystallizes in space group P2_1/n, fw=690.64, a=28.652(5), b=14.108(4), c=7.424(3) ;β=90.09(1); V=3001(2)~3; Z=4, Dc=1.53g/cm^3. Final R factor is 0.041. The structure consists of a discrete cation [Co~ⅢCl_2(py)_4]^+ and an anion [Co~Ⅱ Cl_3(py)]^-. The Co~Ⅲ ion is coordinated by two Cl^- and four pyridine nitrogen atoms to form an octahedral geometry, and Co~Ⅱ is coordinated by three Cl^- and one pyridine nitrogen atom to form the apices of a tetrahedron. The variable-temperature magnetic susceptility measurement shows no magnet-exchange interaction between Co~Ⅲ and Co~Ⅱ ions.

Syntheses of Coordination Compounds of 2-Amino-3-Methylbutanoic Acid Their Mixed Ligand Complexes and Antibacterial Activities

Coordination compounds of 2-amino-3-methylbutanoic acid were synthesized with chromium(III) and oxovanadium(IV) ions. M:L;1:2. Adducts of these complexes using 1,10-phenantroline and ethylenediamine were further synthesized, M:L, (1:2). These compounds were characterized using electronic, infra-red spectrophotometry, magnetic susceptibility measurement and percentage metal analyses. The zones of inhibition and minimum inhibitory concentrations of the compounds against eight microbes were studied. The results obtained indicated an octahedral geometry for the Cr(III) complexes, indicative of additional coordination of two water molecules. On the other hand a square pyramid geometry was obtained for the binary oxovanadium complex and its 1,10-phenantroline adduct. However, for the oxovanadium ethylenediamine adduct a distorted octahedral geometry was proposed. The result for the antibacterial studies indicated that both mixed ligand complexes of 1,10-phenantroline exhibited good antibacterial activity, and in some cases better activity than the standard, streptomycin.

Syntheses, Characterization and Biological Activity of Coordination Compounds of 3-Hydroxy-2-methyl-4<i>H</i>-pyran-4-one and Its Mixed Ligand Complexes with 1,2-Diaminocyclohexane

Coordination compounds of 3-hydroxy-2-methyl-4H-pyran-4-one with iron(III), cobat(III) and chromium(III) were synthesized with M:L (1:2). Mixed ligand coordination compounds of 3-hydroxy-2-methyl-4H-pyran-4-one and 1,2-diaminocyclohexane using the same metal ions were also synthesized M:L1:L2 (1:1:1) where L1 is 3-hydroxy-2-methyl-4H-pyran-4-one and L2 is 1,2-diaminocyclohexane. The coordination compounds obtained were characterized using electronic and infrared spectral analyses, magnetic susceptibility and percentage metal analysis. They were also evaluated for their cytotoxic and antioxidant activities. The result obtained suggested that octahedral geometry was obtained for all the compounds, as a result of additional two molecules of the solvent coordinated to the metal ions. Both the primary and secondary ligands coordinated in a bidentate fashion. The synthesized compounds exhibited moderate cytotoxicity, although none was as active as the standard. The cobalt(III) mixed ligand complex elicited the highest activity. The synthesized compounds all exhibited good to moderate antioxidant activity.

Halogen Mediated Self-assembly of Three Mixed Valent Cu(Ⅰ)/Cu(Ⅱ)Complexes

Reaction of the ligand dmpt（dmpt=6,7-dimethylbenzo[f][1,10]phenanthroline）with CuCl2 afforded mixed valent Cu（Ⅰ）/Cu（Ⅱ） discrete tetranuclear complexes[Cu（Ⅱ）Cl2（dmpt）Cu（Ⅰ）Cl]（1）,while the reaction of ligand dppz（dppz = dipyrido[3,2-a：20,30-c]phenazine） with divalent halogen copper salt CuX2（X=Cl,Br） gave one-dimensional chain mixed valent Cu（Ⅰ）/Cu（Ⅱ） complexes [Cu（Ⅱ）Cl2（dppz）Cu（Ⅰ）Cl]n（2） and discrete mixed valent Cu（Ⅰ）/Cu（Ⅱ）complexes [Cu（Ⅱ）Br2（dppz）（DMF）Cu（Ⅰ）Br]（3）. Complex 2 consists of a one-dimensional chain-dppzC u（Ⅱ）-Clμ2-Cu（Ⅰ）-Cl-dppzC u（Ⅱ）-Clμ2-Cu（Ⅰ）-with Cu（Ⅱ） and Cu（Ⅰ） atoms linked together by chloride anion. Complex 3 is a discrete complex,which is the same as complexes 1 and 2 involving two different copper valent Cu（Ⅰ） and Cu（Ⅱ）. The Cu（Ⅰ） ion presents a pseudo-trihedral geometry,while the Cu（Ⅱ） ion presents a slightly distorted square-pyramidal geometry. This fact proved that halogen ions play a vital role in the assembly procedure. Our research results demonstrate the structural diversification that can be achieved by halogen ions mediated. Moreover,halogen ions-mediated self-assembly may provide useful information for further design of compounds with novel structures and properties.

