Analysis of relations between covariance weights and corresponding maximum Eigen values

This paper studies on how to get an idea through maximum eigen values, when allocating weights to covariance matrix. The eigen density distribution with respect to the largest eigen value is analysed. This study will help to determine the fluctuation of the eigen distribution with respect to allocated weight of the covariance matrix. This can be used to develop the classic portfolio asset allocation model by adding investors‘ ideas as parameters or weights. The maximum eigen value is 2.24 and the corresponding weight is 1.6, the minimum eigen value is 0.24 and the corresponding weight is 0.9. There are two peaks of the eigen values at 0.62 and 2.24 respectively 0.5 and 1.6 of weights. Two minimum points identified with corresponding eigen values are 0.43 and 0.24 respectively 0.2 and 0.9 of weights. For comparison the density function is plotted with Q = 3.22 and variance 0.85: this theoretical value was obtained assuming that the matrix is purely random except for its highest eigen value. The fact that the lower edge of the density is strictly positive (Except for the Q = 1); then there are no eigen values between 0 and the minimum eigen value

Structural Probe of a Glass Forming Liquid: Generalized Compressibility

We introduce a new quantity to probe the glass transition. This quantity is a linear generalized compressibility which depends solely on the positions of the particles. We have performed a molecular dynamics simulation on a glass forming liquid consisting of a two component mixture of soft spheres in three dimensions. As the temperature is lowered (or as the density is increased), the generalized compressibility drops sharply at the glass transition, with the drop becoming more and more abrupt as the measurement time increases. At our longest measurement times, the drop occurs approximately at the mode coupling temperature $T_C$. The drop in the linear generalized compressibility occurs at the same temperature as the peak in the specific heat. By examining the inherent structure energy as a function of temperature, we find that our results are consistent with the kinetic view of the glass transition in which the system falls out of equilibrium. We find no size dependence and no evidence for a second order phase transition though this does not exclude the possibility of a phase transition below the observed glass transition temperature. We discuss the relation between the linear generalized compressibility and the ordinary isothermal compressibility as well as the static structure factor.Comment: 18 pages, Latex, 26 encapsulated postscript figures, revised paper is shorter, to appear in Phys. Rev.

Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder

We have studied how 2- and 3- dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and applied stress. For each configuration, there is a unique jamming threshold, $\phi_c$, at which particles can no longer avoid each other and the bulk and shear moduli simultaneously become non-zero. The distribution of $\phi_c$ values becomes narrower as the system size increases, so that essentially all configurations jam at the same $\phi$ in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close-packing. In fact, our results provide a well-defined meaning for "random close-packing" in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold, Point J, occurring at zero temperature and applied stress and at the random close-packing density, has properties reminiscent of an ordinary critical point. As Point J is approached from higher packing fractions, power-law scaling is found for many quantities. Moreover, near Point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J. However, Point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally, as Point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. All of these results suggest that Point J may control behavior in its vicinity-perhaps even at the glass transition.Comment: 21 pages, 20 figure

Branching Fractions for D0 -> K+K- and D0 -> pi+pi-, and a Search for CP Violation in D0 Decays

Using the large hadroproduced charm sample collected in experiment E791 at Fermilab, we have measured ratios of branching fractions for the two-body singly-Cabibbo-suppressed charged decays of the D0: (D0 -> KK)/(D0 -> Kpi) = 0.109 +- 0.003 +- 0.003, (D0 -> pipi)/(D0 -> Kpi) = 0.040 +- 0.002 +- 0.003, and (D0 -> KK)/(D0 -> pipi) = 2.75 +- 0.15 +- 0.16. We have looked for differences in the decay rates of D0 and D0bar to the CP eigenstates K+K- and pi+pi-, and have measured the CP asymmetry parameters A_CP(K+K-) = -0.010 +- 0.049 +- 0.012 and A_CP(pi+pi-) = -0.049 +- 0.078 +- 0.030, both consistent with zero.Comment: 10 Postscript pages, including 2 figures. Submitted to Phys. Lett.

Asymmetries between the production of D+ and D- mesons from 500 GeV/c pi- nucleon interactions as a function of xF and pt**2

We present asymmetries between the production of D+ and D- mesons in Fermilab experiment E791 as a function of xF and pt**2. The data used here consist of 74,000 fully-reconstructed charmed mesons produced by a 500 GeV/c pi- beam on C and Pt foils. The measurements are compared to results of models which predict differences between the production of heavy-quark mesons that have a light quark in common with the beam (leading particles) and those that do not (non-leading particles). While the default models do not agree with our data, we can reach agreement with one of them, PYTHIA, by making a limited number of changes to parameters used

Search for Rare and Forbidden Dilepton Decays of the D+, Ds, and D0 Charmed Mesons

