The type problem for random walks on trees

We consider the question of whether the simple random walk (SRW) on an infinite tree is transient or recurrent. For random-trees (all vertices of distancen from the root of the tree have degreed _n , where {d _n } are independent random variables), we prove that the SRW is a.s. transient if lim inf _n n E(log(d _n-1))>1 and a.s. recurrent if lim sup _n n E(log(d _n-1))<1. For random trees in which the degrees of the vertices are independently 2 or 3, with distribution depending on the distance from the root, a partial classification of type is obtained.Research supported in part by NSF DMS 8710027.     

Ligand exchange method for determination of mole ratios of relatively weak metal complexes: a comparative study

Ligand exchange method is introduced as an alternative to Job’s and mole ratio methods for studying the stoichiometry of relatively weak metal complexes in solutions. The method involves adding varying amounts of a ligand (L) to an excess constant amount of a colored complex (MX) with appropriate stability and molar absorptivity. The absorbance of each solution is measured at the λ_max of the initial complex, MX, and plotted against the concentration of the studied ligand, L. If the newly formed complex ML does not absorb at the λ_max of the initial complex, then attenuation of the absorbance of the initial complex on adding varying quantities of the investigational ligand gives an inverse calibration line that intersects with the calibration curve of initial complex at a given point. If a line parallel to the ordinate is drawn from this point to the x-axis, the ratio of the two parts of the x-axis to the left and to the right (α/β) gives the metal to ligand molar ratio in the complex formed, ML. The new method has been applied to the study of the composition of iron (III) complexes with three bisphosphonate drugs: alendronate, etidronate, and ibandronate. The mole ratio was found to be 1:1 with the three investigated bisphosphonates and results were further confirmed by Job’s and mole ratio methods. The ligand exchange method is simpler, quicker, easier to perform and more accurate than Job’s and mole ratio methods for studying weak and relatively weak complexes.

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Correction to: Convolutional neural networks based time–frequency image enhancement for the analysis of EEG signals

Multidimensional Systems and Signal Processing -     

Gold nanoparticles film for Q-switched pulse generation in thulium doped fiber laser cavity

Passively Q-switched thulium doped fiber laser (TDFL) has been successfully demonstrated using gold nanoparticles (GNPs), which were embedded into polyvinyl alcohol as saturable absorber (SA). The stable self-starting Q-switched laser was generated to operate at 1 891 nm when a tiny piece of the prepared film was slot in between two fiber ferrules and incorporated into the laser cavity. The repetition rate can be adjusted from 48.54 kHz to 49.64 kHz while the pulse width decreased from 3.52 μs to 2.38 μs with the increase of 1 550 nm pump power from 840 mW to 930 mW. The corresponding pump power output power linearly increased from 3.62 mW to 6.3 mW with a slope efficiency of 2.53%. The maximum peak power and pulse energy were recorded at about 39 mW and 0.12 µJ, respectively at pump power of 930 mW. The Q-switching operation was caused by the surface plasmon resonance absorption of GNPs.     

Effect of gamma-irradiation on surface and catalytic properties of CuO−ZnO/Al2O3 system

A copper, zinc and aluminium mixed oxides sample having the nominal composition 0.25 CuO/0.03 ZnO/Al₂O₃ was prepared by impregnating Al(OH)₃ with copper and zinc nitrate solutions, drying at 100 °C then heating in air at 600 °C. The obtained solid was exposed to different doses of -rays (20–160 Mrad). The surface characteristics namelyS _BETV_P andr of different treated adsorbents were determined from N₂ adsorption isothems measured at –196 °C. The catalytic activity of various irradiated solids was determined by following up the kinetics of CO-oxidation by O₂ at 150–200 °C. The results showed that the doses up to 80 Mrad resulted in no significant change in theS _BET but increased slightly theV _P (20%) of the treated adsorbents. The irradiation at 160 Mrad caused an increase of 20% in theS _BET of the irradiated solid sample. The catalytic activity increased progressively by increasing the dose, a dose of 160 Mrad brought about an increase of 140% in the catalyst's activity. The apparent activation energy of the catalytic reaction decreased monotonically by increasing the absorbed dose of -rays which was attributed to a parallel induced decrease in the value of pre-exponential term of the Arrhenius equation. The observed increase in the catalytic activity due to -irradiation has been interpreted as a result of increasing the concentration of catalytically-active sites contributing in chemisorption and catalysis of CO-oxidation via a possible fragmentation of CuO crystallites.     

