部分子结式性质的改进证明

为了更好的计算两个单变元多项式的最大公因式,20世纪初有Burside和Panton首先提出了结式的概念,在结式的基础上又提出了子结式的概念,这使得求最大公因式有了一个更系统的算法.计算机代数中关于子结式的经典定义过于繁琐,文献[1]中给出了子结式的一种简洁的定义.主要是借助文献[1]新定义的方法给出部分子结式的性质的证明及一些相应的例题,并对部分结论进行了一定的推广.     

Coordination modes of 3-hydroxypicolinic acid: Synthesis and structural characterization of polymeric mercury(II) complexes

Novel mercury(II) compounds of 3-hydroxypicolinic acid (HpicOH; IUPAC name: 3-hydroxy-2-pyridinecarboxylic acid) were synthesized and characterized. HgCl(picOH) (1) and HgBr₂(HpicOH) (2) were obtained as reaction products from the reaction of the corresponding mercury(II) halide with HpicOH, irrespective of the molar ratio of the reactants. From the reaction of HpicOH and mercury(II) acetate, Hg(picOH)₂ (3) was obtained, while mercury(II) nitrate monohydrate gave the 1/1 solvate with water Hg(picOH)₂ · H₂O (3a). Infrared, ¹H and ¹³C NMR spectroscopic data were analyzed for complexes 1, 2 and 3. X-ray crystal structure analysis of 1 and 2 revealed their polymeric nature and different coordination modes of HpicOH. In 1 the deprotonated picolinic acid is N,O-chelating and bridging, while in 2 HpicOH is a O-monodentate weakly bound ligand. Compound 1 consists of HgCl(picOH) moieties with two linear covalent bonds, Hg–N 2.143(4) and Hg–Cl 2.298(1) Å, and four additional Hg?O contacts (2.460(3)–2.904(3) Å) in which both oxygen atoms from the carboxylic group are bridging and involved in coordination to three neighboring mercury atoms, thus forming infinite layers. The coordination of mercury is 2 + 4. 2 consists of {HgBr₂(HpicOH)} moieties, which are linked into chains by means of mercury to bromine secondary long range interactions. The coordination sphere of mercury can be described as irregular 2 + 3 formed by two covalently bonded bromine atoms (Hg–Br 2.277(1) and 2.366(1) Å), two bridging bromine atoms (Hg?Br 3.309(1) and 3.247(1) Å) and by the HpicOH ligand attached to mercury in the zwitterionic form via the carboxylic oxygen atom (Hg?O 2.602(7) Å).     

A study of complex scaling transformation using the Wigner representation of wavefunctions

The complex scaling operator exp(-θ ?x?p/?), being a foundation of the complex scaling method for resonances, is studied in the Wigner phase-space representation. It is shown that the complex scaling operator behaves similarly to the squeezing operator, rotating and amplifying Wigner quasi-probability distributions of the respective wavefunctions. It is disclosed that the distorting effect of the complex scaling transformation is correlated with increased numerical errors of computed resonance energies and widths. The behavior of the numerical error is demonstrated for a computation of CO(2+) vibronic resonances.     

The electrochemical behavior of PtRu- and Pt-modified zeolite X in alkaline solution

Zeolite NaX was modified by Pt and Pt/Ru nanodispersed metallic clusters. The procedure of impregnation with acetylacetonate salt/acetone solution was applied. Scanning electron microscope analysis confirmed partial zeolite framework destruction. According to energy dispersive X-ray analysis, Pt/Ru ratio in sample was about 1. Electrochemical behavior of PtRu- and Pt-modified zeolites was investigated in alkaline solutions, 5 mM NaOH?+?1 M Na₂SO₄ and 0.1 M NaOH. The shape of cyclic voltammograms of 13XPtRu electrode, recorded in slightly alkaline solution, was greatly affected by the presence of hydrogen that remained in the sample after synthetic procedure. Oxygen reduction reaction (ORR) was investigated in an O₂-saturated aqueous 0.1-M NaOH solution. The obtained Tafel slopes indicated ORR mechanism that involves one-electron discharge-determining step. According to Koutecky–Levich slope, the oxygen reduction reaction followed 4e^? mechanism on both 13XPtRu and 13XPt electrode. The onset of ORR on 13XPtRu electrode was shifted toward more positive potentials in comparison to 13XPt electrode.     