Luminescent Properties of Bi-Rare Earth Complexes with m-methylbenzoic Acid and 1,10-phenanthroline

The bi rare earth complexes EuTb( m MBA) 6(phen) 2·2H 2O, TbY( m MBA) 6(phen) 2·2H 2O were synthesized by the reaction of RECl 3 with m methylbenzoic acid and 1,10 phenanthroline in ethanol solution, where m MBA=m methylbenzoate and phen=1,10 phenanthroline. The luminescence properties of the title complexes were studied in comparison with the corresponding complexes Eu 2( m MBA) 6(phen) 2·2H 2O and Tb 2( m MBA) 6(phen) 2·2H 2O respectively. The results indicate that the emission intensity from europium ion can be greatly enhanced by the terbium ion, while the emission from terbium ion was strongly quenched by europium ion in EuTb( m MBA) 6(phen) 2·2H 2O; the emission intensity from terbium ion can be greatly enhanced by yttrium ion in TbY( m MBA) 6(phen) 2·2H 2O. The mechanism about the results was discussed.

A novel image fusion algorithm based on 2D scale-mixing complex wavelet transform and Bayesian MAP estimation for multimodal medical images

In this paper,we propose a new image fusion algorithm based on two-dimensional Scale-Mixing Complex Wavelet Transform(2D-SMCWT).The fusion of the detail 2D-SMCWT cofficients is performed via a Bayesian Maximum a Posteriori(MAP)approach by considering a trivariate statistical model for the local neighboring of 2D-SMCWT coefficients.For the approx imation coefficients,a new fusion rule based on the Principal Component Analysis(PCA)is applied.We conduct several experiments using three different groups of multimodal medical images to evaluate the performance of the proposed method.The obt ained results prove the superiority of the proposed method over the state of the art fusion methods in terms of visual quality and several commonly used metrics.Robustness of the proposed method is further tested against different types of noise.The plots of fusion met rics establish the accuracy of the proposed fusion method.

Isolation and Spectroscopic Characterization of Protonated Mixed [Tetrakis (4-pyridyl)porphyrinato] (phthalocyaninato)Rare Earth (Ⅲ)Double-decker Compounds

The treatment of tetrakis (4-pyridyl) porphyrin H2TPyP with a hydrated rare earth (III) acetylacetonate RE(acac)3 · nH2O (RE=Y, Eu, Gd) in 1,2, 4-trichlorobenzene (TCB) pro- duced a monomeric porphyrinato rare earth compound RE (TPyP) acac, which further reacted with dicyanobenzene in amyl alcohol in the presence of 1, 8-diazabicyclo [5. 4. 0] undec-7-ene (DBU), giving HRE(TPyP) (Pc) in a good yield. Upon exposure to air, part of the protonated mixed double-deckers in CHC13 solutions converted slowly to the corresponding neutral complexes RE (TPyP) (Pc). These protonated complexes were characterized by means of UV-V is, IR, NMR, mass spectroscopies. The quaternarization of these protonated mixed double-deckers with methyl iodide produced the salts of tetramethylated cations [HRE(TMPyP) (Pc)]4+.

