Canonical Cartan connection and holomorphic invariants on Engel CR manifolds

We describe a complete system of invariants for 4-dimensional CR manifolds of CR dimension 1 and codimension 2 with Engel CR distribution by constructing an explicit canonical Cartan connection. The four essential invariants arising from the Cartan curvature are geometrically interpreted. We also investigate the relationship between the Cartan connection and the normal form of the defining equation of an embedded Engel CR manifold. This work was carried out in the framework of Australian Research Council Discovery Project DP0450725.     

The $ B\to\pi K$ puzzle and its relation to rare B and K decays

The standard-model interpretation of the ratios of charged and neutral rates, R _c and R _n, respectively, points towards a puzzling picture. Since these observables are affected significantly by colour-allowed electroweak (EW) penguins, this puzzle could be a manifestation of new physics in the EW penguin sector. Performing the analysis in the R _n- R _c plane, which is very suitable for monitoring various effects, we demonstrate that we may, in fact, move straightforwardly to the experimental region in this plane through an enhancement of the relevant EW penguin parameter q. We derive analytical bounds for q in terms of a quantity L, which measures the violation of the Lipkin sum rule, and point out that strong phases around are favoured by the data, in contrast to QCD factorisation. The modes imply a correlation between q and the angle that, in the limit of negligible rescattering effects and colour-suppressed EW penguins, depends only on the value of L. Concentrating on a minimal flavour-violating new-physics scenario with enhanced Z ⁰ penguins, we find that the current experimental values on require roughly . As the data give , L has either to move to smaller values once the data improve or new sources of flavour and CP violation are needed. In turn, the enhanced values of L seen in the data could be accompanied by enhanced branching ratios for the rare decays , , and . Most interesting turns out to be the correlation between the modes and , with the latter depending approximately on a single scaling variable .Received: 8 September 2003, Published online: 12 November 2003     

The 4-particle hydrogen-antihydrogen system revisited

The historical importance of the original quantum mechanical bond theory proposed by Heitler and London in 1927 as well as its pitfalls are reviewed. Modern ab initio treatments of H- systems are inconsistent with the logic behind algebraic Hamiltonians H± =H 0 ± H for charge-symmetrical and charge-asymmetrical 4 unit charge systems like H2 and H . Their eigenvalues E± =E 0± are exactly those of 1927 Heitler-London (HL) theory. Since these 2 Hamiltonians are mutually exclusive, only the attractive one can apply for stable natural molecular H2. A wrong choice leads to problems with antiatom . In line with earlier results on band and line spectra, we now prove that HL chose the wrong Hamiltonian for H2. Their theory explains the stability of attractive system H2 with a repulsive Hamiltonian H0 + H instead of with the attractive one H0-H, representative for charge-asymmetrical system H . A new second order symmetry effect is detected in this attractive Hamiltonian, which leads to a 3-dimensional structure for the 4-particle system. Repulsive HL Hamiltonian H+ applies at long range but at the critical distance, attractive charge-inverted Hamiltonian H- takes over and leads to bond H2 but in reality, H , for which we give an analytical proof. This analysis confirms and generalizes an earlier critique of the wrong long range behavior of HL-theory by Bingel, Preuss and Schmidtke and by Herring. Another wrong asymptote choice in the past also applies for atomic antihydrogen , which has hidden the Mexican hat potential for natural hydrogen. This generic solution removes most problems, physicists and chemists experience with atomic and molecular H , including the problem with antimatter in the Universe.     

Quadratic covariance matrix-based cooperative spectrum sensing method by using an evolutionary algorithm

Cognitive radio (CR) is a practical technology to solve the current low utilization of spectrum resources, and spectrum sensing is the most critical technique in a CR network. In this paper, a genetic simulated annealing algorithm based on quadratic covariance matrix and information geometry is proposed for cooperative spectrum sensing (CSS) to enhance the performance in the low signal-noise ratio (SNR). Firstly, the quadratic covariance matrix of cooperative secondary users (SUs) is used as the characteristic matrix to perform feature extraction. Secondly, based on the information geometry, the characteristic matrix is mapped on the statistical manifold to avoid information loss. Furthermore, the genetic simulated annealing algorithm is used to obtain a classifier on the statistical manifold, and the mutation process is improved by a new mutation operator to accelerate the convergence speed of the whole algorithm. Finally, the classifier is employed to implement spectrum sensing. In the simulation analysis, the proposed method has better spectrum sensing performance than the popular various methods under low SNR and faster convergence speed.     

Calculation of partition functions by measuring component distributions

A new algorithm is presented, which allows us to calculate numerically the partition function Z for systems, which can be described by arbitrary interaction graphs and lattices, e.g., Ising models or Potts models (for arbitrary values q>0), including random or diluted models. The new approach is suitable for large systems. The basic idea is to measure the distribution of the number of connected components in the corresponding Fortuin-Kasteleyn representation and to compare with the case of zero degrees of freedom, where the exact result Z=1 is known. As an application, d=2 and d=3 dimensional ferromagnetic Potts models are studied, and the critical values qc, where the transition changes from second to first order, are determined. Large systems of sizes N=1000(2) and N=100(3) are treated. The critical value qc(d=2)=4 is confirmed and qc(d=3)=2.35(5) is found.     