Reaction of N1, N2-diarylamidines with chloranil and 2,3-dichloro-1,4-naphthoquinone

Nucleophilic attack by N² of N¹ N²-diarylformamides 1a-c on C-2 of chloranil (2) and subsequently by N¹ on C-1 of 2 initiates the formation of benzimidazolinones 8a-c. In contrast, when 1b-e is reacted with 2,3-dichloro-1,4-naphthoquinone (9) , both chlorine atoms are successively substituted by the two nitrogen atoms and 2-(arylamino)-3-(N-formylarylamino)-1,4-naphthoquinones 13b-e result, which (probably via their cyclic tautomers 12b-e ) may be cyclodehydrogenated to form N¹,N³-diarylnaphtho[2,3-d] imidazoline-2,4,9-triones (as 14b,c ). On the other hand, N¹,N²diarylacetamidines 15a-d attack 2 and 9 at C-2 with N² but subsequently exert nucleophilic character at the acetamidine α-carbon attacking C-1 of 2 and 9 , respectively, thus forming 1-aryl-2-(arylimino)-3a-hydroxy-2,3,3a,6-tetrahydro-1N-indol-6-ones 18a-d and 3-aryl-2-(arylimino)-9b-hydroxy-2,3,5,9b-tetrahydro-1-H-benz[e]indol-5-ones 19b,c , respectively. The latter may be thermally dehydrated to the fully conjugated 2,5-dihydro-3H-benz[e]indol-5-ones 20b,c. Unambiguous structural assignments for 18b and 20c are made on the basis of X-ray crystal structure analyses.     

GC-MS and LC-MS Identification of the Phenolic Compounds Present in the ethyl Acetate Fraction Obtained from Senna tora,L. Roxb. seeds

The aim of this work is to characterize the active constituents present in the ethyl acetate fraction of Senna tora, L. Roxb. seeds. Due to the fact that the main biological activity of S. tora, L seeds is attributed to its phenolic compounds which are mainly isolated from Ethyl acetate fraction, to avoid repetition of work and to save time, it was deemed necessary to confirm the identity of these phenolic compounds. This was done by GC-MS and LC-MS analysis of the ethyl acetate fraction where the structures of the isolated compounds were established on the basis of molecular ion peak and their fragmentation pattern. They were identified as Chrysophanol, Chrysarobin, 10-hydroxy-5-methoxy-2-methyl-1, 4-anthracenedione, Rubrofusarin, Parietin, Griseoxanthone-B, Isotorachrysone, and Cumbiasin B.

     

一种新型哒嗪与N-戊烷基咔唑类聚合物的合成与表征

以二氯-1,3-双(二苯基磷)丙烷基镍(Ⅱ)为催化剂,通过3,6-二氯哒嗪格氏试剂与3,6-二溴-N-戊烷基咔唑共聚得到了一种新型共轭聚合物,并使用IR和1H-NMR等测试手段对单体和聚合物的结构进行了表征。该合成方法所得的共聚物收率为75%,共聚物在N,N-二甲基酰胺(DMF)、二甲基亚砜(DMSO)等极性溶剂和CF3COOH、CH3SO3H、HCOOH等常用有机酸中具有较好的溶解性。用红外(FT-IR)、紫外-可见吸收光谱(UV-vis)、荧光光谱(PL)、X射线衍射、循环伏安(CV)等对聚合物的吸收光谱特性、结晶性和电化学活性进行了探讨。结果表明:聚合物具有较高的发光强度,是一种还原型聚合物,结晶性比较差。     

Pyrazolones and quinoxalines from 4-phenyl-2,3-dioxobutyro-1,4-lactone

4-Phenyl-2,3-dioxobutyro-1,4-lactone ( 1 ) gave with phenylhydrazine and ils p-Cl, p-Br, p-I and p-NO₂ derivatives, bishydrazones which were eyclized to 1-aryl-3-(α-hydroxybenzyl)-4,5-dione-4-arylhydrazones. With o-phenylene diamine, compound 1 gave either a Schiff base or a substituted quinoxaline, depending upon the ratio of the reactants.     

Local and global existence of solutions for a class of integro-differential equations with delay

In this article we consider a class of first order nonlinear integro-differential equations with delay. We propose new approach for investigating local and global existence of the solutions of its Cauchy problem. This approach gives new results.