Spencer cohomologies and symmetry groups

We propose the construction of a spectral sequence converging to Spencer cohomologies. By using symmetry groups of differential equations systems, we manage to unify computations by reduction to the invariant systems over a homogeneous space. The conditions of coincidence of Spencer cohomologies with the cohomologies of an invariant Spencer complex we obtain from the arithmetic of a -characteristic manifold with respect to fundamental weights of the homogeneous space.     

Large deviations for martingales with some applications

Let(X _i ) be a martingale difference sequence. LetY be a standard normal random variable. We investigate the rate of uniform convergence

并行“冒泡”排序算法的改进

并行“冒泡”排序算法的改进黄干平（武汉大学计算机科学系,武汉,４３００７２）关键词排序,并行算法,冒泡中国法分类号ｗ３０１．６ＰＢＳＭ并行排序算法是对ＫａｚｕｈｉｒｓＳａｄｏ和ＹｏｓｈｉｈｉｄｅＩｇａｒａｓｈ的并行“冒泡’书ｒ序算法’“的改进,其并行...     

Eigenresonance states in the Kronig-Penney model

We investigate a sandwich of three layer systems with Dirac -functions in the Kronig-Penney model. The inner system ofN=5 atomic layers is enclosed by the two outer systems with different potential strength. The numberM of the atomic layers in the outer system is varied betweenM=9 and infinity, whereas the numberN of the inner layers is held fixed. We obtain the transmission coefficient for the finite system in the region of scattering energies (E>0). An alternating set of transmission gaps, transmission bands and bands of eigenresonance states is obtained. The normalizable eigenresonances occur (forM going to infinity), if a transmission band of the inner system overlaps a transmission gap of the outer systems. The reason for obtaining solutions of standing waves in the band of eigenresonances is the rapid change of the wave phase of a traveling wave, which occurs in a transmission band of the inner system.     

Zero cycles on conic fibrations and a conjecture of Bloch

Let X be a smooth projective surface over a number field k. Let (CH₀(X)) denote the Chow group of zero-cyles modulo rational equivalence on X. Let CH₀(X) be the subgroup of CH ₀(X) consisting of classes which vanish when going over to an arbitrary completion of k. Bloch put forward a conjecture asserting that this group is isomorphic to the Tate-Shafarevich group of a certain Galois module atttached to X. In this paper, we disprove this general conjecture. We produce a conic bundle X over an elliptic curve, for which the group (CH₀(X) is not zero, but the Galois-theoretic Tate-Shafarevich group vanishes.     

Consistency of a rank test against general alternatives of change points (surfaces) and continuous trend

Considered are modifications of a rank test of randomness for the one- and multi-dimensional regular design cases as well as for the one- and multi-dimensional random design cases. The null hypothesis is that all observations are independent and identically distributed. The main result is the proof of consistency of the test in each of the above cases against two general alternatives.Alternative 1: there exists a pairwise disjoint partion U _i =1 ^m D _i =D, where D d1, is a bounded domain inside which one makes observations, such that (1) if an observation point falls insideD _i , then the corresponding observed value is the realization of a random variable _i i = l,...,m; (2) there exists an ordering % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamXvP5wqonvsaeHbfv3ySLgzaGqbaiab-Tha7jabe67a4Hqbdiab% +LgaPnaaBaaaleaacaWGRbaabeaakiab-1ha9naaDaaaleaacaWGRb% Gaeyypa0JaaGymaaqaaiaad2gaaaaaaa!4C2D!\[\{ \xi i_k \} _{k = 1}^m \], where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabe67a4nXvP5wqonvsaeHbfv3ySLgzaGqbdiab-LgaPnaaBaaa% leaacaWGRbaabeaaaaa!454D!\[\xi i_k \] is stochastically smaller than % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabe67a4nXvP5wqonvsaeHbfv3ySLgzaGqbdiab-LgaPnaaBaaa% leaacaWGRbaabeaakmaaBaaaleaacqGHRaWkcaaIXaaabeaakiaacY% cacaWGRbGaeyypa0JaaGymaiaacYcacaGGUaGaaiOlaiaac6cacaGG% SaGaamyBaiabgkHiTiaaigdaaaa!509B!\[\xi i_k _{ + 1} ,k = 1,...,m - 1\], (3) the partition is independent of the number of observation points. Note thatm, this ordering, and the sets D _i are not known a priori: one tests only for the existence of such a partition. Note also that in the one-dimensional case the initial sequence need not be stochastically monotone under the alternative.Alternative 2: there exists an arbitrary asymptotically continuous trend in location. Asymptotically continuous means that the trend converges to some continuous, not identically constant function as the number of data points goes to infinity. This function need not be monotone.A numerical example illustrating the use of the obtained results for image analysis (edge detection) is presented.     

Approximate minimum-cost multicommodity flows in\tilde O(ɛ −2 KNM) timetime

We show that an ε-approximate solution of the cost-constrainedK-commodity flow problem on anN-nodeM-arc network,G can be computed by sequentially solving O(K(? ^?2+logGK) logGM log (G? ^?1 GK)) single-commodity minimum-cost flow problems on the same network. In particular, an approximate minimum-cost multicommodity flow can be computed in $\tilde O$ (G? ^?2 GKNM) running time, where the notation Õ(·) means “up to logarithmic factors”. This result improves the time bound mentioned by Grigoriadis and Khachiyan [4] by a factor ofM/N and that developed more recently by Karger and Plotkin [8] by a factor of? ^?1. We also provide a simple $\tilde O$ (NM)-time algorithm for single-commodity budget-constrained minimum-cost flows which is $\tilde O$ (? ^?3) times faster than the algorithm developed in the latter paper.     

Perturbation analysis of the orthogonal procrustes problem

Given two arbitrary real matricesA andB of the same size, the orthogonal Procrustes problem is to find an orthogonal matrixM such that the Frobenius norm MA – B is minimized. This paper treats the common case when the orthogonal matrixM is required to have a positive determinant. The stability of the problem is studied and supremum results for the perturbation bounds are derived.     

Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant

Summary This work is concerned with the existence and uniqueness of a class of semimartingale reflecting Brownian motions which live in the non-negative orthant of ^d . Loosely speaking, such a process has a semimartingale decomposition such that in the interior of the orthant the process behaves like a Brownian motion with a constant drift and covariance matrix, and at each of the (d-1)-dimensional faces that form the boundary of the orthant, the bounded variation part of the process increases in a given direction (constant for any particular face) so as to confine the process to the orthant. For historical reasons, this pushing at the boundary is called instantaneous reflection. In 1988, Reiman and Williams proved that a necessary condition for the existence of such a semimartingale reflecting Brownian motion (SRBM) is that the reflection matrix formed by the directions of reflection be completely-L. In this work we prove that condition is sufficient for the existence of an SRBM and that the SRBM is unique in law. It follows from the uniqueness that an SRBM defines a strong Markov process. Our results have potential application to the study of diffusions arising as approximations tomulti-class queueing networks.Research supported in part by NSF Grants DMS 8657483, 8722351 and 9023335, and a grant from AT&T Bell Labs. In addition, R.J. Williams was supported in part during the period of this research by an Alfred P. Sloan Research Fellowship     

New Monte Carlo method for the self-avoiding walk

We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We find=2.63820 ± 0.00004 ± 0.00030=1.352 ± 0.006 ± 0.025v=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length 166, using 340 hours CPU time on a CDC Cyber 170–730. We compare our results to previous work and indicate some directions for future research.