Synthesis,anti-oxidant activity,and cytotoxicity of salicyloyl derivatives of estra-1,3,5(10)-triene and androst-5-ene

Since many estrane and androstane derivatives exhibit cytotoxic, anti-oxidant, or anti-hormone activity, new steroidal derivatives were synthesised from appropriate estrogen or androgen precursors in order to obtain potential therapeutics for the treatment of steroid-dependent diseases. Starting from estradiol (I), 6-oxo derivatives V and VII were prepared. 17β-Salicyloyl-6-oxo derivatives VI and VIII were synthesised by the reaction of compounds V or VII with methyl salicylate in the presence of sodium. 17β-Salicyloyloxy estradiol IX was prepared from estradiol. Beckmann fragmentation of 16-oxyimino alcohols XII and XIII with methyl salicylate yielded corresponding D-seco derivatives XIV and XV. Simultaneous fragmentation and acylation of compound XII resulted in 3β-salicyloyl-D-seco derivative XVI which was also obtained from compound XIV. Anti-oxidant assays of the newly synthesised compounds V-IX, XIV, and XVI indicated a stronger capacity for hydroxyl radical scavenging, and a weaker capacity for DPPH radical scavenging, compared with the standard anti-oxidants BHA and BHT. Compounds V, XIV, and XVI showed higher or the same activity as BHT. The cytotoxicity of new compounds was evaluated against human breast and prostate carcinoma cells. Compound VI exhibited strong cytotoxicity against MDA-MB-231 cells; compound XIV exhibited strong cytotoxicity against PC-3 cell line, while compound VII moderately inhibited the growth of PC-3 cells.     

Synthesis of organosoluble polyamides with bulky triaryl imidazole pendent group

New unsymmetrical diamine monomer containing triaryl imidazole pendent group,4-[4-(4,5-diphenyl-1H-imidazol-2-yl)phenoxy] -1,3-benzenediamine,was synthesized via aromatic substitution reaction of 1-chloro-2,4-dinitrobenzene with 4-(4,5- diphenyl-1H-imidazol-2-yl)phenol,followed by palladium-catalyzed hydrazine reduction.This new monomer was further confirmed by FT-IR,~1H NMR and ~(13)C NMR.Novel polyamides having pendant triaryl imidazole group were prepared by the phosphorylation polycondensation of fou...     

[NH4][(CH3)2NH2]2[Ta(C2O4)4]·2H2O: the first (oxalato)tantalate(V) complex structurally characterized

Abstract  The compound [NH₄][(CH₃)₂NH₂]₂[Ta(C₂O₄)₄]·2H₂O has been synthesized and characterized by elemental and TG/DTA analyses, IR spectroscopy and by the single-crystal X-ray diffraction study. The structure comprises the [Ta(C₂O₄)₄]³⁻ anion, NH₄ ⁺ and [(CH₃)₂NH₂]⁺ cations and crystallization water molecules. The Ta atom is octacoordinated by oxygen atoms from four bidentate oxalate groups forming a coordination polyhedron close to the triangular dodecahedron. The charge-assisted hydrogen bonds from both cations connect the [Ta(C₂O₄)₄]³⁻ anions into a three-dimensional framework. Graphical Abstract  The synthesis and properties of [NH₄][(CH₃)₂NH₂]₂[Ta(C₂O₄)₄]·2H₂O, the first structurally characterized compound with the tetra(oxalato)tantalate(V) anion, is reported.      

4f 135s 25p 6-4f 135s 25p 56s transitions in the W VIII spectrum and spectra of isoelectronic hafnium, tantalum, and rhenium ions

Spectra of hafnium, tantalum, tungsten, and rhenium in the range of 145?C350?, excited in a low-inductive vacuum spark, have been recorded on a grazing-incidence vacuum spectrograph using a grating with 3600 lines/mm and a radius of 3 m. The wavelengths and intensities of more than 3800 lines in the tungsten spectrum have been measured. Comparison with the Hartree-Fock calculations showed that most spectral lines should be due to transitions in the W VIII spectrum. Short-wavelength lines due to the 4f ¹³5s ²5p ⁶-4f ¹³5s ²5p ⁵6s transitions have been identified in the W VIII spectrum and the Re IX, Ta VII, and Hf VI isoelectronic spectra.     

Structure identification and site preference of Ta and Cd in Ti–Pd alloys: A first-principle study

By means of a density functional theory approach, we studied the electric field gradients (EFG) in Ta and Cd-doped Ti–Pd intermetallics. Our results confirmed the previous experimental findings that the TiPd₂ low-temperature structure is orthorhombic and established that Ta substitutes for Ti in this structure. The temperature increase above 650 K changes the Ta impurity position in the lattice. Similar changes for the Cd doped system were not confirmed, as Cd is most likely to occupy Pd lattice sites in both low and high-temperature phases. In the case of TiPd, our calculations suggested that Ta substitutes for Ti in the low-temperature phase, while Cd probably can substitute on both Ti and Pd crystallographic sites.