A superlinearly convergent predictor-corrector method for degenerate LCP in a wide neighborhood of the central path with -iteration complexity

An interior point method for monotone linear complementarity problems acting in a wide neighborhood of the central path is presented. The method has -iteration complexity and is superlinearly convergent even when the problem does not possess a strictly complementary solution. Mathematics Subject Classification (2000): 49M15, 65K05, 90C33 Work supported by the National Science Foundation under Grant No. 0139701. An erratum to this article is available at.     

Large Deviations View Points for Heavy-Tailed Random Walks

Let X ₁, X ₂,... be a sequence of i.i.d. non-negative random variables with heavy tails. W e study logarithmic asymptotics for the distributions of the partial sums S _n = X ₁ + ··· + X _n . Our main interest is in the crude estimates P(S _n > n ^x ) large8776.gif" alt="ap" align="MIDDLE" BORDER="0"> n ^{–large945.gif" alt="agr" align="BASELINE" BORDER="0">x + 1} for appropriate values of x where large945.gif" alt="agr" align="BASELINE" BORDER="0"> is a specific parameter. The related conjecture proposed by Gantert (Stat. Probab. Lett. 49, 113–118) is investigated.     

Generic compactness reformulated

We point out a connection between reflection principles and generic large cardinals. One principle of pure reflection is introduced that is as strong as generic supercompactness of large969.gif" alt="ohgr" align="BASELINE" BORDER="0">₂ by large931.gif" alt="Sgr" align="BASELINE" BORDER="0">-closed forcing. This new concept implies CH and extends the reflection principles for stationary sets in a canonical way.Mathematics Subject Classification (2000): 03E50, 03E55     

Supersymmetry at Dø and other new phenomena searches in Run II

The RunII of the Dø experiment was started in March 2001. The first preliminary results on searches for new physics are presented, with a luminosity of ～ 10 pb^?1 from the data collected in 2001-2002. We report results in mSUGRA (jets + missingEt channel), GMSB (diphotons), RPV (trileptons and like sign dileptons) and large extra dimensions (dielectrons and diphotons).     

Structures of large transition metal clusters

The present review surveys the results of X-ray diffraction studies of large stoichiometric transition metal clusters containing from 20 to 145 atoms in metal cores surrounded by ligand shells (72 compounds). Structures of such clusters have fragments of close packings (face-centered cubic (f.c.c.), hexagonal close (h.c.p.), and body-centered cubic (b.c.c.) packings) characteristic of crystalline bulk metals as well as mixed packings (f.c.c./h.c.p.), local close packings with pentagonal symmetry, and strongly distorted large8220.gif" alt="ldquo" align="MIDDLE" BORDER="0">amorphouslarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0"> packings. The observed packing types, their distortions, and the relationship between the atomic structures of metal cores and the atomic radial distribution functions (RDF) are discussed. The structural principles established for the large clusters are applied to analysis of the experimental RDF for metal nanoparticles determined by X-ray diffraction and EXAFS spectroscopy.     

Large Deviations of Empirical Measures Under Symmetric Interaction

We prove the large deviation principle for the joint empirical measure of pairs of random variables which are coupled by a large8220.gif" alt="ldquo" align="MIDDLE" BORDER="0">totally symmetriclarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0"> interaction. The rate function is given by an explicit bilinear expression, which is finite only on product measures and hence is non-convex.     

Moderate Deviations and Large Deviations for Kernel Density Estimators

Let f _n be the non-parametric kernel density estimator based on a kernel function K and a sequence of independent and identically distributed random variables taking values in large8477.gif" alt="Ropf" align="BASELINE" BORDER="0"> ^d . It is proved that if the kernel function is an integrable function with bounded variation, and the common density function f of the random variables is continuous and f(x) large8594.gif" alt="rarr" align="BASELINE" BORDER="0"> 0 as |x| large8594.gif" alt="rarr" align="BASELINE" BORDER="0"> large8734.gif" alt="infin" align="MIDDLE" BORDER="0">, then the moderate deviation principle and large deviation principle for hold.     

非负Ricci曲率开流形的拓扑

我们证明了对于具有非负Rieei曲率,大体积增长且内半径下有界的完备n维Riemann流形,只要存在常数C>0使得 则它微分同胚于欧式空间Rn.我们还证明了在某些pinching条件下具有非负射线曲率的完备n维Riemarm流形微分同胚与Rn,改进了已知的结果.     

Large Deviation Principle for Additive Functionals of Brownian Motion Corresponding to Kato Measures

Let (B _t ,P ^W _x ) be the Brownian motion. Let large956.gif" alt="mgr" align="MIDDLE" BORDER="0"> be a Radon measure in the Kato class and A ^{large956.gif" alt="mgr" align="MIDDLE" BORDER="0">} _t the additive functional associated with large956.gif" alt="mgr" align="MIDDLE" BORDER="0">. We prove that A ^{large956.gif" alt="mgr" align="MIDDLE" BORDER="0">} _t /t obeys the large deviation principle.     

Asymptotic Expansion of the Distribution Density Function for the Sum of Random Variables in the Series Scheme in Large Deviation Zones

The work is designated for obtaining asymptotic expansions and determination of structures of the remainder terms that take into consideration large deviations both in the Cramer zone and Linnik power zones for the distribution density function of sums of independent random variables in a triangular array scheme. The result was obtained using general Lemma 6.1 of Saulis and Statulevilarge269.gif" alt="ccaron" align="BASELINE" BORDER="0">ius in Limit Theorems for Large Deviations (Kluwer, 1991) and joining the methods of characteristic functions and cumulants. The work extends the theory of sums of random variables and in a special case, improves S. A.Book's results on sums of random variables with weights.