Synthesis,Structural Characterization and Magnetic Properties of{[Gd(DMF)_(3)(DMSO)(H_(2)O)_(3)](μ-CN)(Fe)(CN)_(5)]}·2H_(2)O

A new cyano-bridged Gadolinium^(Ⅲ)-Iron^(Ⅲ)complex{[Gd(DMF)_(3)(DMSO)(H_(2)O)_(3)]2H_(2)0(DMF=N,N·-dimethylformamide;DMSO=dimethylsulfoxidel}was synthesized by the grinding reaction method,.It crysta-]llizes in the triclinic.,space group P1 with ceIl parameters:a=O.90363(2)nm,b=1.25078(3)nm,c=1.41303(1)nm,穋m^(-3),Z=2,Mr=756.72,F(000)=760,Ⅲ)and the approxi-mately oriented octahedrally sixfold-coordinated Fe(Ⅲ)are linked by a cyano-bridge group to construct a dinuclear compound.The{[Gd(DMF)_(3)(DMSO)(H_(2)O)_(3)](Ⅲ)-Fe(Ⅲ)interaction is antiferromagnetic.CCDC:223430.

Study on cobalt-carbon and iron-sulfur mixed cluster complexes——Synthesis and conformational analysis of mixed cluster complexes [μ-p-CH_3C_6H_4C_2Co_2 (CO)_6 S](μ-RS)Fe_2(CO)_6

Through complexation reaction of arynyl Fe-S complexes A(μ-p-CH_3C_6H_4C≡CS)(μ- RS)Fe_2(CO)_6 with Co_2(CO)_6, eight mixed cluster complexes B[μ-p-CH_3C_6H_4C_2Co_2(CO)_6S](μ- RS)Fe_2(CO)_6 have been synthesized. Reactivity of the complexation reaction is approximately equi- valent to that of the reaction of diarylacetylene with Co_2(CO)_8. Conformational analysis has shown that R groups in complexes A are linked to sulfur atoms by a-and e-bond, whereas that in B only by art e-type of bond.

Thermodynamical study on the formation of some mixed ligand complexes of non-transition metal ions in solution——Ⅰ. The formation and the stability of some Pb(Ⅱ) mixed ligand complexes

The stability constants of the binary complexes of type PbB, PbB_2, and the mixed ligand complexes of type PbAB have been studied by potentiometric pH titration technique at ionic strength I=0.10 (KNO_3) and at temperature 15, 25, 35 and 45℃ respectively, where A=2,2'-bipyridyl (bipy) or 1, 10-phenanthroline (phen); B=malonate (mal), succinate (suc), or anthranilate (anth). The equalibrium constants logK,~1 G, H, and S of the reaction PbA+PbB=PbAB+Pb^2+ have been calculated. The results show that the discriminating effects^2 between the primary ligand (bipy or phen) and the secondary ligand (real, suc or anth) in those non-transition metal mixed ligand complexes are also evident, and as a measurement of this effect, H is more appropriate than logK. The possible reasons which lead to these results have been discussed.

The synthesis and structural studies of mixed ligand complex,tris(1-phenyl-3-methyl-4-trifluoroacetylpyrazol-5-one)mono(1-phenyl-3-methyl-pyrazol5-one)neodymium(Ⅲ)monohydrate

A mixed ligand neodymium complex containing 1-phenyl-3-methyl-4-trifluoroacetyl- pyrazol-5-one(HPMTFP)and 1-phenyl-3-methyl-pyrazol-5-one(PMP),with molecular formula Nd(PMTFP)_3·PMP·H_2O was synthesized.Its crystal and molecular structure has been determined by single crystal X-ray diffraction method.The complex crystallizes in monoclinic system with space group C_2~5h-P2_(1/n).There are four formula units in a cell of dimensions a=12.837(3),b=23.763(5),c=16.810(4) ,β=109.58(2)°.The structure has been refined by full-matrix least-squares techniques to a final R value of 0.0487 and Rw value of 0.432.The neodymium atom is coordinated to eight oxygen atoms with the average Nd-O bond length 2.439,Its thermostability,and mass spectrum have been discussed.

A Quasi-Funk's Section Theorem in n-Complex Space

The Funk＇s section theorem in the n-complex space Cn is investigated. It turns out that this theorem does not admit an extension for the class of general origin-symmetric star bodies in Cn but for a class of star bodies called generalized complex intersection bodies. A quasi-version of Funk＇s section theorem in Cn is established then.

A Note on the Filtered Decomposition Theorem

We generalize the logarithmic decomposition theorem of Deligne–Illusie to a filtered version.There are two applications.The easier one provides a mod p proof for a vanishing theorem in characteristic zero.The deeper one gives rise to a positive characteristic analogue of a theorem of Deligne on the mixed Hodge structure attached to complex algebraic varieties.