Nondestructive isolation of single cultured animal cells by femtosecond laser-induced shockwave

A shockwave induced by focusing an intense femtosecond laser onto a culture medium under a microscope was used to manipulate single cultured animal cells. Mouse NIH3T3 fibroblasts were cultured on a collagen matrix and placed on a microscope installation that included an intense femtosecond laser. Cells were detached individually from the matrix by the shockwave, after their filopodia were cut by focusing the laser directly on them. The appearance and locomotion of cells after detachment was monitored with a CCD camera. Filopodia of the detached cells were regenerated, and the cell adhered again to the matrix within 4 hrs after detachment. When the shockwave was induced at a pulse energy of 0.72 J/pulse, 80% of cells were successfully detached from the culture plate in a non-destructive manner. The force required to detach a cell was estimated to be a few N/m², which is larger than the photon force resulting from conventional laser trapping. PACS 42.62.Be; 47.40.Nm; 87.80.Rb     

Dimensionality Reduction of SPD Data Based on Riemannian Manifold Tangent Spaces and Isometry

Symmetric positive definite (SPD) data have become a hot topic in machine learning. Instead of a linear Euclidean space, SPD data generally lie on a nonlinear Riemannian manifold. To get over the problems caused by the high data dimensionality, dimensionality reduction (DR) is a key subject for SPD data, where bilinear transformation plays a vital role. Because linear operations are not supported in nonlinear spaces such as Riemannian manifolds, directly performing Euclidean DR methods on SPD matrices is inadequate and difficult in complex models and optimization. An SPD data DR method based on Riemannian manifold tangent spaces and global isometry (RMTSISOM-SPDDR) is proposed in this research. The main contributions are listed: (1) Any Riemannian manifold tangent space is a Hilbert space isomorphic to a Euclidean space. Particularly for SPD manifolds, tangent spaces consist of symmetric matrices, which can greatly preserve the form and attributes of original SPD data. For this reason, RMTSISOM-SPDDR transfers the bilinear transformation from manifolds to tangent spaces. (2) By log transformation, original SPD data are mapped to the tangent space at the identity matrix under the affine invariant Riemannian metric (AIRM). In this way, the geodesic distance between original data and the identity matrix is equal to the Euclidean distance between corresponding tangent vector and the origin. (3) The bilinear transformation is further determined by the isometric criterion guaranteeing the geodesic distance on high-dimensional SPD manifold as close as possible to the Euclidean distance in the tangent space of low-dimensional SPD manifold. Then, we use it for the DR of original SPD data. Experiments on five commonly used datasets show that RMTSISOM-SPDDR is superior to five advanced SPD data DR algorithms.     

Integration by parts formulas and rotationally invariant Sobolev calculus on free loop spaces

We give formulas for integration by parts over the path space and over the loop space of a manifold. We define Sobolev spaces and an Ornstein-Uhlenbeck operator on the loop space. We find some functionals which belong to all the Sobolev spaces.     

广义Kurosawa关系和广义LST关系及其实验验证

在qc?ω条件下,对极性声子频率色散关系进行简化,得到了描述高低频介电函数间关系的广义Kurosawa关系和广义LST(Lyddane-Sachs-Teller)关系。通过测量TGS(硫酸三甘氨酸)晶体的偏振Raman谱,使这一新的理论结果得到了实验验证。 关键词：     

Multi-quasiparticle states in 184 W via multi-nucleon transfer

A multi-nucleon transfer reaction using an 850 MeV ¹³⁶Xe beam incident on a ¹⁹⁸Pt target was used to populate high-spin states in ¹⁸⁴W, 14 nucleons from the target. A 4-quasiparticle isomer with ns has been observed for the first time and its de-excitation through collective and intrinsic structures studied. The results are compared with predictions of blocked BCS Nilsson calculations. Observation of this metastable state completes the tungsten 4-quasiparticle isomer systematics from A = 176 to 186. Mapping out the most yrast 4-quasiparticle isomers in these even-even tungsten isotopes suggests the existence of a highly favoured state in ¹⁸⁸W, within reach of current experimental set-ups.Received: 14 October 2003, Revised: 14 November 2003, Published online: 18 May 2004PACS: 21.10.Tg Lifetimes - 23.20.Lv transitions and level energies - 27.70. + q      

Geometric properties of QCD string from Willmore functional

The extremum of the Willmore-like functional for m-dimensional Riemannian manifold immersed in d-dimensional Riemannian manifold under normal variations is studied and various cases of interest are examined. This study is used to relate the parameters of QCD string action, including the Polyakov–Kleinert extrinsic curvature action, with the geometric properties of the world sheet. The world sheet has been shown to have negative stiffness on the basis of the geometric considerations.     

