Analysis of a Splitting Estimator for Rare Event Probabilities in Jackson Networks

We consider a standard splitting algorithm for the rare-event simulation of overflow probabilities in any subset of stations in a Jackson network at level n, starting at a fixed initial position. It was shown in DeanDup09 that a subsolution to the Isaacs equation guarantees that a subexponential number of function evaluations (in n) suffice to estimate such overflow probabilities within a given relative accuracy. Our analysis here shows that in fact O(n^{2{\beta}+1}) function evaluations suffice to achieve a given relative precision, where {\beta} is the number of bottleneck stations in the network. This is the first rigorous analysis that allows to favorably compare splitting against directly computing the overflow probability of interest, which can be evaluated by solving a linear system of equations with O(n^{d}) variables.Comment: 23 page

Weak magnetism and the Mott-state of vanadium in superconducting Sr2VO3FeAs

We report neutron scattering data and DFT calculations of the stoichiometric iron-arsenide superconductor Sr2VO3FeAs. Rietveld refinements of neutron powder patterns confirm the ideal composition without oxygen deficiencies. Experiments with polarized neutrons prove weak magnetic ordering in the V-sublattice of Sr2VO3FeAs at ~ 45 K with a probable propagation vector q = (1/8,1/8,0). The ordered moment of ~ 0.1 muB is too small to remove the V-3d bands from the Fermi level by magnetic exchange splitting, and much smaller than predicted from a recent LDA+U study. By using DFT calculations with a GGA+EECE functional we recover the typical quasi-nested Fermi-surface even without magnetic moment. From this we suggest that the V-atoms are in a Mott-state where the electronic correlations are dominated by on-site Coulomb-repulsion which shifts the V-3d states away from the Fermi energy. Our results are consistent with photoemission data and clearly reveal that Sr2VO3FeAs is a typical iron-arsenide superconductor with quasi-nested hole- and electron-like Fermi surface sheets, and constitutes no new paradigm. We suggest that intrinsic electron-doping through V3+/V4+ mixed valence is responsible for the absence of SDW ordering.Comment: 5 pages, 5 figure

X-ray scattering studies of charge stripes in transition-metal oxides

This thesis describes the development of single crystal x-ray scattering applied to the study of charge stripes in some exotic transition-metal oxides. Charge stripes in the cuprates and manganites are strongly associated with high T(_c) superconductivity and colossal magnetoresistance, and can be characterised by the satellite reflections located around related Bragg peaks below the charge ordering transition temperature ( T(_co). The intensities of these extremely weak satellite reflections are between l0(^-4) and 10(^-6) less than those of Bragg reflections, thus very high brilliant rotating-anode x-ray and synchrotron radiation sources are required to study them. The structure factors and correlation lengths of the charge stripes can be directly obtained by measurements of the integrated intensities and peak widths of the charge ordering satellite reflections as a function of temperature. The charge stripes in single crystals of Bi(_0.24)Ca(_o.76)MnO(_3), Nd(_0.5)Sr(_0.5)MnO(_3) and La(_5/3)Sr(_1/3)NiO(_4) have been comprehensively characterised using both laboratory and synchrotron radiation x-ray scattering. The measurements on Bi(_0.24)Ca(_0.76)MnO(_3) directly demonstrate a strong relationship between the charge stripe ordering and the first-order structural phase transition, which is common in many perovskite manganites. Direct evidence for the existence of perpendicular charge-ordered domains in manganites was obtained for the first time by x-ray scattering in Nd(_0.5)Sr(_0.5)MnO(_3), and this result demonstrates that charge stripes have complex structures in the mesoscopic length scale. Scattering was also observed at the positions in reciprocal space associated with spin ordering into stripes. These showed evidence of different critical behaviour than the corresponding charge stripe satellites. The quasi two-dimensional feature of the charge stripes in La(_5/3)Sr(_1/3)NiO(_4) was successfully demonstrated by the critical exponents of the charge stripe melting and by the measurements of their m-plane and out-of-plane correlation lengths. Experimental evidence for the existence of electronic liquid crystal phases in La(_5/3)Sr(_1/3)NiO(_4) was obtained, in agreement with recent theoretical prediction

Development of Scoring Standard of English Oral Test in Respects of Research and Practice

This paper aims to summarize the development of international oral test scoring standards since 1980s. The development of scoring standards for oral test mainly includes two aspects: research and practice. In the respect of research, the scoring standard of oral test has gone through three stages: “expert experience”, “practitioner cognition” and “learner development”; In terms of practice, the scoring standard of oral test can be roughly divided into three types: “native speaker”, “being able to express” and “typical characteristics”. Based on the analysis of representative research papers and typical practical cases, this paper sorts out the development of international oral test scoring standards in order to provide suggestions for the research and practice of oral test scoring standards in China

The Application of Self-evaluation in English Reading Teaching

Self-evaluation is an important part of formative evaluation. Students\u27 self-evaluation can not only enable students to find the problems in their learning and timely understand the weak links in their learning, but also enable teachers to clearly grasp the true ideas of students and implement targeted teaching according to the feedback given by students

Tilings of the sphere by congruent quadrilaterals II: edge combination a3ba^3 b with rational angles

Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This second one applies the powerful tool of trigonometric Diophantine equations to classify the case of $a^3b$-quadrilaterals with all angles being rational degrees. There are $12$ sporadic and $3$ infinite sequences of quadrilaterals admitting the $2$-layer earth map tilings together with their modifications, and $3$ sporadic quadrilaterals admitting $4$ exceptional tilings. Among them only $3$ quadrilaterals are convex. New interesting non-edge-to-edge triangular tilings are obtained as a byproduct.Comment: 36 pages, 36 figures, 10 table