Counting Simsun Permutations by Descents

We count in the present work simsun permutations of length n by their number of descents. Properties studied include the recurrence relation and real-rootedness of the generating function of the number of n-simsun permutations with k descents. By means of generating function arguments, we show that the descent number is equidistributed over n-simsun permutations and n-André permutations. We also compute the mean and variance of the random variable X _n taking values the descent number of random n-simsun permutations, and deduce that the distribution of descents over random simsun permutations of length n satisfies a central and a local limit theorem as n ?? +???.     

Gold-catalyzed cycloisomerizations of 1-(2-(tosylamino)phenyl)prop-2-yn-1-ols to 1H-indole-2-carbaldehydes and (E)-2-(iodomethylene)indolin-3-ols

A method to prepare 1H-indole-2-carbaldehydes and (E)-2-(iodomethylene)indolin-3-ols by gold(I)-catalyzed cycloisomerization of 1-(2-(tosylamino)phenyl)prop-2-yn-1-ols with N-iodosuccinimide (NIS) is reported. The reactions were shown to be operationally simplistic and proceed efficiently for a wide variety of substrates, affording the corresponding products in good to excellent yields (70-99%). The mechanism is suggested to involve activation of the alkyne moiety of the substrate by the gold(I) catalyst. This triggers intramolecular addition of the tethered aniline moiety to give a vinyl gold intermediate, which undergoes iododeauration with NIS to give the (E)-2-(iodomethylene)indolin-3-ol adduct. Subsequent 1,3-allylic alcohol isomerization (1,3-AAI) followed by formylation of this vinyl iodide intermediate then gives the 1H-indole-2-carbaldehyde.     

Iron(II)-catalyzed amidation of aldehydes with iminoiodinanes at room temperature and under microwave-assisted conditions

A method for the amidation of aldehydes with PhI=NTs/PhI=NNs as the nitrogen source and an inexpensive iron(II) chloride + pyridine as the in situ formed precatalyst under mild conditions at room temperature or microwave assisted conditions is described. The reaction was operationally straightforward and accomplished in moderate to excellent product yields (20-99%) and with complete chemoselectivity with the new C-N bond forming only at the formylic C-H bond in substrates containing other reactive functional groups. By utilizing microwave irradiation, comparable product yields and short reaction times of 1 h could be accomplished. The mechanism is suggested to involve insertion of a putative iron-nitrene/imido group to the formylic C-H bond of the substrate via a H-atom abstraction/radical rebound pathway mediated by the precatalyst [Fe(py)(4)Cl(2)] generated in situ from reaction of FeCl(2) with pyridine.     

Effect of epoxy and filler concentrations on curing behaviour of isotropic conductive adhesives

Isotropic conductive adhesives (ICAs) are considered as the most promising replacement to lead-based solders due to relatively low melting point, simple processing and fine pitch capability. The study reports on the effect of volume fractions of silver flakes and particles on the curing reaction of ICAs. In addition, the thermal behavior of ICAs formulated with two types of polymeric adhesives: diglycidylether of bisphenol-A (DGEBA) and polyurethane (PU) was also investigated in this work. The increase in silver flakes concentration seem to reduce the melting temperature of the DEGBA and PU-based ICAs, which could be due to retardation of cross-linking of polymers due to silver flakes acting as barrier within the polymer matrix. In addition, the formulation of ICAs containing silver flakes and particles yielded a much higher reaction compared to conventional ICAs. The study showed that use of polyurethane (PU) as opposed to conventional Diglycidylether of bisphenol-A (DGEBA) showed a more stable system.     

Graphs whose critical groups have larger rank

The critical group C(G) of a graph G is a refinement of the number of spanning trees of the graph and is closely connected with the Laplacian matrix. Let r(G) be the minimum number of generators (i.e., the rank) of the group C(G) and β(G) be the number of independent cycles of G. In this paper, some forbidden induced subgraphs are given for r(G) = n − 3 and all graphs with r(G) = β(G) = n − 3 are characterized.     