Towards a gravitation theory in Berwald-Finsler space

Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities satisfied by the Chern curvature to set up a gravitation theory in Berwald-Finsler space. The geometric part of the gravitational field equation is nonsymmetric in general. This indicates that the local Lorentz invariance is violated.     

Towards a gravitation theory in Berwald-Finsler space

Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities satisfied by the Chern curvature to set up a gravitation theory in Berwald-Finsler space. The geometric part of the gravitational field equation is nonsymmetric in general. This indicates that the local Lorentz invariance is violated.     

Born–Infeld Action on Discrete Spaces

We apply Connes' noncommutative geometry to a finite n-point space. The explicit Born-Infeld actions on this n-point space and n copies of a manifold are obtained.     

Canonical Sasakian Metrics

Let M be a closed manifold of Sasaki type. A polarization of M is defined by a Reeb vector field, and for any such polarization, we consider the set of all Sasakian metrics compatible with it. On this space we study the functional given by the square of the L ²-norm of the scalar curvature. We prove that its critical points, or canonical representatives of the polarization, are Sasakian metrics that are transversally extremal. We define a Sasaki-Futaki invariant of the polarization, and show that it obstructs the existence of constant scalar curvature representatives. For a fixed CR structure of Sasaki type, we define the Sasaki cone of structures compatible with this underlying CR structure, and prove that the set of polarizations in it that admit a canonical representative is open. We use our results to describe fully the case of the sphere with its standard CR structure, showing that each element of its Sasaki cone can be represented by a canonical metric; we compute their Sasaki-Futaki invariant, and use it to describe the canonical metrics that have constant scalar curvature, and to prove that only the standard polarization can be represented by a Sasaki-Einstein metric. During the preparation of this work, the first two authors were partially supported by NSF grant DMS-0504367.     

Screening effects in the ultra-high energy neutrino interactions

We study possible saturation effects in the total crosssections describing the interaction of ultra-high energy neutrinos with nucleons. This analysis is performed within two approaches, i.e., within the Golec-Biernat-Wüsthoff saturation model and within the scheme unifying the DGLAP and BFKL dynamics incorporating non-linear screening effects which follow from the Balitzki-Kovchegov equation. The structure functions in both approaches are constrained by HERA data. It is found that screening effects affect the extrapolation of the neutrino-nucleon total cross-sections to ultra-high neutrino energies and reduce their magnitude by a factor equal to about 2 at GeV. This reduction becomes amplified by nuclear shadowing in the case of the neutrino-nucleus cross-sections and an approximate estimate of this effect is performed.Received: 26 March 2003, Revised: 17 April 2003, Published online: 3 July 2003     

Method for construction of operators in Fock space

It is shown, by providing a general method for the construction that any Fock space linear operator defined on the dense linear manifold spanned by the particle number representation basis can be represented in terms of the annihilation and creation operators. The normal form of the representation is unique.     

Percolation Phase Transitions from Second Order to First Order in Random Networks

We investigate a percolation process where an additional parameter q is used to interpolate between the classical Erd¨os–R′enyi(ER) network model and the smallest cluster(SC) model. This model becomes the ER network at q = 1, which is characterized by a robust second order phase transition. When q = 0, this model recovers to the SC model which exhibits a first order phase transition. To study how the percolation phase transition changes from second order to first order with the decrease of the value of q from 1 to 0, the numerical simulations study the final vanishing moment of the each existing cluster except the N-cluster in the percolation process. For the continuous phase transition,it is shown that the tail of the graph of the final vanishing moment has the characteristic of the convexity. While for the discontinuous phase transition, the graph of the final vanishing moment possesses the characteristic of the concavity.Just before the critical point, it is found that the ratio between the maximum of the sequential vanishing clusters sizes and the network size N can be used to decide the phase transition type. We show that when the ratio is larger than or equal to zero in the thermodynamic limit, the percolation phase transition is first or second order respectively. For our model, the numerical simulations indicate that there exists a tricritical point qcwhich is estimated to be between0.2 qc 0.25 separating the two phase transition types.     

高温壁面液体射流冲击瞬态沸腾传热的实验研究

以水作为冷却介质,对高温壁面在射流冲击淬冷时的瞬态换热特性进行了实验研究,获得了介质在不同过冷度、不同射流速度下的完整沸腾曲线。实验结果表明。无论是增大工质过冷度还是提高射流速度,总会使得热壁面的冷却速率加大。在一定的过冷度和射流速度下壁温变化呈现快－慢－快的特点。临界热流密度随平均壁温变化率的增大而增大,二者之间存在线性关系．     

Global Solutions of Einstein—Dirac Equation on the Conformal Space

The difference between the Riemann and Lorentz spinor manifolds of four dimensions is that the Dirac operator of the former is elliptic and that of the latter is hyperbolic.Moreover the spinor group of the former is a compact group and that of the latter is a noncompact group,which is isomorphic to SL(2,C).Hence the results and their interpretation coming from the two theories would be different.In this short note we study only the Lorentz spinor manifold and,especially,the solutions of Einstein-Dirac equations on the conformal space,which is closely related to the AdS/CFT correspondence.