Ampleness of intersections of translates of theta divisors in an abelian fourfold

We prove the ampleness of the cotangent bundle of the intersection of two general translates of a theta divosor of the Jacobian of a general curve of genus . From this, we deduce the same result in a general, principally polarized abelian variety of dimension .

     

Inverse Matroid Intersection Problem

LetM ₁ andM ₂ be matroids onS,B be theirk-element common independent set, andw a weight function onS. Given two functionsb 0 andc 0 onS, the Inverse Matroid Intersection Problem (IMIP) is to determine a modified weight functionw such that (a)B becomes a maximum weight common independent set of cardinalityk underw, (b)c¦w — w¦ is minimum, and (c)¦w — w b. Many Inverse Combinatorial Optimization Problems can be considered as the special cases of the IMIP.In this paper we show that the IMIP can be solved in strongly polynomial time, and give a necessary and sufficient condition for the feasibility of the IMIP. Finally we extend the discussion to the version of the IMIP with Multiple Common Independent Sets.Research partially supported by the National Natural Science Foundation of China     

A renormalization result for the intersection local time of lattice random walks ind≧3 dimensions

In this paper we derive some general conditions on stable walks inZ ^d , under which the central limit theorem holds for their normalized intersection local time. In particular, we prove that the process given by the normalized intersection local time of the simple random walk inZ ^d , withd3, is weakly convergent to the standard Brownian motion.BiBoS; SFB 237 Bochum-Essen-Düsseldorf; CERFIM, Locarno.     

MOLECULAR DESIGN OF NEW KINDS OF AUXETIC POLYMERS AND NETWORKS

Three new kinds of molecular networks are designed and predicted to exhibit negative Poisson ratios. Molecular mechanics calculations on these networks show that the magnitude of Poisson ratios depends on the relative flexibility of beam and arm structures. Several new kinds of auxetic polymers, whose successful synthesis should be easier than that of the corresponding auxetic networks, are then proposed. It is found that the kabob-like polymers with auxegens lying vertically on the main chain can acquire auxeticity while those with auxegens lying horizontally on the main chain cannot. Besides, a half kabob-like or pseudo-ladder polymer with auxegens linked at the intersection of the beam and the arm does show auxeticity when adopting constrictive conformers. It is, however, worthwhile noting that the origins of auxeticity still await and strongly deserve further experimental and theoretical investigations.     

Quenching of Li (2P) by H2: potential energy surfaces, conical intersection seam, and diabatic bases

The quenching of Li (1s ²2p; ²P) to Li (1s ²2s; ²S) by H₂ is considered using coupled-cluster and multireference configuration-interaction techniques. C _{2 v} (²A₁, ²B₂) and C _{∞ v} (²Π,²Σ⁺) sections of the 1²A^′ and 2²A^′ potential energy surfaces are determined. The C _{2 v} portion of the 1²A^′−2²A^′ seam of conical intersection is studied. Perhaps the most significant finding is a surprising trifurcation of this seam into a portion with only C _s symmetry and the aforementioned C _{2 v} portion. The adiabatic-to-diabatic state transformation is considered in the vicinity of the seam of conical intersection using both perturbation theory and the dipole moment operator. The ²B₂ section of the 2²A^′ potential energy surface exhibits an exciplex in the general vicinity of the seam of conical intersection. The ²Π section of the 2²A^′ potential energy surface possesses a global minimum lying 1.86kcal/mol below the Li (²P)+H₂ asymptote. A van der Waals-like minimum with C _{∞ v} symmetry was found on the 1²A^′ potential energy surface. Received: 14 August 1998 / Accepted: 20 August 1998 / Published online: 11 November 1998     

邻氯甲苯光解反应机理的理论研究

采用量子化学从头算CASSCF和CASPT2方法对邻氯甲苯在低激发态上的光解机理进行了理论研究.研究结果表明,在266nm的光激发下邻氯甲苯可以激发到第一单重态上,然后存在两种可能的离解途径:一种是经过S1/S0交叉点内部转换驰豫到基态,然后甲基上的一个H转移形成邻-5-亚甲基-6-氯-1,3-环己二烯,进而C—Cl键断裂生成苄基;另一种是先后经过S1/T2和T2/T1交叉点驰豫到三重态,然后进行C—Cl键断裂,形成邻甲苯基.这两种途径具有相近的反应几率,与实验结果很吻合.     

Quasi‐embeddings of Steiner triple systems,or Steiner triple systems of different orders with maximum intersection

In this paper, we present a conjecture that is a common generalization of the Doyen–Wilson Theorem and Lindner and Rosa's intersection theorem for Steiner triple systems. Given u, v ≡ 1,3 (mod 6), u < v < 2u + 1, we ask for the minimum r such that there exists a Steiner triple system such that some partial system can be completed to an STS , where |?| = r. In other words, in order to “quasi‐embed” an STS(u) into an STS(v), we must remove r blocks from the small system, and this r is the least such with this property. One can also view the quantity (u(u ? 1)/6) ? r as the maximum intersection of an STS(u) and an STS(v) with u < v. We conjecture that the necessary minimum r = (v ? u) (2u + 1 ? v)/6 can be achieved, except when u = 6t + 1 and v = 6t + 3, in which case it is r = 3t for t ≠ 2, or r = 7 when t = 2. Using small examples and recursion, we solve the cases v ? u = 2 and 4, asymptotically solve the cases v ? u = 6, 8, and 10, and further show for given v ? u > 2 that an asymptotic solution exists if solutions exist for a run of consecutive values of u (whose required length is no more than v ? u). Some results are obtained for v close to 2u + 1 as well. The cases where ≈ 3u/2 seem to be the hardest. © 2004 Wiley Periodicals, Inc.     

A simple closure condition for the normal cone intersection formula

In this paper it is shown that if and are two closed convex subsets of a Banach space and , then whenever the convex cone, , is weak* closed, where and are the support function and the normal cone of the set respectively. This closure condition is shown to be weaker than the standard interior-point-like conditions and the bounded linear regularity condition.

     

Fibrés d'intersection

Let f:XSbe a projective morphism of Noetherian schemes. We assume fpurely of relative dimension dand finite Tor-dimensional. We associate to d+1 invertible sheaves on Xa line bundle I _X/S ( ) on Sdepending additively on the , commuting to good base changes and which represents the integral along the fibres of fof the product of the first Chern classes of the . If d=0, I _X/S ( ) is the norm N _X/S ( ).     

Cycles on Arithmetic Surfaces

We develop a localized intersection theory for arithmetic schemes on the model of Fulton's intersection theory. We prove a Lefschetz fixed point formula for arithmetic surfaces, and give an application to a conjecture of Serre on the existence of Artin's representations for regular local rings of dimension 2 and unequal characteristic.