Variations in the Concentrations of Cu and Zn and in the Ratio of Cu to Zn in Whole Blood and Hair Samples from Hepatocellular Carcinoma Patients and from Healthy Controls in Taiwan

An atomic absorption spectrophotometer was used to determine concentrations of copper and zinc and the ratio of Cu to Zn in samples of whole blood and hair from hepatocellular carcinoma (HCC) patients (n=51) and from healthy controls (n=50) in Taiwan. Our results indicate that the HCC patients have higher copper concentrations and higher ratios of Cu to Zn than do the healthy controls both in whole blood and hair samples, but only the concentration of copper and the ratio of Cu to Zn in whole blood were significantly different (p<0.001 and p<0.05). Conversely, a lower concentration of zinc was found in whole blood and hair samples of HCC patients. Similarly, only the concentration of zinc in whole blood showed a significant difference (p<0.001). We concluded that the whole blood concentrations of copper and zinc and the ratio of Cu to Zn seemed to have a higher correlation with HCC. Thus, we suggest that a sample of whole blood may be a more suitable diagnostic sample than is a hair sample for HCC.     

Some addition reactions of bisgermavinylidene

The reaction of bisgermavinylidene [(Me₃SiN?PPh₂)₂C?Ge→Ge?C(PPh₂?NSiMe₃)₂] ( 1 ) with AdNCO (Ad = Adamantyl) afforded the [2 + 2] cycloadditon product [(Me₃SiN?PPh₂)₂CGeC(O) NAd] ( 2 ). Similar reaction of 1 with Ph₃SiOH in tetrahydrofuran (THF) yielded the base‐stabilized germanium(II) triphenylsiloxide [H₂C(PPh₂?NSiMe₃)₂Ge(OSiPh₃)₂] ( 3 ). The results suggested that reactive germavinylidene may exist in solution and is capable of forming addition reaction products. The X‐ray structures of 2 and 3 were determined. Copyright © 2007 John Wiley & Sons, Ltd.     

Synthesis and light‐emitting properties of platinum‐containing oligoynes and polyynes derived from oligo(fluorenyleneethynylenesilylene)s

A series of blue‐light‐emitting oligo(fluorenyleneethynylenesilylene)s (OFESs) of the general formula HC?CRC?C(EC?CRC?C)_mEC?CRC?CH (E = SiPh₂, SiMe₂, or SiMe₂? SiMe₂; m = 0–2; R = 9,9‐dihexylfluorene‐2,7‐diyl) and their phosphorescent platinum‐containing oligoynes and polyynes were synthesized and characterized. The solution properties and regiochemical structures of this new structural class of organosilicon‐based polyplatinayne polymers {trans‐[? Pt(PBu₃)₂C ?CRC?C(EC?CRC?C)_mEC?CRC?C? ]_n} were studied with IR and NMR (¹H, ¹³C, ²⁹Si, and ³¹P) spectroscopy. The optical absorption and photoluminescence spectra of these metallopolymers were examined and compared with their discrete oligomeric model complexes. Our studies led to a novel approach of using the sp³‐silyl moiety as a conjugation interrupter to limit the effective conjugation length in metal polyynes, which could boost the phosphorescence decay rates essential for light‐energy harvesting from the triplet excited state. The influence of the heavy platinum atom and the group 14 silyl unit possessing different side‐group substituents on the thermal and phosphorescence properties was investigated in detail. We also established the goal of studying the evolution of the lowest singlet and triplet excited states with chain length m of OFESs and the nature of E in these metallopolymers. This work indicated that the phosphorescence emission efficiency harnessed through the heavy‐atom effect of platinum in the main chain did not change very much with oligomer chain length m but generally decreased with the E group in the order SiMe₂ > SiMe₂? SiMe₂ > SiPh₂. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4804–4824, 2006     

A companion matrix approach to the study of zeros and critical points of a polynomial

In this paper, we introduce a new type of companion matrices, namely, D-companion matrices. By using these D-companion matrices, we are able to apply matrix theory directly to study the geometrical relation between the zeros and critical points of a polynomial. In fact, this new approach will allow us to prove quite a number of new as well as known results on this topic. For example, we prove some results on the majorization of the critical points of a polynomial by its zeros. In particular, we give a different proof of a recent result of Gerhard Schmeisser on this topic. The same method allows us to prove a higher order Schoenberg-type conjecture proposed by M.G. de Bruin and A. Sharma.