We report the results of a search for flavor-changing neutral current, lepton-flavor violating, and lepton-number violating decays of D+, Ds, and D0 mesons (and their antiparticles) into modes containing muons and electrons. Using data from Fermilab charm hadroproduction experiment E791, we examine the pi,l,l and K,l,l decay modes of D+ and Ds and the l+l- decay modes of D0. No evidence for any of these decays is found. Therefore, we present branching-fraction upper limits at 90% confidence level for the 24 decay modes examined. Eight of these modes have no previously reported limits, and fourteen are reported with significant improvements over previously published results.Comment: 12 pages, 3 figures, LaTeX, elsart.cls, epsf.sty, amsmath.sty Submitted to Physics Letters

Search for CP Violation in Charged D Meson Decays

We report results of a search for CP violation in the singly Cabibbo-suppressed decays D+ -> K- K+ pi+, phi pi+, K*(892)0 K+, and pi- pi+ pi+ based on data from the charm hadroproduction experiment E791 at Fermilab. We search for a difference in the D+ and D- decay rates for each of the final states. No evidence for a difference is seen. The decay rate asymmetry parameters A(CP), defined as the difference in the D+ and D- decay rates divided by the sum of the decay rates, are measured to be: A(CP)(K K pi) = -0.014 +/- 0.029, A(CP)(phi pi) = -0.028 +/- 0.036, A(CP)(K*(892) K) = -0.010 +/- 0.050, and A(CP)(pi pi pi) = -0.017 +/- 0.042.Comment: 13 pages, 5 figures, 1 table; Elsevier LaTe

Measurement of the form-factor ratios for D+ --> K* l nu

The form factor ratios rv=V(0)/A1(0), r2=A2(0)/A1(0) and r3=A3(0)/A1(0) in the decay D+ --> K* l nu, K* -->K-pi+ have been measured using data from charm hadroproduction experiment E791 at Fermilab. From 3034 (595) signal (background) events in the muon channel, we obtain rv=1.84+-0.11+-0.09, r2=0.75+-0.08+-0.09 and, as a first measurement of r3, we find 0.04+-0.33 +-0.29. The values of the form factor ratios rv and r2 measured for the muon channel are combined with the values of rv and r2 that we have measured in the electron channel. The combined E791 results for the muon and electron channels are rv=1.87+-0.08+-0.07 and r2=0.73+-0.06+-0.08.Comment: 9 pages + 3 figures ; submitted to PL

Differential cross sections, charge production asymmetry, and spin-density matrix elements for D*(2010) produced in 500 GeV/c pi^- nucleon interactions

We report differential cross sections for the production of D*(2010) produced in 500 GeV/c pi^- nucleon interactions from experiment E791 at Fermilab, as functions of Feynman-x (x_F) and transverse momentum squared (p_T^2). We also report the D* +/- charge asymmetry and spin-density matrix elements as functions of these variables. Investigation of the spin-density matrix elements shows no evidence of polarization. The average values of the spin alignment are \eta= 0.01 +- 0.02 and -0.01 +- 0.02 for leading and non-leading particles, respectively.Comment: LaTeX2e (elsart.cls). 13 pages, 6 figures (eps files). Submitted to Physics Letters

Mass Splitting and Production of Σc0\Sigma_c^0 and Σc++\Sigma_c^{++} Measured in 500GeV500 {GeV} π−−\pi^- -N Interactions

From a sample of $2722 \pm 78$ $\Lambda_c^+$ decaying to the $pK^-\pi^+$ final state, we have observed, in the hadroproduction experiment E791 at Fermilab, $143 \pm 20$ $\Sigma_c^0$ and $122 \pm 18$ $\Sigma_c^{++}$ through their decays to $\Lambda_c^+ \pi^{\pm}$. The mass difference $M(\Sigma_c^0) - M(\Lambda_c^+$) is measured to be $(167.38\pm 0.29\pm 0.15) {MeV}$; for $M(\Sigma_c^{++}) - M(\Lambda_c^+)$, we find $(167.76\pm 0.29\pm0.15) {MeV}$. The rate of $\Lambda_c^+$ production from decays of the $\Sigma_c$ triplet is (22\pm 2\pm 3) {%} of the total $\Lambda_c^+$ production assuming equal rate of production from all three, as measured for $\Sigma_c^0$ and $\Sigma_c^{++}$. We do not observe a statistically significant $\Sigma_c$ baryon-antibaryon production asymmetry. The $x_F$ and $p_t^2$ spectra of $\Lambda_c^+$ from $\Sigma_c$ decays are observed to be similar to those for all $\Lambda_c^+$'s produced.Comment: 15 pages, uuencoded postscript 3 figures uuencoded, tar-compressed fil