A Genus-3 Topological Recursion Relation

In this paper, we give a new genus-3 topological recursion relation for Gromov-Witten invariants of compact symplectic manifolds. This formula also applies to intersection numbers on moduli spaces of spin curves. A by-product of the proof of this formula is a new relation in the tautological ring of the moduli space of 1-pointed genus-3 stable curves. Research of the first author was partially supported by NSF grant DMS-0204824 Research of the second author was partially supported by NSF grant DMS-0505835     

A C + + computational environment for biomolecular sequence management

The wide production of biomolecular data of the last 30 years, mainly due to the rapid evolving of technologies as well as to the accomplishment of the Genome Projects, led to the necessity of appropriate computational approaches for data storage, manipulation and analyses, giving place to a fast evolving area of Biology: Computational Biology or Bioinformatics.We propose here a new method for the storage of the sequences and their analyses using the C + + programming language, checking the effectiveness of an object oriented approach for new models, suitable to manage data representation and analyses, to improve the efficiency of computational methodologies to solve problems of general interest in bioinformatics. We developed a framework with the aim to decrease the computational costs for the storage and some basic manipulations of nucleic acid sequences. The remarkable reduction of memory requirements with no loss of efficiency makes this approach a first well promising step in order to get a more efficient environment for the manipulation and the management of nucleic acid data sets, in a field of research with hard challenges for Computer and Life Sciences.Mathematics Subject Classification: 68U99G. Toraldo, via Universita’ 100, 80055 Portici, Napoli, Italy     

Palladium-catalyzed novel addition-elimination reaction of alkenyltin reagents to norbornene

Palladium-catalyzed reaction between 1-alkenyltin trichlorides and norbornene resulted in stereoselective formation of 3-alkylidenepentacyclo[9.2.1.^5,81.^1,110.^2,100^4,9]pentadecane instead of an expected simple alkenylstannylation product. Generation of trichlorostannane and its decomposition product, tin(II) chloride, was confirmed by trapping it with methyl propiolate and norbornene and analysis of the reaction by ¹¹⁹Sn NMR, respectively.     

Performance of noise barriers with various edge shapes and acoustical conditions

The performances of barriers having different shapes and surface conditions were tested using the boundary element method in a well-controlled environment. The heights and widths of the barriers were standardized and the insertion losses for six receiver positions were averaged and compared. Figures displaying the results allow for straightforward barrier performance estimation. It was shown that absorbing and soft edges significantly improve the efficiency of the barrier, but configuration modifications provide only a slight improvement. The soft T-shaped barrier produces the highest performance. A 3 m high T-shaped barrier provides the same performance as a 10 m high plain barrier. The spectral efficiency was also investigated. The insertion loss spectra for the absorbing and the soft barriers exhibit a similar shape, but the rigid barrier differs from these two.     

Adsorption of fission products onto soils using a fission multitracer

The adsorption behavior of fission products to various soils was studied using a multitracer. The multitracer was prepared by neutron irradiation of ²³⁵U. Distribution coefficients of fission products were obtained for seventeen kinds of Japanese soils. It was found that zirconium, niobium, and rare earth elements show high distribution coefficients for all soil samples, however, elements like alkali metals show varied values.     

Living anionic polymerization of N‐methoxymethyl‐N‐isopropylacrylamide: Synthesis of well‐defined poly(N‐isopropylacrylamide) having various stereoregularity

Anionic polymerization of N‐methoxymethyl‐N‐isopropylacrylamide ( 1 ) was carried out with 1,1‐diphenyl‐3‐methylpentyllithium and diphenylmethyllithium, ‐potassium, and ‐cesium in THF at ?78 °C for 2 h in the presence of Et₂Zn. The poly( 1 )s were quantitatively obtained and possessed the predicted molecular weights based on the feed molar ratios between monomer to initiators and narrow molecular weight distributions (M_w/M_n = 1.1). The living character of propagating carbanion of poly( 1 ) either at 0 or ?78 °C was confirmed by the quantitative efficiency of the sequential block copolymerization using N,N‐diethylacrylamide as a second monomer. The methoxymethyl group of the resulting poly( 1 ) was completely removed to give a well‐defined poly(N‐isopropylacrylamide), poly(NIPAM), via the acidic hydrolysis. The racemo diad contents in the poly(NIPAM)s could be widely changed from 15 to 83% by choosing the initiator systems for 1 . The poly(NIPAM)s obtained with Li⁺/Et₂Zn initiator system possessed syndiotactic‐rich configurations (r = 75–83%), while either atactic (r = 50%) or isotactic poly(NIPAM) (r = 15–22%) was generated with K⁺/Et₂Zn or Li⁺/LiCl initiator system, respectively. Atactic and syndiotactic poly(NIPAM)s (42 < r < 83%) were water‐soluble, whereas isotactic‐rich one (r < 31%) was insoluble in water. The cloud points of the aqueous solution of poly(NIPAM)s increased from 32 to 37 °C with the r‐contents. These indicated the significant effect of stereoregularity of the poly(NIPAM) on the water‐solubility and the cloud point in water © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4832–4845, 2006     

A note on unit and class number of real quadratic fields

Letp be an odd prime withp1 (mod 4) andQ(p) be the real quadratic field. Also let andh denote the fundamental unit and the class number of Q(p), respectively. The main purpose of this paper is to study the explicit expressions of ^h and ^2h , and to discuss the problems related to the conjecture of Ankeny-Artin-Chowla.