scholarly journals Joint global fluctuations of complex Wigner and deterministic matrices

2021 ◽  
pp. 2250015
Author(s):  
Camile Male ◽  
James A. Mingo ◽  
Sandrine Péché ◽  
Roland Speicher
Keyword(s):  
Second Order ◽  
Hadamard Products ◽  
Wigner Matrices ◽  
Mild Conditions ◽  
Global Fluctuations

We characterize the limiting fluctuations of traces of several independent Wigner matrices and deterministic matrices under mild conditions. A CLT holds but in general the families are not asymptotically free of second-order and the limiting covariance depends the limiting [Formula: see text]-distribution of the deterministic matrices and their transposes and Hadamard products.

scholarly journals Mean square calculus and random linear fractional differential equations: Theory and applications

2017 ◽  
Vol 2 (2) ◽  
pp. 317-328 ◽  
Author(s):  
C. Burgos ◽  
J.C Cortés ◽  
L. Villafuerte ◽  
R.J. Villanueva
Keyword(s):  
Stochastic Process ◽  
Second Order ◽  
Initial Condition ◽  
Mean Square ◽  
Initial Value ◽  
Mild Conditions ◽  
Fractional Differential ◽  
Linear Differential ◽  
Linear Fractional Differential Equations ◽  
Statistical Functions

AbstractThe aim of this paper is to study, in mean square sense, a class of random fractional linear differential equation where the initial condition and the forcing term are assumed to be second-order random variables. The solution stochastic process of its associated Cauchy problem is constructed combining the application of a mean square chain rule for differentiating second-order stochastic processes and the random Fröbenius method. To conduct our study, first the classical Caputo derivative is extended to the random framework, in mean square sense. Furthermore, a sufficient condition to guarantee the existence of this operator is provided. Afterwards, the solution of a random fractional initial value problem is built under mild conditions. The main statistical functions of the solution stochastic process are also computed. Finally, several examples illustrate our theoretical findings.

scholarly journals A Filter Algorithm with Inexact Line Search

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Meiling Liu ◽  
Xueqian Li ◽  
Qinmin Wu
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Local Convergence ◽  
Numerical Experiments ◽  
Line Search ◽  
Second Order ◽  
Lagrangian Function ◽  
Order Correction ◽  
Inexact Line Search ◽  
Mild Conditions

A filter algorithm with inexact line search is proposed for solving nonlinear programming problems. The filter is constructed by employing the norm of the gradient of the Lagrangian function to the infeasibility measure. Transition to superlinear local convergence is showed for the proposed filter algorithm without second-order correction. Under mild conditions, the global convergence can also be derived. Numerical experiments show the efficiency of the algorithm.

scholarly journals Cucker-Smale Flocking with Bounded Cohesive and Repulsive Forces

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Qiang Song ◽  
Fang Liu ◽  
Jinde Cao ◽  
Jianlong Qiu
Keyword(s):  
Theoretical Analysis ◽  
Multiagent Systems ◽  
Initial Energy ◽  
Second Order ◽  
Initial State ◽  
Numerical Examples ◽  
Mild Conditions ◽  
Two Agents ◽  
Repulsive Forces

This paper proposes two Cucker-Smale-type flocking models by introducing both cohesive and repulsive forces to second-order multiagent systems. Under some mild conditions on the initial state of the flocking system, it is shown that the velocity consensus of the agents can be reached independent of the parameter which describes the decay of communication rates. In particular, the collision between any two agents can always be avoided by designing an appropriate bounded repulsive function based on the initial energy of the flock. Numerical examples are given to demonstrate the effectiveness of the theoretical analysis.

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

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